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CONCORDIA UNIVERSITY / OTHER / PHYS 284 / What is the center of millions of orbiting objects?

What is the center of millions of orbiting objects?

What is the center of millions of orbiting objects?

Description

School: Concordia University
Department: OTHER
Course: Introduction to Astronomy
Professor: Mario d'amico
Term: Spring 2017
Tags: astronomy
Cost: 50
Name: Phys 284 Midterm, Lessons 1-4
Description: These notes cover lessons 1-4
Uploaded: 10/05/2017
35 Pages 2 Views 15 Unlocks
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Lesson 1: An Unexpected Journey  


What is the center of millions of orbiting objects?



VIDEOS  

Video #1: The Scale of the Universe

Observation and Theory  

• We know about size and structure of Universe is deducted from observation (LIGHT) and  theories of physics  

• Laws of nature  

• Available theories: physics  

Light Years and Astronomical Units  

• Earth is the centre of millions of orbiting objects  

• When we see a star, we see it as it is  

• Truths:  

• Earth’s role: not the centre of the universe  

• Speed of light: velocity of light is called “speed of light” estimated at 300,000 kilometres per  second and we see stars as they were in the past  

• Light year: it’s really the measure of distance  

• Distance travelled by light in one earth year  

• One light year is equal to 9.46 trillion kilometres  

• Astronomical unit: the distance from the earth to the sun (150 million kilometres) is taken as a  standard unit in Astronomy or “astronomical unit” or AU (1AU = 150 million kilometres)  


What is the Speed of light?



The Solar System  

• Solar means sun  

• Number of plants went from 9 to 8 because definition of planet changed  • To be called a planet: it is a large object orbiting the sun who gravitational force is strong  enough to have "cleared its neighbourhood" of smaller objects around its orbit  We also discuss several other topics like What is the most common lipid consumed by ruminants?

• When solar system formed, objects closer to the sun did not survive the heat  • …unless they were made of heavier atoms: iron, silicon and other rocky materials  • These planets are called terrestrial planets from the word “terra” meaning land  • Mercury: 0.40 AU or 40% distance from earth to the sun  

• Second terrestrial planet is Venus: 0.70 AU  

• Earth is 1 AU and Mars is 1.5 AU  

• These 4 are the Terrestrial planets (Mercury, Venus, Earth, Mars) and composed  of silicate rocks and metals  

• The next 4 planets (Jupiter, Saturn, Uranus, Neptune) are called the Jovian planets  • Jovian: like Jupiter  


What is a Light year?



• Jupiter: 5.2 AU  

• Saturn: 9.6 AU  

• Uranus: 19.2 AU  

• Neptune: 30.1 AU  

• Made of gases and frozen materials  

• Jupiter and Saturn are the gas giants (contain mainly hydrogen and helium)

• Uranus and Neptune are the ice giants (contain water, ammonia, and methane)  • All 4 contain a ice and rocky core  If you want to learn more check out what is public opinion?

Solar system boundaries extend from 70,000 AU  

Within this boundary, we have 3 regions where swarm of objects, both round and irregular shaped  are found in large numbers  

These regions are:  

1) Asteroid Belt: contains a few millions asteroids spread over a large volume of space orbiting  around the sun  

2) Farther out, passed Neptune, 30 AU and 50 AU: Kuiper Belt  

20 times as wide and heavy as the Asteroid Belt  

Icy and used to contain former planet Pluto which is not a dwarf planet (Eris)  3) Third one is the Oort Cloud: extended shell of icy objects that exist in the outermost reaches of  the solar system  

Contains trillions of objects  

The Milky Way Galaxy  

• Our solar system is 1 star out of billion stars clustered together in a spiral shape cluster of  stars called the Milky Way Galaxy  

• We are located at about 1.7 billion AU from the centre of the milky way core in one of the spiral  arms called the Orion arm  

• Total diameter of the milky way is 6 to 10 billion AU  

• Thickness of the disk is 120 million AU  

• The closest stars to ours is a group of 3 stars called: Alpha Centauri system  • Alpha Centauri A and Alpha Centauri B which form the binary star called Alpha Centauri AB  (also named Rigil Kentaurus) and a small faint red dwarf, Alpha Centauri C (also named  Proxima Centauri)  

• 270,000 AU - those two stars from us  

• Second closest star is the Barnard’s Star  

• Milky way is visible without a telescope  

• Cloud of dust extending from one part of the sky to the other end  If you want to learn more check out What is communication?

• Appears thickest in regions representing the dense galaxy core  

• We are located 1.7 billion AU from the centre of it  

• We will see different parts of the milky way throughout the years as the earth orbits around the  sun  

Clusters and Galaxies  

• Observable universe  

• Just like stars cluster together to form stable groups of galaxies  

• Galaxies cluster together too!! To form groups of galaxies  

• Observable universe looks like this:  

• Billions of galaxies in the universe  

• Galaxies can be isolated or found in groups  

• The milky way is one of approximately 40 galaxies grouped together called a "local group"  • A group of galaxies with a few dozens of galaxies close together is called a "galaxy cluster"  Don't forget about the age old question of What is social anxiety disorder?

• Farther out we have galaxies clusters and galaxies concentrated into superclusters  • Zoom out as far as possible, universe looks like a black wall with white bumps  • Regions of the wall where galaxies and galaxy clusters are concentrated  • The white bumps on the wall are called superclusters

Andromeda Galaxy  

• On a clear night, there are 4 bright stars that make up the great square, the constellation  Pegasus  

• If you follow the top 2 stars to the left, you'll see the brightest stars in the constellation  Andromeda  

• One of which is being pointed at the right side of the W shaped constellation Cassiopeia  • Andromeda galaxy: also known as M31  

• These stars help locate this  

• Located at about 2 and a half million light years away!  

• Disc of the galaxy is 100,000 light years in diameter  Don't forget about the age old question of what is front lighting?

• Far side of the galaxy is located at about 100,000 light years farther away from us than the near  side  

• Is farther side greater than, equal to, or less than near side???  

• Light travel time from far side is GREATER  

• It's 100,000 light years farther away  

• Space and time become intertwined  

What have we learned?  

• What is our place in the universe?  

Earth is part of the solar system, which is the Milky Way galaxy, which is a member of the Local  Group of galaxies in the Local Supercluster  

• How big is the universe?  

The distances between planets are huge compared to their sizes - on a scale of 1 to 10 billion,  Earth is the size of a ball point and the Sun is 15 meters away  

On the same scale, the stars are thousands of km away  

It would take more than 3000 years to count the stars in the Milky Way Galaxy at a rate of one per  second, and they are spread across 100,000 light years  

Observable universe is 14 billion light years in radius and contains over 100 billion galaxies with a  total number of stars comparable to the number of grains of sand on all of Earth's beaches  Don't forget about the age old question of What is strategic business unit?

Knowledge Check  

Distance from Earth from farthest to nearest:  

1) Star on far side of Andromeda Galaxy  

2) Star on near side of Andromeda Galaxy  

3) Star on far side of Milky Way Galaxy  

4) Star near centre of Milky Way Galaxy  

5) Orion Nebula  

6) Alpha Centauri  

7) Pluto  

8) The Sun  

Light from more distant objects takes a longer time to travel to Earth  

Light takes a longer time to travel to Earth  

This means that we see more distant objects as they were longer ago  

For example, if an object is 10 light years away, then we see it as it was 10 years ago  If it is 20 light years away, we see it as 20 years ago  

More distant objects have aged more since their light left on its way to Earth  Video #2: The History of the Universe

The Discipline of Cosmology  

• Estimated age of the universe is 13.7 billion years  

• We know this from cosmological studies

• Every galaxy in the universe is moving away from any other galaxy  

• Cosmology: scientific models of origin, evolution, and future of our universe  • From Greek "cosmos", meaning "world"  

• We know the age of the universe because we know the speed of the galaxies as they move  away from each other  

• This is known as Hubble law!!  

• Hubble law is: speed of recession of a galaxy is proportional to its distance from an observer  • We can work backward to trace the time where galaxies were at a single point  • The prevailing cosmological model for the universe is called the big bang theory!  • The big bang theory: universe began from a condensed point at time t=0; expanded, cooled  down, and believed to be expanding at an accelerated rate  

• Began as a single point, and like a balloon, expanded  

• Dots on a balloon and when it's inflated the dots get farther away from the other dots (imagine)  

Stages After the Big Bang  

• Time 0  

• There are about 100 billion galaxies in the observable universe  

6 stages  

1) It was really hot and when it expanded, it became cool and less dense (expansion and cooling)  2) As temperature cooled, atoms formed, clouds of atoms collapsed and formed stars and planets  (formation of atoms, stars, and planets)  

3) The large size of stars, mainly hydrogen, compressed and formed heavier atoms called fusion  (stellar nuclear fusion produced heavier atoms)  

4) Stars systems clustered together to form galaxies  

5) Galaxies clustered to form local groups  

6) Larger clumps of galaxies formed galaxy clusters  

The Cosmic Calendar  

• Karl Segan  

• Huge history of Universe is scaled down to 1 year  

• January 1: Big Bang at midnight  

• The present is mapped until the end of 31st  

• February: Milky Way Forms  

• September 3: Earth forms  

• September 22: Early life on Earth  

• December 31: 9 PM Early hominids evolve  

• December 31: 11:58 PM Modern humans evolve  

• 1 second is 438 years  

• 1 hour 1.5 million years  

• A day is 37.8 million years  

What have we learned?  

• How did we come to be?  

The matter in our bodies came from the big bang, which produced hydrogen and helium  All other elements were constructed from hydrogen and helium in stars and then recycled into  new star systems, including our solar system  

• How do our lifetimes compare to the age of the Universe?  

On a cosmic calendar that compresses the history of the Universe into 1 year  Human civilization is just a few seconds old, and a human lifetime is a fraction of a second  

Video #3: Spaceship Earth

Earth Rotations  

• Earth rotates around its axis everyday  

• The axis is an imaginary line drawn from the North pole to the South pole  • Rotates counter clockwise  

• Earth's rotational speed is constant  

• Due to its spherical shape different points on Earth travel at different speed  • This is because a larger circumference must be covered at the same time  • The speed of revolution depends where you are on Earth  

• A point on the equator travels at 1670 km/hour  

• As the Earth rotates it also orbits around the sun once every year  

• Or about every 365 days  

• Earth takes 1 year to orbit the Sun at an average speed of 107,000 km/hour  • Since the average distance from the sun is 1 AU, or 150 million km  

• Earth's orbital speed is about 100,000 km per hour  

• The motion of the Earth around the sun forms an orbital plane called the ecliptic plane  • The Earth's axis is tilted at an angle of 23.5 degrees from along a line perpendicular to the  ecliptic plane  

• Earth's axis remains pointed in the same direction (towards Polaris) throughout the year  • Polaris is a star located at the end of the handle of the Little Dipper (btw)  • Polaris is also called the North star  

• The South Pole does not have an equivalent South star  

Earth's Rotation and Orbit  

• Earth rotates once each day around its axis  

• An axis is a line connecting the North and South poles  

• Earth rotates from West to East which is why the sun, moon, planet, stars all appear to rise in  the East and set in the West each day  

• The stars motion across the sky is a result of Earth's rotation  

• Earth rotates from West to East  

• See the star from East to West  

• Earth's rotation is counter clockwise  

• The rotation's speed is high  

• If you're on the equator, Earth's rotation carries you around the axis at a speed of about 1670  km/hour  

• Your rotation speed is slower if you live closer to the poles  

• But it is still more than 1100 km/h  

• 0 km/h only at the poles  

• At the same time that Earth rotates, it also orbits the Sun completing one orbit each year  • Earth's orbital path: Ecliptic plane  

• Earth's axis is tilted at about 23.5 degrees from a line perpendicular to the plane  • We usually draw the Ecliptic plane horizontal, Earth has an axis tilt of 23.5 degrees  • Question: Earth is at the other side of its orbit - axis orientation? It was A!  • Because Earth's axis points at the same direction in space throughout the year  • Earth's orbit goes in the same counter clock wise direction as its rotation  • The axis points at the star Polaris which is why Polaris is the North star and is always found in a  direction of due North when you see it in the sky :)  

• Earth's distance from the Sun varies slightly over the course of each year  • But the average is about 150 million km which we call 1 AU (astronomical unit0  • Earth's orbital speed is really fast  

• If you divide the circumference of Earth's orbit by the 1 year it takes to complete each orbit,  we're moving around the Sun at an average speed of 107,000 km/hr

Galaxy Rotations  

• Our solar system is located at about 27,000 light years from the galactic centre  • Solar system orbits the galaxy once every 230 million years with a speed of 800,000 km/hr  • The masses of the galaxies are greater than observed, located in outer regions, and invisible to  telescopes: called "dark matter"  

• Galaxies in the universe have random motions  

• In Local Group, galaxies move toward us and away from us, and some orbit Milky Way Galaxy  

Outside Local Group, there are Hubble's observations:  

1) Almost every galaxy is moving away from us  

2) The farther away, the faster it appears to be moving  

What have we learned?  

• How is Earth moving through space?  

It rotates on its axis once a day and orbits the Sun at a distance of 1 AU = 150 million km  Stars in the Local Neighbourhood move randomly relative to one another and orbit the centre of  the Milky Way in about 230 million years  

• How do galaxies move within the Universe?  

All galaxies beyond the Local Group are moving away from us with expansion of the Universe: the  more distant they are, the faster they're moving  

Knowledge Check  

• Which of the following lies in the ecliptic plane?  

Earth's orbital path around the Sun  

• In January, Earth's rotation axis points in the direction of the star Polaris, where does it point in  July?  

Toward the star Polaris  

Earth's axis does not change its orientation in space over the course of each year so it remains  pointed toward Polaris at all times  

Random facts  

• Our entire solar system orbits around the centre of the Milky Way Galaxy about once every 230  million years  

• The Milky Way and Andromeda galaxies are among a few dozen galaxies that make up our  Local Group  

• The Sun appears to rise and set in our sky because Earth rotates once each day  • You are one year older each time Earth orbits around the Sun  

• On average, galaxies are getting farther apart with time, which is why we say our universe is  expanding  

• Our solar system is moving toward the star Vega at about 70,000 km/hr  Video #4: The Human Adventure of Astronomy  

Development of Civilization  

• 384 BC: Aristotle - promoted the view that celestial objects rotated around the Earth  • 310 BC: Aristarchus of Samos - presented the first known model that placed the Sun at the  centre of the known Universe, with the Earth revolving around it  

• 1543: Copernicus began the revolution that Earth is not the centre of the Universe  • 1572 to 1609: Tycho Brahe and Galileo each contributed evidence to help spur the acceptance  of Copernican ideas  

• 1687: Isaac Newton - his laws of motion and theory of gravity

Technological and Scientific Progress  

• Space time, travel, and artificial intelligence  

• Hubble space telescope  

• James Webb telescope  

• Scientific progress is accelerating rapidly and continues to play a role in our future  

What have we learned?  

• How has the study of astronomy affected human history?  

Throughout history, astronomy has provided an expanded perspective on Earth that has grown  hand in hand with social and technological developments  

TEXTBOOK  

Chapter 1: A Modern View of the Universe

1.1 The Scale of the Universe

Our Cosmic Address  

• Earth-centered: geocentric  

• Hubble Space telescope takes nice pictures  

• Nearly every object within it is a galaxy filled with billions of stars  

• Earth is a planet in our solar system, which consists of the Sun, the planets and their moons,  and countless smaller objects that include rocky asteroids and icy comets  • The Sun is a star  

• Solar system belongs to the huge, disk-shaped collection of stars called the Milky Way Galaxy • A galaxy is a great island of stars in space, all held together by gravity and orbiting a common  centre  

• Milky Way: contains more than 100 billion stars  

• Solar system is located a little over halfway from the galactic centre to the edge of the galactic  disk  

• A lot of galaxies throughout space  

• Milky Way is one of the two largest among more than 70 galaxies  

• These make up the Local Group

• Groups of galaxies with many more large members are called: galaxy clusters • The regions in which galaxies and galaxy clusters are most tightly packed are called:  superclusters (they're really just clusters of galaxy clusters)  

• Galaxy, galaxy clusters, superclusters  

• Our Local Group is located in the outskirts of the Local Supercluster (Laniakea: meaning  immense heaven)  

• All these structures make up the universe

• Universe is: SUM TOTAL of all matter and energy  

Astronomical Distance Measurements  

• 2 units often used: AU and light year  

• Astronomical unit (AU): Earth's average distance from the Sun - 150 million km  • We use AU for distances within solar system  

• Light year (ly): Distance that light can travel in 1 year - 10 trillion km  

• We use light year for describing the distances of stars and galaxies  

• Light year is a unit of distance, not time  

• Light travels at the speed of light - 300,000 km/second  

• One light-second is about 300,000 km (that is the distance that light travels in one second)

• Light travels about 10 trillion km in one year so that distance represents a light year  

Looking Back in Time  

• Stars are so far away and their light takes years to reach us, which is why we measure their  distances in light years  

• Sirius: brightest star in the night sky, located at about 8 light years away  • We see Sirius as it was 8 years ago  

• Orion Nebula: giant cloud in which stars and planets are forming, located about 1350 light years  from Earth  

• We see Orion Nebula as it was 1350 years ago  

• We cannot know about the events that happened to these stars (if it happened right now)  • The farther away we look in distance, the further back we look in time • Andromeda Galaxy: 2.5 million light years away  

Basic Astronomical Definitions  

• An object can be considered a planet only if it:  

1) Orbits a star  

2) Is large enough for its own gravity to make it round  

3) Has cleared most other objects from its orbital path  

An object that meets the first two criteria but has not cleared its orbital path is called a dwarf  planet (like Pluto)  

• Moon: object that orbits a planet  

• Satellite: object orbiting another object  

• Asteroid: orbits a star (small and rocky)  

• Comet: orbits a star (ice-rich object)  

• Small solar system body: asteroid, comet, other objects that orbits a star but is too small to  qualify as a planet or dwarf planet  

Collections of Astronomical Objects  

• Solar system: the Sun and material that orbits it (planets, dwarf planets, small solar system  bodies)  

• Star system: a star and any planets and other materials that orbit it  

• Galaxy: a great island of stars in space  

• Cluster of galaxies: collection of galaxies  

• Larger collections are called clusters  

• Supercluster: gigantic region of space in which many groups and clusters of galaxies are  packed more closely together than elsewhere in the universe  

• Universe (or cosmos): sum total of all matter/energy (all galaxies/everything between them)  • Observable universe: portion of entire universe that can be seen from Earth    

Terms Relating to Motion  

• Rotation: the spinning of an object around its axis  

• Earth rotates once each day around its axis (imaginary line connecting the North and South  Poles)  

• Orbit (or revolution): the orbital motion of one object around another due to gravity (ex: Earth  orbits the Sun once each year)  

• Expansion (of the universe): increase in the average distance between galaxies as time  progresses  

• Picture of a distant galaxy: space and time  

The Observable Universe

• The distance of 14 billion light years therefore marks the boundary (or horizon) of our  observable universe  

• The portion of the entire universe that we can potentially observe  

• Light year means DISTANCE, not time  

• Equation: 1-lightyear = (speed of light) times (1 year)  

Scale of the Solar System  

• The Voyage scale model solar system  

• Shows the Sun and planets, and the distances between them, at one ten-billionth of their actual  sizes and distances  

• Storm of Jupiter: Great Red Spot  

• The Moon lies 4 cm from Earth in the Voyage model  

• Trip to Mars is more than 150 times as far as the trip to the Moon  

• Pluto: took more than 9 years  

Distances to the Stars  

• Alpha Centauri: 3 star system - 4.4 light years away  

• Roughly about the distance across the US (on the 10-billion scale)  

• Voyager 2: spacecraft  

• Jupiter: 1979  

• Saturn: 1981  

• Uranus: 1986  

• Neptune: 1989  

The Size of the Milky Way Galaxy  

• Do not use the 1-10 billion scale for distances beyond nearest stars  

• Distant stars would not fit  

• Reduce it more to imagine the galaxy  

• Scale of 1 to 10^19  

• Each light year then becomes 1 mm  

• 100,000 light year diameter of Milky Way becomes 100 m (length of football field)  

The Observable Universe  

• Solar system: single star system  

• Galaxy: collection of more than 100 billion star systems  

1.2 The History of the Universe  

The Big Bang, Expansion, and the Age of the Universe  

• Universe is expanding  

• This means that average distances between galaxies are increasing with time  • Galaxies must have been closer together in the past  

• Beginning of Big Bang! Occurred about 14 billion years ago  

• While the universe as a whole continues to expand, individual galaxies and galaxy clusters (and  objects within them such as stars as planets) do NOT expand  

Stellar Lives and Galactic Recycling  

• Gravity drives the collapse of clouds of gas and dust to form stars and planets  • Stars go through life cycles but are not living organisms  

• A star is born when gravity compresses the material in a cloud to the point at which the centre  becomes dense enough and hot enough to generate energy by nuclear fusion: the process in

which lightweight atomic nuclei smash together and stick (or fuse) to make heavier nuclei  • The star lives as long as it can shine with energy from fusion  

• Star dies when it exhausts its unstable fuel  

• Massive stars die in titanic explosions called supernovae

• New stars can be born with the leftover gas mixes  

• Cosmic recycling plants  

Star Stuff  

• Hydrogen and helium (and a trace of lithium): early universe contained only these chemical  elements  

• We and Earth are made of other elements: carbon, nitrogen, oxygen, iron  • Where did they come from? From stars, some through nuclear fusion, nuclear reactions  • Earlier generations of stars had already converted up to 2% of our galaxy's original hydrogen  and helium into heavier elements  

• Cloud that gave birth to our solar system was made of 98% hydrogen and helium  • The other 2% is small but it made up the small rocky planets of our solar system  

How do our lifetimes compare to the age of the universe?  

• Cosmic calendar: compressed in 1 year  

• Big Bang occurred: January 1  

• Present is the stroke of midnight on December 31

• Milky Way Galaxy: February  

• Solar system and planet: early September  

• Late September, life on Earth was flourishing  

• Recognizable animals: mid-December  

• Early dinosaurs: day after Christmas  

• Death of dinosaurs: 65 million years ago (on calendar: yesterday)  

• Small furry animals  

• 9 PM on December 31: human ancestors  

• Human civilization: last half-minute  

1.3 Spaceship Earth  

• Rotation and Orbit  

• Basic motions of Earth:  

• Daily rotation

• Yearly orbit around the Sun  

• Earth rotates once each day around its axis (imaginary line connecting North Pole to South  Pole)  

• Earth rotates from west to east  

• Counterclockwise as viewed from above the North Pole  

• Earth's axis at a speed of more than 1000 km per hour  

• Same time as it rotates, Earth orbits the Sun (one orbit each year)  

• We are racing around the Sun at a speed in excess of 100,000 km per hour  • Earth's orbital path defines a flat plane: called the ecliptic plane

• Earth's axis is tilted by 23.5 degrees from a line perpendicular to the ecliptic plane  • This axis tilt is oriented so that the axis points at Polaris (the North Star)  • The tilt has no meaning in space  

• There is no absolute up or down  

• Up: away from the centre of the Earth  

• Down: toward the centre of Earth  

• Earth's axis remains pointed in the same direction throughout the year

• Earth orbits the Sun in the same direction that it rotates on its axis: COUNTERCLOCKWISE as  viewed from above North Pole  

Motion Within the Local Solar Neighbourhood  

• Local solar neighbourhood: region of the Sun and nearby stars  

• Sun is moving relative to nearby stars at a speed of about 70,000 km/h  

• Stars are really far away so we don't notice how fast we go (like looking at an airplane)  

Galactic Rotation  

• Solar system is located at about 27,000 light years from the galactic centre  • Solar system completes one orbit of the galaxy in about 230 million years  • Most of the mass of the galaxy seems to be located outside the visible disk (occupying the  galactic halo that surrounds and encompasses the disk)  

• Matter that makes up this mass is completely invisible to our telescopes  • We know little of this so it's called dark matter (because of the lack of light from it)  • Dark matter must be the dominant source of gravity that has led to the formation of galaxies,  clusters, superclusters  

• There's the mysterious dark energy  

How do galaxies move within the universe?  

• Milky Way and Andromeda galaxies are moving toward each other at about 300,000 km/h  • We don't need to worry about a collision anytime of soon - maybe in billions of years  

When we look outside the Local Group, 2 facts recognized in 1920s by Edwin Hubble (for whom  the Hubble Space Telescope was named):  

1) Every galaxy outside the Local Group is moving away from us  

2) More distant the galaxy, faster it appears to be racing away  

• Local Raisin

• Space itself is growing between galaxies  

• Faster the rate of expansion, the more quickly the galaxies reached their current positions, and  therefore the younger the universe must be  

The Real Universe  

• Cake has centre and edges  

• Not the same for universe  

• We can't actually see the galaxies moving apart with time  

• We measure the speeds of galaxies by spreading their light into spectra and observing what we  call Doppler shifts  

Motion Summary  

1) Earth rotates around its axis once each day, carrying people in most parts of the world around  its axis at more than 1000 km/h  

2) Earth orbits the Sun once each year, moving at more than 100,000 km/h  3) The Solar System moves relative to nearby stars, at a speed of 70,000 km/h  4) Milky Way rotates, carrying our Sun around its centre once every 230 million years, at a speed  of about 800,000 km/h  

5) Our galaxy moves relative to others in the Local Group; we are travelling toward the  Andromeda Galaxy at about 300,000 km/h  

6) Universe expands: the more distant an object, the faster it moves away from us; the most  distant galaxies are receding from us at speeds close to the speed of light

1.4 The Human Adventure of Astronomy

How has the study of astronomy affected human history?  

• Copernican revolution: Earth is not the centre of the universe but rather just one planet  orbiting the Sun  

• Tycho Brahe, Johannes Kepler, and Galileo: provided the key evidence that eventually led to  wide acceptance of the Copernican idea  

• Isaac Newton: law of motion and gravity  

• Fate of Galileo: Vatican put under house arrest in 1633 for his claims that Earth orbits the Sun  • Church then said he was right  

Smallest to biggest  

1) Earth  

2) Solar System  

3) Milky Way  

4) Local Group  

5) Local Supercluster

Lesson 2: The View from Earth

VIDEOS

Video #1 Patterns in the Night Sky  

Worldwide Telescope  

• The stars are at vastly different distances from Earth  

• They appear to be close to each other because we lack depth perception when we look into the  night sky  

• The ancient Greeks mistook this illusion for reality  

• They imagined the stars to lie on a great celestial sphere surrounding Earth  • Although the idea that Earth is in the centre of a giant ball of stars is not correct, we can still use  the concept of a celestial sphere to help us map the sky  

• The point in the sky directly above Earth's North Pole is called North Celestial Pole  • The star Polaris is currently at the location of the North Celestial Pole; this star is commonly  called the North Star  

• The point in the sky directly above Earth's South Pole is called the South Celestial Pole  • There is not currently a star at that location, so we don't have a corresponding South Star  

• The celestial equator is the projection of Earth's equator into space  

• The path of the Sun appears to follow a circle around the celestial sphere (we call this path the  ecliptic)  

• We never see the entire celestial sphere because the ground blocks our view of half the sky  • The half of the celestial sphere we see at any time is called our local sky  • The boundary between the ground and the sky defines the horizon  

• An imaginary half-circle in the sky that goes from south on the horizon to north on the horizon is  called the meridian  

• The point in the sky directly overhead is called the zenith  

• Since we don't know how far away objects are from us, we cannot judge the true sizes of

objects or distances between them  

• However, we can measure the angular sizes and distances without knowing how far away they  actually are  

• The angle between two objects in the sky is called the angular distance • For example, the angular distance between the two "pointer stars" in the Big Dipper is about 5  degrees - about half the size of your first held at arm's length  

• If you watch the night sky for a few hours, you will notice that the stars appear to travel from  east to west  

• Although it appears that the sky that is moving, it is actually Earth's rotation that causes the  motion of the sky  

• In the northern sky, stars that are near the north celestial pole never dip below the horizon  • If we could watch them throughout the night, they would appear to move in circles around the  north celestial pole  

• These stars are called circumpolar stars  

• As Earth orbits the Sun throughout the year, the Sun appears to move compared to the stars of  the constellations  

• We can't see the stars and the Sun at the same time  

• If we could, we'd see the Sun move eastward along the ecliptic  

• The Sun's apparent motion along the ecliptic determines what constellations are visible at night  • For example, in late August the Sun is in the constellation Leo, so we can't see the constellation  of Leo at that time of year, since it is only visible during the day (Aug 31)  

• However, we can see Aquarius since it is opposite Leo in the celestial sphere  • Six months later, the Sun is in the constellation Aquarius and Leo is visible in the night sky (Feb  28)  

What have we learned?  

• What does the Universe look like from Earth?  

We can see more than 2000 stars ad the Milky Way with our naked eyes, and each position on  the sky belongs to one of 88 constellations  

We can specify the position of an object in the local sky by its altitude above the horizon and its  direction along the horizon  

• Why do stars rise and set?  

Because of Earth's rotation  

• Why do the constellations we see depend on latitude and time of year?  

Your location determines which constellations are hidden by Earth  

Time of year determines the location of the Sun on the celestial sphere  

Knowledge Check  

• Which of the following statements about the celestial equator is true at all latitudes?  It represents an extension of Earth's equator onto the celestial sphere  

• What makes the North Star special?  

It appears very near the north celestial pole  

Video #2 The Reason for Seasons

Earth's Axis Tilt  

• The Earth is closest to the Sun in the winter and furthest from the Sun in the summer

• Variation in the distance between Earth and Sun are small  

• About 3%  

• This small variation is overwhelmed by the effects of axis tilt  

• Reason for season change is: has to do with the Earth's tilt  

• Seasons occur because Earth's tilt causes rays of light from the Sun (flux) to be more intense  because the rays will cover more surface area  

• Earth's axis points in the same direction towards Polaris all year round  

• Its orientation relative to the sun changes as earth orbits the sun  

• Summer occurs in your hemisphere and sunlight hits it more directly  

• Winter occurs when sunlight is less direct  

• Because of the earth's tilt, the north and south will experience summer and winter at opposite  times  

• When it is summer in the north, when the Earth's northern part is tilted towards the sun, it will be  winter in the south since the Earth's southern portion is tilted away from the sun  • In June - the summer solstice - the North hemisphere is tilted toward the Sun and the Southern  Hemisphere away from the Sun  

• In December - the winter solstice - the opposite occurs  

• During the equinoxes (March and September), the northern and southern parts receive the  same intensity (flux) of the Sun  

Earth's Rotations  

• A day is what takes the Earth to spin 360 degrees on its axis  

• Even after a 360 degree turn, the Sun is not directly above the same point on Earth that it was  at the beginning of the spin  

• The 360 rotation is called a sidereal day  

• The noon to noon rotation is called a solar day

• Earth orbits the Sun once for about every 366.26 sidereal days  

• And once for every 365.26 solar days  

• The length of the solar day varies throughout the year for 2 different reasons  • 1) Because of its orbit is an eclipse and not a circle the Earth moves faster when it is near the  Sun and slower when it is further from the Sun  

• The little extra amount of rotation that the Earth needs to do to get from noon to noon changes  throughout the year  

• 2) Because the Earth is tilted on its axis, the little extra rotation to get from noon to noon is  largest at the solstice and smallest at the equinoxes  

• Solar days grow longer as we move from equinox marked in September to the solstice in June  and December  

• Solstice is the longest day or shortest day  

• Equinox is a day with equal duration of day and night  

• The Earth's spin is slowing down  

• Length of solar day is increasing  

• Due to gravitational tides, between Earth and moon, the length of the mean solar day is  increasing at a rate of approximately 1.4 milliseconds every century  

• 2 billion years ago, there were about 750 days in a year  

• Day time let's talk about it!!: period of 24 hours where it is light outside  

• Due to refraction and scattering of light in the atmosphere, there can be daylight even when the  Sun is slightly below the horizon  

• Day length is usually the Sun's disk being on or above the horizon  

• Day begins the moment the Sun's disk appears during sunrise  

• And ends the moment the Sun's disk disappears during sunset

• At equator, day light and night time are equal (a few minutes)  

• The distances north and south of the equator, the length of the day varies with the season  • At the poles, once the sun is risen, it stays up for 6 months before it sets again  • Course of each day, completes a full circle around the edge of the sky  

• Because the Earth travels at different speeds than its orbit, the Sun is north of the equator or  almost 4 days more than half a year  

• The length of an average day in the northern hemisphere exceeds the length of the average  day of the southern hemisphere by a few minutes  

• In the northern hemisphere, the arctic circle is the southern most latitude where 24 hour day  light can occur at least one day in a year  

• In the southern hemisphere, the antarctic circle is the northern most latitude where 24 hour day  light can occur at least one day in a year  

• Daylight savings time, is like the man who cut off one end of the blanket and sowed it at the  other end to make it longer  

Earth's Precession  

• Although the Earth's axis seems fixed in human time scales, it actually precesses  • Coin - wobble  

• A spinning object will have a slight wobble as it loses energy: precession • The Earth precesses once every 26,000 years (this does not affect the seasons)  • It doesn't affect the seasons because it doesn't affect the axial tilt the Earth has relative to the  Sun  

• It only has the effect of offsetting the seasons by a very small amount 126 thousandths of the  year  

• Or 20.2 minutes every year  

• The precession has 3 important consequences  

Due to Earth's precession:  

1) A year is 20 minutes longer than the time from one vernal equinox to the next  2) The northern star will change (15,000 years from now, Vega will be the northern star)  3) The positions of equinoxes shift around the orbit  

The signs of the zodiac are constantly changing constellations with time  

Spring equinox, once an Aries, is now in Pisces  

What have we learned?  

• What causes the seasons?  

The tilt of the Earth's axis causes sunlight to hit different parts of the Earth more directly during the  summer and less directly during the winter  

We can specify the position of an object in the local sky by its altitude above the horizon and its  direction along the horizon  

The summer and winter solstices are when the Northern Hemispheres gets its most and least  direct sunlight, respectively  

The spring and fall equinoxes are when both hemispheres get equally direct sunlight  • How does the orientation of Earth's axis change with time?  

The tilt remains about 23.5 degrees (so the season pattern is not affected)  But Earth has a 26,000 year precession cycle that slowly and subtly changes the orientation of  Earth's axis  

Knowledge Check  

• Greater the axis tilt, more extreme the seasonal temperature differences  • Greater axis tilt means longer daylight and a higher summer Sun making summers warmer  • Winter day: greater axis tilt means shorter daylight and a lower winter sun making winters

colder  

Video #3 The Moon: Phases and Eclipse

The Moon's Orbit  

• The Moon's orbit is tilted 5 degrees to the ecliptic (or the apparent path of the Sun) and takes  27.3 days to orbit around Earth relative to the stars in a counterclockwise direction (orbital  period) or 29.5 days relative to the Sun (synodic period)  

• Moon's orbital period: orbit around Earth, relative to the stars, in counterclockwise direction  • Synodic period: if we calculate the moon's orbit around the earth relative to the sun  • This difference occurs because each day the earth changes its location along its orbit or around  the sun  

• Soooo the moon must travel a longer distance around the earth relative to the sun than it does  around the earth relative to the stars  

• The combined motion of the Moon and Earth's rotation causes the observed phases of the  Moon  

• Half of the moon is illuminated by the sun and the other half remains dark  • The phases of the Moon are the projection of the Sun's light on the Moon during its orbit around  the Earth  

Phases and Face of the Moon  

• Moon directly behind the Earth (relative to the Sun): full - it's fully visible  • Imagine the volleyball situation  

• New Moon: moon moves away from the Sun: waxing (getting fuller)  

• Counterclockwise: Full moon, Waning Gibbous, First Quarter, Waning Crescent, New  Moon, Waxing Crescent, Waxing last/Third quarter, Waxing Gibbous and back to full  • 9 am and see a Moon with half its face bright and half dark, what phase? Waxing third quarter  • How will the moon look tomorrow? More lit up entering waxing gibbous phase  • Why do we see only one side? Synchronous rotation: the Moon's orbit is gravitationally locked  with the Earth (rotates once in an orbit) - as it orbits around the Earth, it always shows only one  side  

Eclipses  

• Eclipse occurs when a celestial object casts its shadow on another object  • Lunar eclipse: Earth casts a shadow on the Moon  

• Node: the intersection of the orbit plane of some celestial body, such as the Moon, a planet, or  comet, with the plane of the ecliptic (the apparent path of the Sun among the stars) as projected  on the celestial sphere  

• Solar eclipse: when the moon is between the Sun and the Earth, the moon can cast its shadow  on the Earth  

• Planetary eclipse: a planet casts a shadow a on another planet  

• Eclipses are rare: they require the orbit of the objects involved lie on the same plane  • Celestial objects are rarely perfectly aligned  

• They are in general tilted at different angles and travel orbits with orbital planes that are tilted at  different angles  

• On rare occasion, the orbit intersect forming nodes and causing the objects to align so eclipses  are possible at these points  

• In addition to orbital nodes, shadows have a role too in eclipses  

• Shadow cast on objects by the Sun is a cone with two regions:  

• A central "umbra" where sunlight is completely blocked  

• Surrounding "penumbra" where the sunlight is only partially blocked

• Because of the nature of eclipses, lunar eclipses can only occur at full Moon and are  penumbral, partial, or total  

• Solar eclipses occur only at new Moon and are partial, total, or annular  

• Moon passes through penumbra area of the shadow sometimes, penumbral lunar eclipse occurs  

• If part of the moon passes through umbra (between umbra and penumbra), then it's partial  lunar eclipse

• Likewise, since the orbit of the Moon around the Earth forms an elipse, not perfectly round,  there will be times when the Moon is closer to the Earth and times where the Moon is farther  away  

• Shadows casted in these two situations result in Total Solar Eclipse and an Annular Solar  Eclipse

• We can also have a Partial Solar Eclipse

The Moon's Orbit, Phases and Eclipses  

• Radius of moon is 3.7 times less than that of the Earth  

• Translational motion of the Moon from the north side of the solar system, the Moon rotates  counterclockwise around the Earth  

• For each complete revolution the Moon around the Earth, the Earth has rotated on its South  more than 27 times  

• The Moon takes to go 360 degrees around its orbit 27 days, 7 hours, 43 minutes: sidereal  month  

• The Moon must travel more than 360 degrees so the 3 bodies align again (the Sun, Earth,  Moon)  

• Synodic month: 29 days, 12 hours, 44 minutes  

• The inclination of the lunar orbit to the ecliptic plane is 4 degrees 58 - 5 degrees 19  • The lunar nodes precess around the ecliptic, completing a revolution in 18.6 years  • Lunar/solar eclipses occur when the nodes align with the sun  

• Moon does not coincide with the plane of the ecliptic  

• Translational and rotational periods of the moon are the same  

• Nearside of the moon: hemisphere  

• Farside of the moon: hemisphere  

• Humans for first time saw the far side of the moon on October 7, 1959  • Soviet probe LUNA 3  

• GRAIL mission by NASA, five decades later, offers on detailed map of the moon  

• Lunar phases:  

• North Pole: moon looks like D  

• South Pole: moon looks like C  

• Between 14 and 15th day, full moon appears  

• During the full Moon, the Earth is between the Sun of the Moon  

• Last quarter: Day 22: North Pole: moon is like C  

• Day 22: South Pole: moon is like D  

• Distance at apogee: 407,000 km  

• Distance at perigee: 357,000 km  

The Saros Cycle  

• The perfect coinciding of the Moon's crossing with the ecliptic and the occurrence of a full or  new Moon recur in a 18-year, 11 1/3 day saros cycle

• During a saros cycle, the exact type of eclipse (partial, total, etc.) varies with location on Earth

• Next one should be March 20, 2034 (other one was March 9, 2016)  

What have we learned?  

• Why do we see phases of the Moon?  

Half the Moon is lit by the Sun, half is in shadow, and its appearance to us is determined by the  relative positions of Sun, Moon, and Earth  

• What causes eclipses?  

Lunar eclipse: caused by Earth's shadow on the Moon  

Solar eclipse: caused by Moon's shadow on Earth  

Tilt of Moon's orbit means eclipses occur during two periods each year  

Knowledge Check  

• Waxing phases means on the way to full moon  

• Waning phases mean after full moon  

• A solar eclipse that occurs when the new moon is to far from Earth to completely cover the Sun  can be either a partial solar eclipse or an annual eclipse

• Anyone looking from the night side of Earth can see a total lunar eclipse • During some lunar eclipses, Moon's appearance changes only slightly because it passes only  through the part of Earth's shadow called the penumbra  

• A total solar eclipse can occur only then the Moon is new and has angular size larger than the  Sun in the sky  

• A partial lunar eclipse begins when the Moon first touches Earth's umbra • A point at which the Moon crosses Earth's orbital plane is called a node

Video #4: The Ancient Mystery of Planetary Motions

Relative Motions  

• Like the Sun and Moon, planets usually drift eastward relative to the stars  • Sometimes they move westward  

• Apparent retrograde (backward) motion: when a planet turns westward  • Relative motion describes only the difference in the motion and not what each object is doing  • Mathematical equation describing an Earth-centred system is more complicated than equations  describing a Sun-centred system  

• Jupiter: retrograde in 2004 and 2005  

Apparent Retrograde  

• Video: Earth orbiting the Sun with Mars (Earth orbiting faster)  

• Retrograde: once every 2 years  

• Retrograde motion occur as Earth passes by Mars in its orbit which happens once every 2  years  

The Concept of Parallax  

• Little trick: putting finger in front of face and closing one eye and then closing the other  • Objects behind finger appear to shift  

• The Greeks reasoned that if the Earth was not the centre, then a phenomenon known as  parallax should be observed  

• Greeks rejected the right idea because they thought the stars couldn't be that far away  • Less than 1 arc second (stars)  

• No such phenomenon was spotted with ancient instruments  

• Most Greeks concluded that Earth must be stationary, because they thought the stars could not  be so far away as to make parallax undetectable

Knowledge check  

• The middle of a period of apparent retrograde motion occurs when Mars is closest to Earth in its  orbit and in a full phase as viewed from Earth, which is why it is brightest in our sky at that time  • It is also directly opposite the Sun in the sky at that time which is why it crosses the meridian at  midnight

TEXTBOOK  

Chapter 2: Discovering the Universe for Yourself

2.1 Patterns in the Night Sky  

Constellations

• A constellation is a region of the sky with well-defined borders; the familiar patterns of stars  merely help us locate the constellations

• 88 official constellations

• Northern Hemisphere: names can be tracked back to civilizations of the ancient Middle East • Southern Hemisphere: constellations carry names that originated with 17th century European  explorers

• Stars and constellations appear to lie on a celestial sphere that surround Earth • This is an illusion created by our lack of depth perception in space

The Celestial Sphere

• We lack perception when we look into space  

• Earth seems to be in the centre of the celestial sphere  

• The north celestial pole is the point directly over Earth's North Pole

• The south celestial pole is the point directly over Earth's South Pole

• The celestial equator, which is a projection of Earth's equator into space, makes a complete  circle around the celestial sphere

• The ecliptic is the Sun's apparent annual path around the celestial sphere • The ecliptic crosses the celestial equator at a 23.5 degree angle because that is the tilt of  Earth's axis  

The Milky Way

• Passes through the celestial sphere

• Dark lanes that run down the centre contain the dentist clouds, obscuring our view of stars  behind them  

The Local Sky

• Local sky: the sky as seen from wherever you happen to be standing  

• Local sky looks like a dome (hemisphere)  

• Boundary between Earth and sky defines the horizon  

• The point directly overhead is the zenith

• The meridian is an imaginary half circle stretching from horizon due south, through the zenith  to the horizon due north

• We can pinpoint the position of any object in the local sky by stating its direction along the  horizon (sometimes stated as azimuth, which is degrees clockwise from due north) • And its altitude above the horizon  

Angular Sizes and Distances

• Angular size of an object is the angle it appears to span in your field of view • Angular size depends on distance

• Angular distance: between a pair of objects in the sky is the angle that appears to separate  them  

• For greater precision, we subdivide each degree into 60 arc minutes (symbolized by ') and  each arc minute into 60 arc seconds (symbolized by ")

Why do stars rise and set?

• It is Earth that rotates daily, not the rest of the universe

• Stars near the north celestial pole are circumpolar meaning they remain perpetually above the  horizon, circling (counterclockwise) around the north celestial pole each day • Stars near the south celestial pole never rise above the horizon at all

• All other stars have daily circles that are partly above the horizon and partly below it which  means they appear to rise in the east and set in the west

Why do the constellations we see depend on latitude and time of year?  

Variation with Latitude  

• Latitude measures north-south position on Earth  

• Longitude measures east-west position

• Latitude is 0 degrees at equator increasing to 90 degrees at North Pole and 90 degrees at  South Pole

• Longitude is defined to be 0 degrees along the prime meridian which passes through  Greenwich England

• Sky varies with latitude and not with longitude

• They see the same set of constellations at night (cities with same latitude) • The Sun lies north of the celestial equator for half of each year (why the Sun remains above the  horizon for 6 months)

• During these six months, it circles the sky at the North Pole just like a circumpolar star • The altitude of the celestial pole in your sky is equal to your latitude

• You can determine your latitude by finding the celestial pole in your sky

• Looking northward in the Northern hemisphere: sky appears to turn counterclockwise around  the north celestial pole

• Looking southward in the Southern hemisphere: sky appears to turn clockwise around the  south celestial pole

Variation with Time of Year

• From our vantage point on Earth, the annual orbit of Earth around the Sun makes the Sun  APPEAR to move steadily eastward along the ecliptic

• Constellations along the ecliptic make up the zodiac

• Tradition places 12 constellations along the zodiac but the official borders include a 13th  constellation, Ophiuchus

• Sun's location along ecliptic determines which constellations we see at night 2.2 The Reasons for Seasons  

What causes the seasons?

• Tilt of Earth's axis causes sunlight to fall differently on Earth at different times of year  • It is not caused by any change in Earth's distance from the Sun

• 4 special moments in the year: each corresponds to one of the four special positions in Earth's  orbit

• June solstice: called the summer solstice by people in the Northern Hemisphere, occurs  around June 21 and is the moment when the Northern Hemisphere is tipped most directly  toward the Sun and receives the most direct sunlight

• The December solstice, called the winter solstice by people in the Northern Hemisphere,  occurs around December 21 and is the moment when the Northern Hemisphere receives the  least direct sunlight

• The March equinox, called the spring equinox (or vernal equinox) by people in the Northern  Hemisphere, occurs around March 21 and is the moment when the Northern Hemisphere goes  from being tipped slightly away from the Sun to being tipped slightly toward the Sun

• The September equinox, called the fall equinox (or autumnal equinox) by people in the  Northern Hemisphere, occurs around September 22 and is the moment when the Northern  Hemisphere first starts to be tipped away from the Sun

First Day of Seasons

Equinox and solstice marks first day of a season

Seasons Around the World

• High latitudes have more extreme seasons

• Seasons also differing equatorial regions, because the equator gets its most direct sunlight on  the two equinoxes and its least direct sunlight on the solstices  

• Instead of four sisters experienced at higher latitudes, equatorial regions generally have rainy  and dry seasons, with the rainy seasons coming when the Sun is higher in the sky

Why Orbital Distance Doesn't Affect Our Seasons

• Northern Hemisphere seasons are slightly more extreme than those of the Southern  Hemisphere

• The Southern Hemisphere's larger amount of ocean moderates its climate • Northern Hemisphere: more land, less ocean; heats up and cools down more easily, which is  why it has the more extreme seasons

How does the orientation of Earth's axis change with time?

• Calendar keeps solstices and equinoxes around the same dates each year  • Constellations associated with them change gradually over time

• Reason is precession: a gradual wobble that alters the orientation of Earth's axis in space • It occurs with many rotating objects  

• Top's axis precesses (spinning a top)

• Earth is the same but far more slowly  

• Each cycle of Earth's precession takes about 26,000 years  

• This gradually changes the direction in which the axis points in space

• Precession does not change the amount of the axis tilt and does not affect the pattern of the  seasons

• Precession changes the points in Earth's orbit at which the solstices and equinoxes occur and  therefore changes the constellations that we see at those times

• The latitude at which the Sun is directly overhead on the June solstice (23.5 degrees N) is  called the Tropic of Cancer (it was named back when the Sun appeared in Cancer on this  solstice)

• Precession is caused by gravity's effect on a tilted, rotating object

• Spinning top example again (falls when you put it on the top, but if you spit it fast it doesn't fall) • The spinning top stays upright because rotating objects tend to keep spinning around the  same rotation axis (a consequence of the law of conservation of angular momentum)

• Friction slows the top's spin  

• The spinning (rotating) Earth precesses because of gravitational tugs from the Sun and Moon • They try to "straighten out" Earth's axis tilt  

2.3 The Moon, Our Constant Companion  

Why do we see phases of the Moon?

• As Moon orbits Earth, it returns to the same position relative to the Sun in our skin every 29.5  days

• This is the lunar phases, in which the Moon's appearance in our sky changes as its position  relative to the Sun changes  

• This 29.5 day period is the origin of the word month

Understanding Phases

• Ball exercise (point a flashlight in front of a ball)

• Half the ball always faces the Sun (or flashlight) and there is bright, while the other half faces  away from the Sun and is dark  

• As you look at the ball at different positions in its "orbit" around your head, you see different  combinations of its bright and dark faces

• Moon's phase also determines the times of day at which we see it in the sky • Phases from new to full are waxing which means increasing  

• Phases from full to new are waning or decreasing

• No phase is "half moon"

The Moon's Synchronous Rotation

• We do not see many faces of the Moon

• This happens because the Moon rotates on its axis in the same amount of time it takes to orbit  Earth: synchronous rotation  

• It is a consequence of Earth's gravity affecting the Moon in much the same way the Moon's  gravity causes tides on Earth

The View from the Moon

• New moon occurs when the Moon is between Sun and Earth

• Dark portion of the lunar face is not totally dark  

• Sunlight reflected by Earth faintly illuminates the "dark" portion of the Moon's face: illumination  is called the ashen light or earthshine and it enables us to see the outline of the full face of the  Moon even when the Moon is not full

What causes eclipses?

• The Moon and Earth both cast shadows in sunlight, and these shadows can  create eclipses when the Sun, Earth, and Moon fall into a straight line

• Eclipses come in two basic types:

• A lunar eclipse occurs when Earth lies directly between the Sun and Moon, so Earth’s shadow  falls on the Moon

• A solar eclipse occurs when the Moon lies directly between the Sun and Earth, so the Moon’s  shadow falls on Earth

Conditions for Eclipses

• Moon's orbit is slightly inclined by about 5 degrees to the ecliptic plane (plane of Earth's orbit  around the Sun)

• Moon spends most of its time either above or below the surface

• It crosses through this surface only twice during each orbit  

• Nodes of the Moon's orbit: two points in each orbit at which the Moon crosses the surface • Eclipses can only occur when  

• 1) The phase of the Moon is full (for a lunar eclipse) or new (for a solar eclipse)  • 2) The new moon or full moon occurs at a time when the Moon is very close to a node • Central umbra: where sunlight is completely blocked

• Surrounding penumbra: where sunlight is only partially blocked

Lunar Eclipses

• A lunar eclipse begins at the moment when the Moon’s orbit first carries it into Earth’s  penumbra

• After that, we will see one of three types of lunar eclipse

• If the Sun, Earth, and Moon are nearly perfectly aligned, the Moon passes through Earth’s  umbra and we see a total lunar eclipse  

• If the alignment is somewhat less perfect, only part of the full moon passes through the umbra  (with the rest in the penumbra) and we see a partial lunar eclipse  

• If the Moon passes through only Earth’s penumbra, we see a penumbral lunar eclipse  • Total lunar eclipses are the most spectacular; the Moon becomes dark and eerily red  during totality, when the Moon is entirely engulfed in the umbra

• Totality usually lasts about an hour, with partial phases both before and after

Solar Eclipses

• Also 3 types of solar eclipse

• If a solar eclipse occurs when the Moon is in a part of its orbit where it is relatively close to  Earth, the Moon’s umbra can cover a small area of Earth’s surface (up to about 270 kilometers in diameter): within this area you will see a total solar eclipse  

• If the eclipse occurs when the Moon is in a part of its orbit that puts it farther from Earth, the  umbra may not reach Earth’s surface, leading to an annular eclipse—a ring of sunlight  surrounding the Moon— in the small region of Earth directly behind the umbra

• In either case, the region of totality or annularity will be surrounded by a much larger region  (typically about 7000 kilometers in diameter) that falls within the Moon’s penumbral shadow:  here you will see a partial solar eclipse, in which only part of the Sun is blocked from view

• The combination of Earth’s rotation and the Moon’s orbital motion causes the Moon’s shadows  to race across the face of Earth at a typical speed of about 1700 kilometers per hour • As a result, the umbral shadow traces a narrow path across Earth, and totality never lasts more  than a few minutes in any particular place

• Corona can be seen when the Moon completely blocks the normally visible disk of the Sun  

Predicting Eclipses

• Thales predicted the year that a total eclipse of the Sun would be visible in the area where he  lived

• Eclipse seasons: the nodes of the Moon's orbit are closely aligned with the Sun • Nodes slowly move around the Moon's orbit often called precession of the nodes which has a  period of 18.6 years causing the eclipse seasons to occur slightly less than 6 months apart  (about 173 days apart)

• Saros cycle: the combination of the changing dates of eclipse seasons and the 29.5 day cycle  of lunar phases makes eclipses recur in a cycle of about 18 years, 11 1/3 days • We can predict eclipses today because we know the precise details of the orbits of Earth and  the Moon

2.4 The Ancient Mystery of the Planets

Why was planetary motion so hard to explain?  

• Earth's rotation makes them appear to rise in the east and set in the west  • Sometimes they move the opposite  

• Apparent retrograde motion  

Why did the ancient Greeks reject the real explanation for planetary motion?  • Stellar parallax: the apparent shift in the position of a nearby star (relative to distant objects)  that occurs as we view the star from different positions in Earth’s orbit of the Sun each year • People used to have two ideas:  

• 1) Earth orbits the Sun, but the stars are so far away that stellar parallax is undetectable to the  naked eye

• 2) There is no stellar parallax because Earth remains stationary at the centre of the universe • They rejected the first idea because they couldn't imagine that stars could be that far

Lesson 3: The Development of Science

TEXTBOOK  

Chapter 3: The Science of Astronomy  

3.1 The Ancient Roots of Science

Practical Benefits of Astronomy

• Ancient cultures discovered that astronomy had practical benefits for timekeeping, keeping  track of seasonal changes, and navigation  

• Example: people of central Africa  

• They developed a skill, people in some regions learned to predict rainfall patterns by making  careful observations of the Moon

• The horns of a waxing crescent moon: orientation of those would help them • In tropical regions (distinct rainy and dry seasons) - the orientation of the crescent moon can  be used to predict how much rainfall should be expected over coming days and weeks • Seven days of the week - named after the seven planets of ancient times, sun, moon and the  planets visible to the naked eye

Determining the Time of Day

• Ancient Egyptians built huge obelisks, often decorated in homage to the Sun, served as simple  clocks maybe

• Ancient people: they estimated time from position/phase of Moon

• OR by observing constellations

• Star clocks to estimate time of night

• Egyptians divided daytime and nighttime into 12 equal parts each (how we got our 12 hours  each AM and PM)  

• AM: ante meridiem

• PM: post meridiem

• Before the middle of the day and after the middle of the day

• Egyptians soon abandoned star clocks

• They went to clocks that measure time by flow of water though an opening of a particular size

• Water clocks were then replaced by mechanical clocks and then electronic clocks • Sundials were common throughout ancient times (reminder that Sun and stars were our only  guides to time)

Making the Seasons

• Stonehenge  

• Templo Mayor: important for astronomical observations

• Many cultures aligned buildings and streets with the cardinal directions

• This made it easier to keep track of the rise and set positions of the Sun over the course of the  year

• Other structures marked special dates such as the winter or summer solstice • Sun Dagger is a remarkable one

• A single dagger of sunlight pierced the centre of the spiral only at noon on the summer  solstice, while two daggers of light bracketed the spiral at the winter solstice • Sun Dagger also used to mark a special cycle of the Moon  

Solar and Lunar Calendars

• We use a solar calendar today: a calendar that is synchronized with the seasons so that  seasonal events such as the solstices and equinoxes occur on approximately the same dates  each year

• Some cultures made lunar calendars: 12 months and some months lasting 29 days and others  lasting 30

• Moon's phase was always the same on the first day of each month

• This calendar is still used in Muslim religion: Ramadan  

• Lunar calendars are sometimes roughly synchronized with solar calendars • Lunar phases repeat on the same solar dates about every 19 years (Metonic cycle) • Fun fact: Easter: different Sundays

Learning about Ancient Achievements  

• We must piece together their astronomical achievements by studying the physical evidence  they left behind

• This study is called archaeoastronomy

• Example: astronomical alignments in Inca cities and ceremonial centres were deliberate  • Navigator: people who had acquired knowledge of astronomy for their broad navigational  sense

• Navigator memorized all his knowledge and passed it to the next generation  3.2 Ancient Greek Science

Three Philosophical Innovations

• First, a tradition of trying to understand nature without relying on supernatural explanations  (debate and challenge each other's ideas)

• Second, Greeks used math to give precision to their ideas (explored the implications of new  ideas in much greater depth than would have otherwise been possible)

• Third, Greeks saw the power of reasoning from observations  

• An explanation could not be right if it disagreed with observed facts

Models of Nature

• Scientific model is a conceptual representation created to explain and predict observed

phenomena  

From Greece to the Renaissance

• Greek models  

• Earth centered model of the universe

• Alexander the Great had an interest in science  

• Aristotle was his tutor  

• The Library was an important research centre for awhile  

• Hypatia - female scholar  

• Mathematics and algebra and many new instruments and techniques for astronomical  observation (scholars)

• Many official constellation/star names come from Arabic  

• The Greek geocentric model of the cosmos - so named because it placed a spherical Earth at  the centre of the universe - developed gradually over a period of several centuries  

Early Development

• We trace the origin of Greek science to Thales, a Greek philosopher  

• He did a prediction of a solar eclipse  

• He guessed the universe consists of water and that Earth is a flat disk floating in an infinite  ocean - was not accepted

• Anaximander suggested that Earth floats in empty space surrounded by a sphere of stars and  two separate rings along which the Sun and Moon travel  

• We credit Anaximander for inventing the idea of a celestial sphere

• The idea that Earth was round was about at 500 BC by Pythagoras

• Heavenly spheres in 400 BC (Earth is a sphere that rests in the centre)  • Eudoxus created a model of the Sun, Moon, planets and they had their own spheres that  nested within several other spheres

• Earth's position at the centre used to be explained as a natural consequence of gravity  • Aristotle argued that gravity pulled heavy things toward the centre of the universe  • Aristotle was wrong about gravity and Earth's location  

• Ptolemaic model: accounted for apparent retrograde motion (each planet is assumed to move  around a small circle that turns upon a larger circle)

Ptolemy's Synthesis

• Greek modelling of the cosmos culminated in the work of Ptolemy

• His geocentric model was the Ptolemaic model to distinguish it from other geocentric models • Each planet moved around Earth on a small circle that turned upon a larger circle (small circle  is called epicycle and larger circle is called deferent)  

• In the end, he created and published a model that could correctly forecast future planetary  positions to within a few degrees of arc, which is about the angular size of your hand held at  arm's length against the sky  

3.3 The Copernican Revolution  

Copernican

• Copernican revolution: the dramatic change, that occurred when we learned that Earth is a  planet orbiting the Sun rather than the centre of the universe

• He calculated each planet's orbital period around the Sun and its relative distance from the  Sun in terms of the Earth-Sun distance

Tycho

• He decided to observe a widely anticipated alignment of Jupiter and Saturn  • He set about compiling careful observations of stellar and planetary positions in the sky • He observed the nova, meaning new star

• He proved the nova was much farther away than the Moon  

• Today, we know that he saw a supernova, the explosion of a distant star • Over a period of 3 decades, Tycho and his assistants compiled naked-eye observations  accurate to within less than 1 arc minute, less than the thickness of a fingernail viewed at  arm's length  

• Tycho never succeeded in coming up with a good explanation for planetary motion • He was convinced that the planets must orbit the Sun

Kepler

• He was religion

• He believed that understanding the geometry of the heavens would bring him closer to God • Kepler eventually found a circular orbit that matched all of Tycho's observations of Mars's  position along the ecliptic (east-west) to within 2 arc minutes  

• He found that some of his predictions differed from Tycho's observations by as much as 8 arc  minutes

• Kepler's key discovery: planetary orbits are not circles but instead are a special type of oval:  ellipse

• Example: string and pencil - stretch the string around 2 tacks  

• Location of the two tacks are called: foci or focus of the ellipse

• The long axis of the ellipse is called its major axis, each half of which is called a semi major  axis  

• Short axis is called the minor axis  

• By alternating the distance between the two foci while keeping the length of string the same,  you can draw ellipses of varrying eccentricity, a quantity that describes how much an ellipse  is stretched out compared to a perfect circle  

• A circle is an ellipse with zero eccentricity and greater eccentricity means a more elongated  ellipse

Kepler's three laws of planetary motion

• Kepler's first law: the orbit of each planet about the Sun is an ellipse with the Sun at one focus  • A planet's distance from the Sun varies during its orbit  

• Its closest point: perihelion

• Farthest point: aphelion  

• The average of a planet's perihelion and aphelion distances is the length of its semi major  axis  

• Kepler's second law: a planet moves faster in the part of its orbit nearer the Sun and slower  when farther from the Sun, sweeping out equal areas in equal times

• Sweeping: imaginary line connecting the planet to the Sun and keeping the areas equal means  that the planet moves a greater distance when it is near perihelion than it does in the same  amount of time near aphelion

• As a planet moves around its orbit, an imaginary line connecting it to the Sun sweeps out  equal areas in equal times  

• Kepler's third law: more distant planets orbit the Sun at slower average speeds, obeying the  precise mathematical relationship

• p^2 = a^3

• P stands for the planet's orbital period in years  

• A for its average distance from the Sun in AU

• Relates orbital distance to orbital time (period), we can use the law to calculate the planet's  average orbital speed

• More distant planets move more slowly so it led Kepler to suggest that planetary motion might  be the result of a force from the Sun  

• Might be related to magnetism but he was wrong

• He was right about the existence of a force

• Isaac Newton then discovered it was gravity  

How did Galileo solidify the Copernican revolution?

• Three basic objections, all rotted in the 2000 year old beliefs of Aristotle and other ancient  Greeks

• First, Aristotle had held that Earth could not be moving because if it were, objects such as  birds, falling stones, clouds, would be left behind as Earth moved along its way • Second, the idea of noncircular orbits contradicted Aristotle's claim that the heavens - the  realm of the Sun, Moon, planets, stars, must be perfect and unchanging

• Third, no one had detected the stellar parallax that should occur if Earth orbits the Sun • Galileo answered all 3 objections

Galileo's Evidence

• He used experiments with rolling bats to demonstrate that a moving object remains in motion  unless a force acts to stop it  

• This explained why objects that share Earth's motion through space, should stay with Earth  rather than falling behind as Aristotle had said  

• Galileo shattered the idea of heavenly perfection after he built a telescope - 1609 • He saw sunspots of the Sun, which were considered imperfections at the time  • He also had strong evidence that stars were far more numerous and more distant than Tycho had believed

Stealing the Case

• Galileo observed four moons clearly orbiting Jupiter, not Earth  

• It showed that moons can orbit a moving planet like Jupiter, which overcame some critics'  complaints that the Moon could not stay with a moving Earth  

3.4 The Nature of Science  

Science from nonscience?

• Hypothesis: educated guess

• Scientific method

• Intuition and personal beliefs can influence someone's work

Hallmarks of Science

• 3 basic characteristics

• 1) Modern science seeks explanations for observed phenomena that rely solely on natural  causes

• 2) Science progresses through the creation and testing of models of nature that explain the  observations as simply as possible

• 3) A scientific model must make testable predictions and natural phenomena that will force us

to revise or abandon the model if the predictions do not agree with observations

Occam's Razor

• The idea that scientific should prefer the simpler of two models that are equally well with  observations is called Occam's razor

Verifiable Observations

• We cannot accept eyewitness testimony by itself as evidence in science

Science and Pseudoscience

• Pseudoscience: false science  

• Check whether a claim exhibits all 3 hallmarks of science

Objectivity in Science

• Some scientists let their personal beliefs interfere

• Paradigm: a general pattern of thought that tends to shape scientific study during a particular  time period

• Science ultimately provides a means of bringing people to agreement  

Scientific theory?

• When a powerful yet simple model makes predictions that survive repeated and varied testing,  scientists elevate its status and call it a theory

• Simple physical principles to explain many observations and experiments  • Anything that qualifies as a scientific theory must be supported by a large, compelling body of  evidence

3.5 Astrology  

How is astrology different from astronomy?

• Astrology - parent positions of the Sun, Moon, and planets among the stars in our sky -  influence human events

Testing Astrology

• A scientific test of astrology requires evaluating many horoscopes and comparing their  accuracy to what would be expected by pure chance  

• The methods of astrology are useless for predicting the past, present, or future Lesson 4: Physics of Matter

TEXTBOOK  

Chapter 4: Making Sense of the Universe - Understanding Motion, Energy, Gravity  4.1 Describing Motion: Examples from Daily Life  

• It was Isaac Newton who put all the pieces together into a simple system of laws describing  both motion and gravity

Speed, Velocity, and Acceleration

• Speed of a car tells us how far it will go in certain time  

• Velocity of a car tells us both speed and direction  

• The car has an acceleration if its velocity is changing in any way, whether in speed or  direction or both

The Acceleration of Gravity

• Acceleration caused by gravity - important  

• Air resistance causes differences in acceleration  

• Acceleration of gravity: acceleration of a falling object (abbreviated g)

• On Earth, the acceleration of gravity causes falling objects to fall faster by 9.8 meters/s • In the absence of air resistance, its speed will continue to increase by about 10 m/s each  second until it hits the ground (dropping a rock from a tall building example) • The acceleration of gravity is about 10 meters per second per second - g = 9/8m/s^2

Momentum and Force

• An object's momentum is the product of its mass and velocity

• Momentum = mass x velocity

• The only way to change an object's momentum is to apply a force to it • Example: fly hitting your car vs. big truck hitting your car at same velocity • Truck imparts enough of its momentum to cause a dramatic change to your car • You feel the sudden change in momentum as a force and it can do great damage • The net force (overall force) acting on an object represents the combined effect of all the  individual forces put together

• Changing an object's momentum means changing its velocity, as long as its mass remains  constant

• Net force that is not zero causes object to accelerate

Moving in Circles

• Example of ice skater spinning

• Her spin gives her angular momentum (or circling momentum or tuning momentum)  • Object that is spinning or moving along a curved path has angular momentum  • Earth has angular momentum due to its rotation (rotational angular momentum) and to its orbit  around Sun (orbital angular momentum)

• An object's angular momentum can only change when a special type of force is applied to it • Example: opening a door

• The type of force that can change an object's angular momentum is called a torque (twisting  force)  

• Depends where you apply the force

How is mass different from weight?

• Mass is amount of matter in your body

• Weight: force that a scale measures when you stand on it; weight depends both on your mass  and on the forces (including gravity) acting on your mass

• Elevator example: scale shows a weight different from your normal weight only when the  elevator is accelerating, not when it is going up or down at constant speed • Your mass depends on the amount of matter in your body and is the same anywhere but your  weight can vary because the forces acting on you can vary

Free-Fall and Weightlessness

• The elevator and you are in free fall if elevator breaks (falling without any resistance to slow

you down)  

• Free fall has made you weightless  

• You float freely above it, scale reads zero because you are no longer held to it • You are in free wall whenever there's nothing to prevent you from falling • Weightlessness probably only lasts a short time (like jumping off a chair) • When elevator accelerates up, you weight more and when it accelerates downward, you weigh  less

Weightlessness in space

• Astronauts are in free fall

• The Space Station and all other orbiting objects stay in orbit because they are constantly  falling around Earth  

4.2 Newton's Laws of Motion  

How did Newton change our view of the universe?

• Newton eliminated Aristotle's distinction between the two realms and brought the heavens and  Earth together as one universe

• This insight also heralded the birth of the modern science of astrophysics, which applies  physical laws discovered on Earth to phenomena throughout the cosmos

Newton's First Law

• Restates Galileo's discovery that objects will remain in motion unless a force acts to stop them • An object moves at constant velocity if there is no net force acting upon it • Objects at rest (velocity = 0) tend to remain at rest, and objects in motion tend to remain in  motion with no change in either their speed or their direction

• Example: plane (as long as plane is travelling at constant velocity, no net force is acting on it or  on you)

Newton's Second Law

• Tells us what happens to an object when a net force is present

• Force = mass x acceleration (F = ma)  

• Force = rate of change in momentum  

• Baseball example (why you can throw a baseball farther than you can throw a shot in the shot  put)

• Mass of the shot vs. mass of baseball  

• We use this law to also understand acceleration around curves: swinging a ball on a string  around head example

• Taut string must be applying a force to the ball

• When string is intact, force must be pulling the ball inward to keep it from flying off

Newton's Third Law

• For any force, there is always an equal and opposite reaction force

• Objects always attract each other through gravity

• Examples: rockets, you falling towards Earth instead of Earth falling towards you 4.3 Conservation Laws in Astronomy  

• Three conservation laws for astronomy, conservation of momentum, of angular momentum,  and of energy

Why do objects move at constant velocity if no force acts on them?

• Conservation of momentum states that as long as there are no external forces, the total  momentum of interacting objects cannot change; that is; their total momentum is conserved  • Object can gain or lose momentum only if some other object's momentum changes by a  precisely opposite amount

• Rocket example: forces between rocket and axes are always equal and opposite • When no net force acts on an object, there is no way for the object to transfer any momentum  to or from any other object  

• No net force, object's momentum must remain unchanged - which means the object must  continue to move exactly as it has been moving

• Pool table example: collision transfers momentum from the first ball to the second

What keeps a planet rotating and orbiting the Sun?

• The law of conservation of angular momentum states that as long as there is no external  torque, the total angular momentum of a set of interacting objects cannot change  • Object can change its angular momentum only by transferring some angular momentum to or  from another object  

• Both cases of rotation and orbit are below

Orbital Angular Momentum

• Earth's angular momentum at any point in its orbit:

• Angular momentum = m x v x r

• M is Earth's mass

• V is its orbital velocity  

• R is the radius of the orbit (distance from the sun)  

• Earth's orbit:

• 1) Earth needs no fuel or push of any kind to keep orbiting the Sun

• 2) Because Earth's angular momentum at any point in its orbit depends on the product of its  speed and orbital radius, Earth's orbital speed must be faster when it is nearer to the Sun and  slower when it is farther from the Sun

Rotational Angular Momentum

• Spinning skater example: in the product m x v x r extended arms means larger radius and  smaller velocity of rotation

• Bringing in her arms decreases her radius and therefore increases her rotational velocity  

Where do objects get their energy?

• Law of conservation of energy tells us that like momentum and angular momentum, energy  cannot appear out of nowhere or disappear into nothingness  

• Objects can gain or lose energy only by exchanging energy with other objects  • All actions involve exchanges of energy or the conversion of energy from one form to another  

Basic Types of Energy  

• Energy is what makes matter move

• 3 categories of energy

• 1) Energy of motion: or kinetic energy (motion)  

• Kinetic energy of a moving object is 1/2 mv^2 where m is the object's mass and v is its speed • 2) Energy carried by light or radiative energy

• All light carries energy, which is why light can cause changes in matter

• 3) Stored energy or potential energy, which might later be converted into kinetic or radiative  energy  

• Most familiar units of energy are Calories

• In science, standard unit of energy is the joule

• One food Calorie = 4184 joules

Thermal Energy - The Kinetic Energy of Many Particles

• Subcategory of kinetic energy: thermal energy (particles moving randomly within a substance  - solid, gas, etc.)

• Thermal energy measures the total kinetic energy of all the randomly moving particles in a  substance, while temperature measures the average kinetic energy of the particles • Kelvin temperature scale

• Starts from the coldest possible temperature, known as absolute zero (0 K) • Density is important  

• The air in a hot oven is hotter than the boiling point water in the pot but the water in the pot  contains more thermal energy because of its much higher density

Potential Energy in Astronomy

• Two types of potential energy: gravitational potential energy and the potential energy of  mass itself, or mass-energy

• Object's gravitational potential energy depends on its mass and how far it can fall as a result of  gravity  

• Object has more gravitational potential energy when it is higher and less when it is lower • For an object near Earth's surface, its gravitational potential energy is mgh where m is its  mass, g is the acceleration of gravity, h is its height above the ground

• Mass-energy: amount of potential energy contained in mass is E = mc^2 • E is the amount of potential energy, m is mass, c is speed of light  

• Mass can be converted into other forms of energy

• Energy can be transformed into mass as well

• Particle accelerators: large machines to create subatomic particles from energy  4.4 The Universal Law of Gravitation  

What determines the strength of gravity?

• Universal law of gravitation  

• 1) Every mass attracts every other mass through a force called gravity

• 2) The strength of the gravitational force attracting any two objects is directly proportional to  the product of their masses

• Doubling the mass of one object doubles the force of gravity between the two objects • 3) The strength of gravity between two objects decreases with the square of the distance  between their centres

• We say that the gravitational force follows an inverse square law  

• Doubling the distance between two objects weakens the force of gravity by a factor of 2^2 or 4 • All 3 statements can be combined into a single equation

• Symbol G is a constant called gravitational constant  

How does Newton's law of gravity extend Kepler's laws?

• Newton showed that the inverse square law for gravity leads naturally to elliptical orbits for  planets orbiting the Sun (with the Sun at one focus) which is Kepler's first law • Kepler's second law: arises as a consequence of conservation of angular momentum

• Kepler's second law was a planet moves faster when it is closer to the Sun  • Kepler's third law (average orbital speed is slower for planets with larger average orbital  distance) arises from the fact that gravity weakens with distance from the Sun • Newton removed all remaining doubt about the legitimacy of the Sun-centered solar system  

Ellipses Are Not the Only Possible Orbital Paths

• Ellipses are the only possible shapes for bound orbits - orbits in which an object goes around  another object over and over again

• Newton discovered that objects can also follow unbound orbits - paths that bring an object  close to another object just once  

• For example, comets (enter inner solar system, loop around sun, and never return) • Newton showed that bound orbits are ellipses, while unbound orbits can be either parabolas or  hyperbolas

• Conic sections: these shapes are known as this

• Objects on unbound orbits still listen to Kepler's second law: they move faster when they are  closer to the object they are orbiting, and slower when they are away

Objects Orbit Their Common Centre of Mass

• Newton showed that two objects attracted by gravity actually BOTH orbit around their  common centre of mass - the point at which the two objects would balance if they were  somehow connected

• This applies for the Sun and planets as well

Other Characteristics Tells Us the Masses of Distant Objects

• Newton's version of Kepler's third law is important

• We can use any units

• It also shows that the orbital period of a small object orbiting a much more massive object  depends only on its orbital distance, not on its ass

4.5 Orbits, Tides, Acceleration of Gravity  

Orbital Energy

• Planet's total orbital energy - the sum of its kinetic and gravitational potential energies - stays  the same

• Orbits cannot change spontaneously  

Gravitational Encounters

• Orbits can change through exchanges of energy

• One way that two objects can exchange orbital energy is through a gravitational encounter,  in which they pass near enough that each can feel the effects of the other's gravity

Atmospheric Drag

• Friction can cause objects to lose orbital energy

Escape Velocity

• An object that gains orbital energy moves into an orbit with a higher average altitude • Escape velocity: the speed necessary for an object to completely escape the gravity of a large  body such as a moon, planet, star

• Escape velocity does depend on whether you start from the surface or form someplace high  above the surface

How does gravity cause tides?

• Gravitational attraction between Earth and the Moon

The Moon's Tidal Force

• Because the strength of gravity declines with distance, the gravitational attraction of each part  of Earth to the Moon becomes weaker as we go from the side of Earth facing the Moon to the  side facing away from the Moon

• Difference in attraction created a stretching force or "tidal force" that stretches the entire Earth  to create 2 tidal builds, one facing the Moon and one opposite the Moon

• Example: rubber band

The Tidal Effect of the Sun

• Gravitational force between Earth and Sun is indeed much greater than Earth and Moon which  is why Earth orbits the Sun

• However, the much greater distance to the Sun... compared to the Moon, means that the  difference in the Sun's pull on the near and far sides of Earth is relatively small • Spring tides

• Neap tides

Tidal Friction

• Because tidal forces stretch Earth itself, the process creates friction, called tidal friction  • Moon's gravity tries to keep the tidal bulges on the Earth-Moon line, while Earth's rotation tries  to pull the bulges around with it

• This keeps the bulges just ahead of the Earth-Moon line at all times

• Misalignment of tidal bulges with the Earth-Moon line causes 2 important effects • 1) Moon's gravity always pulls back on the bulges, slowing Earth's rotation • 2) Gravity of the bulges pulls the Moon slightly ahead in its orbit, adding orbital energy that  causes the Moon to move farther from Earth  

• The Moon's growing orbit gains the angular momentum and energy that Earth loses as its  rotation slows

The Moon's Synchronous Rotation

• Synchronous rotation: rotation of an object that always shows the same face to an object  that it is orbiting because its rotation period and orbital period are equal

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