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Astronomy Week 6 Notes

by: Erin Bleck

Astronomy Week 6 Notes EESC1150

Erin Bleck
Harvard University
GPA 3.91

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About this Document

These notes cover what was taught in Astronomy at Boston College with Professor Kuchar.
Dr. Thomas Kuchar
Class Notes
Prograde/RetrogradeMotion, TychoBrahe, JohannesKepler, Kepler'sLaws, galileo, IsaacNewton, Newton'sLaws, CircularMotion, CapsuleHistoryofGravity, Newton'sUniversalGravity
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This 7 page Class Notes was uploaded by Erin Bleck on Tuesday July 19, 2016. The Class Notes belongs to EESC1150 at Boston College taught by Dr. Thomas Kuchar in Summer 2016. Since its upload, it has received 28 views. For similar materials see Astronomy in Earth and Environmental Sciences at Boston College.

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Date Created: 07/19/16
Notes February 23, 2016 The Use of Precision Measurements and Telescopic Observations - Review: o Prograde – West  East  Moon and Sun o Retrograde – East  West  Planets  Much slower than the rotation of the Earth (dominates) o All relatith to the background stars! - Astronomers of 16 Century o Astronomy was often a pursuit of rich noblemen  Had to fund themselves (no government funding) o Though interested in science, they still held on to beliefs we would call pseudoscience (prejudices of how the universe should actually be)  Heavens, circular motion  Alchemy  Numerology  Astrology - Tycho Brahe (1546-1601) o Danish o Had artificial wooden and silver noses o Rumored to have died of a bladder burst o Known for being the world’s best naked-eye astronomer o Major accomplishments  Built “Meridian Circle” to measure the positions of celestial objects very accurately (~1 arc minute)  Aligned with the meridian (north-south)  Would read off the measurements that he would see a star, planet, the Moon, etc. through his window (latitude coordinate)  Helper would read off the time that the star crossed the meridian  Built catalogues of motions  Made the most continual and accurate observations of stars and planets (particularly Mars) for his time  Found that comets moved outside of the Earth’s atmosphere  Showed that the heavens were changing o People had believed that comets must be within Earth’s atmosphere because the heavens would not change  Witnessed a supernova (1572) and concluded that it was much farther away than any celestial object  Couldn’t detect parallax motion in the stars (the apparent shift of looking at one particular thing with different perspectives)  Meaning that the stars were immensely distant from the Earth (contradicted the ideas of the perfect heavens since supernova changes the heavens)  Created his own hybrid geo-heliocentric model of the solar system – planets go around the Sun, but the Sun, in turn, orbits around the Earth - Why were Tycho’s parallax distances important? o Disproved ancient ideas about the heavens  The supernova in 1572 showed that the heavens were both changing and had a dimension of distance  Comets were thought to be atmospheric occurrences, not objects in the region of the planets  This troubled scholars who previously thought the heavens were unchanging - Johannes Kepler (1571-1630) o German o Wrote children’s books about the heavens o He was a deeply religious man and a family man o Tycho Brahe’s assistant but rumored to have hated Tycho o Inherited Tycho’s data after his death. With that data he changed the understanding of motion of heavenly bodies forever o Known for creating first a theoretical model to explain planetary motions - How did (Copernicus), Tycho, and Kepler challenge the Earth-centered model? o Kepler first tried to match Tycho’s observations with circular orbits o But an 8-arcminute discrepancy led him eventually to ellipses - Kepler’s Three Laws of Planetary Motion o First Law: The orbit of each planet around the Sun is an ellipse (elongated circle) with the Sun at one focus  One long axis (major axis)  Half = semimajor axis  One shorter axis (minor axis)  2 foci  Sun is at one focus and the other has nothing  Perihelion = when a planet is closest to the Sun  Aphelion = when a planet is farthest from the Sun  Eccentricity – how squashed or “out of round” an ellipse is  A number ranging from 0 (circle) to 1 (straight line)  0 = perfect circle o Foci meet at the center o Semimajor and semiminor axes are equal  The Earth’s orbit is very close to being a circle (e = 0.017) o Second Law: A line joining a planet and the Sun sweeps out equal areas in equal intervals of time  All areas are equal despite looking different  The distance from the Sun and speed of the planet changes throughout the year, but the time remains constant (1 month in lecture)  Perfect circle  All areas are the same  All distances from the Sun are the same  All speeds of the planet are the same  Consequences (larger consequences the more eccentric an orbit is)  Orbital speed is not constant for an ellipse; only for a circle  Planets move faster when near the Sun (perihelion)  Planets move slower when they are far from the Sun (aphelion)  The speed a planet travels during its orbit is related to the distance from the star  When the planet is near the Sun the planet goes faster than when the planet is farther from the Sun o Third Law: The size of the orbit determines the orbital period  Planets that orbit near the Sun orbit with shorter periods than planets that are far from the Sun  Earth orbital period = 1 year  Closer to the Sun = less than 1 year  Farther from the Sun = more than 1 year  a^3 = p^2  a = distance from Sun (AU) o The semimajor axis of the orbit (because planets are at different distances from the Sun throughout their orbits)  p = orbital period (years)  SIZE AND MASS OF THE PLANET DOES NOT MATTER!  If we moved Jupiter to Earth’s orbit, it would take 1 year to orbit the Sun (despite it being much larger than Earth) - February 25, 2016 - The great scientist Galileo made discoveries that strongly supported a heliocentric cosmogony o One of the principal founders of the experimental method for studying scientific problems o Using a Dutch-designed telescope that he built himself, he made several observations that disproved ancient thinking about the Universe (1610) - Galileo (1564-1642) o Italian o Known for being the first telescope observations of the Sun o Was blind at the time of his death o Was labeled a heretic by the church o Telescopic Observations:  Saturn: A being with ears  Contradicted that idea of everything has to just be a circular shape in the heavens o Saturn is not a sphere (ears)  Circles and spheres do not dominate the heavens  Milky Way  With a telescope, Milky Way resolves into thousands (billions) of stars o Today, we know that there are billions of stars in the Milky Way  Implication: the Universe is bigger than previously imagined  The Moon  The Moon has craters (some with rays) and mountains  The Moon is not a “perfect” heavenly body o Actually started to look like the Earth (which contradicts the idea that the heavens are perfect and made up of perfect spheres and circles)  Sunspots  The Sun is not a perfect heavenly body (because it has spots)  The Sun rotates about its own axis (because spots moved)  More observations showed the Sun’s axis is tilted, direction of axis varied with Earth’s seasons and repeated annually: clue Earth was orbiting the Sun!  Venus went through phases like the Moon (new through full) which showed that Venus must orbit the Sun and strongly supported a heliocentric model  Could only occur if Venus orbits the Sun (Gibbous and Full phases seen!)  Saw that Venus was going around the Sun and that it would come closer to the Earth and farther from the Earth o New Phase is close to the Earth o Full Phase is far from the Earth  Seeing the Gibbous and Full Phases contradicted Ptolemy and what the Universe would look like with a geocentric model o Not in the Ptolemic model!  Jupiter’s “stars”  Saw 4 “stars” going around Jupiter on successive nights  Today – 4 largest moons of Jupiter are known as the Galilean Moons o Io (closest to Jupiter) o Europa o Ganymede o Callisto (furthest from Jupiter) Introduction to Gravity - Sir Isaac Newton (1642-1727) o Described the fundamental laws covering the motion of bodies o Had to invent his own mathematics (Calculus) to do it! o And he did most of it before his 24 birthday o British o Best known for creating first theoretical model for explaining gravity o How he changed our view of the Universe?  Realized the same physical laws that operate on Earth also operate in the heavens  One Universe  Formulated laws of motion and gravity  Much more: experiments with light, first reflecting telescope, calculus o Formulated three laws of motion and the law of gravitation – these laws describe the motion of our physical world  First Law – A body remains at rest or moves in a straight line at a constant speed unless acted upon by an outside (net) force  Aka Law of Inertia  An object at rest stays at rest  An object in motion stays in motion  A body continues in a state of rest or in uniform motion (i.e., in a straight line at a constant speed), unless made to change that state by forces acting on it  Or, more simply, a body maintains the same velocity unless forces act on it  Rockets will coast (no engines) in space along a straight line at constant speed  A hockey puck glides across the ice at constant speeds until it hits something  Second Law – (net) Force = mass x acceleration or Fnet = m x a  Acceleration is the rate of change in velocity or how quickly your motion is changing  Why net force? o Balanced forces = no change in velocity  If an object’s velocity is not changing, either there are no forces acting on it, or the forces are balanced and cancel each other out  If a force (F) acts on an object of a certain mass (m), the force causes an acceleration (a) o For the same force applied to a heavier object (larger mass), there is a small acceleration o For the same force applied to a lighter object (smaller mass), there is a large acceleration  Third Law – Whenever a body exerts a force on a second body, the second body exerts an equal and opposite force on the first body  When two bodies interact, they create equal and opposite forces on each other  Relates to Newton’s Universal Law of Gravitation - Circular Motion o Law of inertia (1) says that the ball should go in a straight line o A change in direction (circular motion) also indicates an acceleration and therefore a force (F = m x a)  Tension on the string changes the ball’s velocity = force (picture)  If the string breaks, what happens?  No longer apply a force, so it goes in a straight line - Capsule history of gravity o Aristotelian view  Prevalent until Galileo  Not “gravity” per se – objects seek their “proper place” based on their “element”  Objects are a mixture of earth, water, air, fire  Lighter objects fall more slowly than heavier ones  Different concept of inertia  Natural state was rest  Remove a force and an object will come to rest o No concept of acceleration – force caused motion - Newton’s Universal Gravity o Wasn’t first to propose a force like gravity  First to have a working formulation o Hypothesized a force keeping the Earth in orbit  Apple story may be apocryphal  Cannon “thought experiment”  Lead to his theory of gravity - Newton’s Universal Law of Gravitation 1. Every mass attracts every other mass 2. Attraction is directly proportional to the product of their masses 3. Attraction is inversely proportional to the square of the distance between their centers a. The further apart two objects are, the weaker gravity is; the closer two objects are, the stronger gravity is o Fg = G((M1M2)/R^2) o More simply:  Everything pulls on everything else  The larger the masses, the greater the pull  Objects close together pull more on each other than objects farther apart o Ex.  M1 = your mass  M2 = Earth’s mass  R = that’s how far from Earth’s center you are  Fg = your weight o Relationships  Double the distance  1/4F  ½ the distance  4F  Double one of the masses  2F  ½ one of the masses  1/2 F o Question:  Say M1 has twice the mass of M2. Which has the stronger pull on the other?  Equation states the forces are equal! o Look at the equation!  Newton’s 3 law infers forces are equal and opposite, too! - Applying Newton’s Laws and Universal Gravity o Galileo’s Experiment  Dropped spheres of differing masses – measured their acceleration  Aristotle would predict heavier would fall faster – hit the ground first  Actual result: hit at the same time (No difference in acceleration!)  Why: Apply Newton’s 2 Law to his Universal Gravitation (F = m x a)  G((M1M2)/R^2) = M1 x a  G((M2)/R^2) = a  Shows that acceleration is the same (because M1 does not matter) and things will fall at the same rate and hit the ground at the same time o Without the resistance of air/wind


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