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AST 101, Week 7 Notes

by: Bethany Marsfelder

AST 101, Week 7 Notes 101

Marketplace > Syracuse University > Astronomy > 101 > AST 101 Week 7 Notes
Bethany Marsfelder

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About this Document

This set of notes covers Newton's laws of motion and conservation, as well as celestial mechanics, and the connection between Kepler and Newton. I have added supplements from the textbook as well, ...
Our Corner of the Universe
Professor Walter Freeman
Class Notes
astronomy, Astronomy 101, SUAST101, newton, newton's laws, Newton’s Laws, Newton's 3rd Law, kepler, Johannes Kepler, JohannesKepler, Kepler'sLaws, celestialmechanics, lawsofmotion, lawsofconservation, Syracuse University, syracuse
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This 5 page Class Notes was uploaded by Bethany Marsfelder on Monday October 17, 2016. The Class Notes belongs to 101 at Syracuse University taught by Professor Walter Freeman in Fall 2016. Since its upload, it has received 38 views. For similar materials see Our Corner of the Universe in Astronomy at Syracuse University.


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Date Created: 10/17/16
October 11, 2016 AST 101: Professor Freeman Lecture: The law of gravity; Newton’s laws of motion Textbook Pages: 90-100 Lecture Tutorials: 29-32  Newton’s Ideas o Objects move in a straight line at a constant speed unless a force acts on them o Forces cause their velocities to change size and direction (accelerate) o Gravity is such a force!  Newton’s First Law o No motive force is required to keep things moving. They do that on their own. o Space/astronomy is great to study physics because there is no friction acting upon an object; the “distracting things” are removed, so things “coast” forever without another force to change their motion  Newton’s Second Law o Biggest idea o Force causes objects to accelerate o F = ma o F/m = a o The strength of a force, divided by the mass of the thing it acts on, gives that thing’s acceleration  Acceleration o Acceleration has a direction: it can increase, decrease, or redirect an object’s velocity:  Apply engine power to a car going East: force to the East, thus it goes East faster  Apply brakes to a car going East: force to the West, thus it goes East more slowly  Turn steering wheel left: force to the North, thus car starts traveling Northeast  The force of gravity o Newton discovered:  F(grav) = G x (mass of object A) x (mass of object B)/(distance between them)^2  F(grav) = G(m1)(m2)/(r^2)  G is just a number telling us how strong gravity is: about a ten-billionth of the weight of an apple for two kilogram objects a meter apart  Switching the order of m1 and m2 doesn’t affect the result  “For every action there is an equal and opposite reaction” – if the Earth’s gravity pulls a person down with a force of 160 pounds, a person pulls up on the Earth with the same force of 160 pounds  Forces come in pairs  Gravity lessens the further something is away (so, we are not affected by Polaris’ gravity.)  Thus, if we increase the distance between something by a factor of 2, the denomination of the fraction increases by a factor of 4  The Wobbly Sun o Does the Sun move? o Do the planets enact gravitational force on the Sun? o If the Sun does wobble, why can’t we see it, if the force on the Sun is the same as the force pulling on the planets?  The Sun’s mass is just so incredibly big that this force doesn’t affect it that much  We do see this wobble if we look closely enough  Somebody else might see it, too.  We can see stars “wobble” if they have planets around them  Doppler Shift; higher frequency when moving closer, lower frequency when moving away  Additional o Speed – how far an object will go in a certain amount of time o Velocity – an object’s speed and direction o Acceleration – if an object’s velocity is changing in any way (speed, direction, or both) o Acceleration of gravity – g, the acceleration of a falling object. On Earth, g = 9.8 m/s^2 o Momentum – the product of its mass and its velocity o Force – the only way to change an object’s momentum o Net force – represents the combined effect of all the individual forces acting on an object put together o Mass - the amount of matter in one’s body or in an object o Weight – dependent upon both the mass and the forces (including gravity) acting upon an object’s mass o Free-fall – falling without any resistance October 13, 2016 AST 101: Professor Freeman Lecture: Celestial mechanics/Conservation laws and planetary orbits Textbook Pages: 90-100 Lecture Tutorials: 29-32  Newton’s laws of motion o Objects continue moving in a straight line at a constant velocity unless a force acts on them o Forces make object accelerate  These terms have particular meanings: o Velocity – the speed and direction of an object’s motion o Acceleration – a change in an object’s velocity (speed up, slow down, change direction)  Newton’s Second Law o Can be written as:  Object’s acceleration = the force applied to object/object’s mass  F = ma  Newton and Kepler o A mathematical comparison:  Fg = ma  Fg – GMm/(r^2)  ma = GMm/(r^2)  a = Gm/(r^2)  The acceleration does not depend on mass!  This explains why Kepler’s third law, about orbital times, does not depend on the mass of the planet; the acceleration from gravity doesn’t depend on the mass being accelerated.  Gravity makes everything accelerate at the same time.  Circular motion o Without a force, things travel in straight lines at constant speeds (Newton’s first law). o It requires a force, directed toward the center, to hold something in circular motion.  The tension in the string caused Otto to move in a circle towards Professor Freeman’s hand.  The aluminum track is pushing on the ball. If a section is removed, it will go straight. o Consider a planet orbiting a star.  Gravity always pulls the planet inward.  A force directed towards the center is required for a circular orbit  Very specific balance between orbital speed and distance required for a circle (otherwise, we get an ellipse!)  The planet’s velocity is always pointed in the direction it is moving.  The planet’s acceleration is always pointed towards the Sun. o What about elliptical orbits?  For gravity, the force depends on the distance from the center, as we know.  Speeding up/slowing down is consequence of planetary gravity/orbit.  Thus:  If a comet is closer to the Sun, that means: o The gravitational force is higher o The acceleration is higher o The comet’s velocity changes directions faster o It “whips around the Sun” near perihelion (point of close approach)  When it is further from the Sun: o The gravitational force is very small o It takes a long time to change direction o The Sun’s gravity takes a long time to arrest the comet’s motion and turn it back around  Angular momentum – something any spinning/revolving object has and a consequence of Newton’s laws o Angular momentum = (mass) x (how far it is from the center of motion) x (how fast it is moving around the center o Angular motion is conserved – unless an outside agent messes with it, the product will remain the same  Thus, if a planet’s distance from the Sun increased, the speed it would move around the Sun must decrease to keep angular momentum the same  Or, the speed of a planet when closer to the sun is larger than when it is farther away o Distance from the center x how fast something moves o Gyroscope experiment o Kepler’s second law is a consequence of the conservation of angular momentum!  Hypothetical o Fgrav = Gm1m2/(r^2) o If the Sun is more massive, what changes?  Not gravity  Not distance  Not earth’s mass  Just m1  So the fractional value doubles  Additional o The law of conservation of angular momentum tells us that total angular momentum can never change. An individual object can change its angular momentum only by transferring some angular momentum to or from another object  Angular momentum: m x v x r o The law of conservation of energy tells us that, like momentum and angular momentum, energy cannot appear out of nowhere or disappear into nothingness. Objects gain or lose energy only by exchanging energy with other objects.  Three types of energy:  Kinetic energy – energy of motion; falling rocks, orbiting planets, and molecules moving in the air o Thermal energy – represents the collective kinectic energy of the many individual particles (atoms and molecules) moving randomly within a substance like a rock or the air or the gas in a distant star  Temperature – measure of average kinetic energy  Kelvins  Radiative energy – energy carried by light; all light carries energy, which is why light can change matter.  Potential energy—stored energy; a rock perched on a ledge has gravitational potential energy (depends on its mass and how far it can fall as a result of gravity) because it will fall if it slips over the edge o Universal law of gravitation – Every mass attracts every other mass through the force called gravity.  The strength of gravitational force attracting any two objects is directly proportional to the product of their masses  The strength of gravity between two objects decreases with the square of the distance between their centers (inverse square law) o Bound orbits – orbits in which an object goes around another object over and over again o Unbound orbits – paths that bring an object close to another object just once o Orbital energy – the sum of its kinetic and gravitational potential energies o Gravitational encounter – where two objects pass near enough that each can feel the effects of the other’s gravity


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