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PHY134 Introductory Astronomy . Newton and Gravity. What Newton Told Us. . The rest is details If we can figure out forces this is a way to predict from where things are today where they will be in future (or were in past ):. positions, velocities. forces.

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Phy134 introductory astronomy

PHY134Introductory Astronomy

Newton and Gravity


What newton told us
What Newton Told Us

  • . The rest is details

  • If we can figure out forces this is a way to predict from where things are today where they will be in future (or were in past):

positions, velocities

forces

accelerations

advance t


Conservation laws
Conservation Laws

  • Mathematical theorems follow from Newton

  • Momentum then is rate of change of

  • So if A and B act on each other, does not change – they exchange momentum but can’t create or destroy it. Momentum conserved


More conservation
More Conservation

  • With a little more math, see that a circular version – angular momentum is also conserved

  • This will be incredibly important to us – things in space spin

  • Earth spins at constant rate because it once did


Energy
Energy

  • If gravity is the only force acting on an object, can show that total energy is constant

  • In general, other forces act. Find that this introduces more kinds of energy: sound, light, heat, chemical, electric, nuclear, etc. but total is conserved

  • Units of energy:


Attractive logic
Attractive Logic

  • If an object of mass moves in a circle of radius with uniform speed there must be a force acting, directed to center, of magnitude

  • Moon orbits Earth so force directed towards Earth

  • We notice Earth applies such a force to apples. Could this be the same force?

  • Planets orbit Sun in (almost) circular orbits at (almost) uniform speed. Does Sun apply the force this implies on all planets?

  • If so, Earth must apply a force to Sun directed towards Earth

  • It all hangs together!!


Kepler and newton
Kepler and Newton

  • Planet of mass orbits Sun at radius with speed

  • Force Sun applies to planet is thus

  • Kepler says

  • Find


It s universal
It’s Universal

  • Sun applies a force given by to each planet, with same

  • So each planet applies force of same magnitude to Sun

  • Law does not single out planet from Sun, so must have so


Really universal
Really Universal

  • Earth also attracts the Moon, and all objects near it.

  • So Moon and all other objects attract Earth.

  • Everything attracts everything else!

  • Measured Newton’s constant:


Thinking about orbits
Thinking about Orbits

  • Why doesn’t the Moon fall on Earth?

  • It does! Moon is constantly accelerating towards Earth. Orbiting is falling without ever hitting the ground


Success
Success!

  • Newton’s equations predict Kepler’slaws.

  • Also show there are other types of orbits.

  • New successes: Halleypredicts return of comet (1757).

  • Neptune discovered mathematically in details of Uranus’s orbital motion.


Even more generally
Even More Generally

  • Newton’s law is Universal. Apply to any two objects orbiting under mutual gravity. Find elliptical orbit about center of mass with


Example low earth orbit
Example: Low-Earth Orbit

  • ISS orbits at an altitude so has orbital radius

  • Period given by


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