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# PHY134 Introductory Astronomy - PowerPoint PPT Presentation

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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### PHY134Introductory Astronomy

Newton and Gravity

• . 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

• 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

• 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

• 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:

• 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

• Planet of mass orbits Sun at radius with speed

• Force Sun applies to planet is thus

• Kepler says

• Find

• 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

• 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:

• Why doesn’t the Moon fall on Earth?

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

• 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.

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

• ISS orbits at an altitude so has orbital radius

• Period given by