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Unveiling the Universe: Newton's Laws of Gravity and Motion

Explore the foundational principles of physics through Newton's groundbreaking laws of gravity and motion. Discover how these laws predict the movement of celestial bodies and explain the conservation of energy and momentum in the cosmos.

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Unveiling the Universe: Newton's Laws of Gravity and Motion

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  1. PHY134Introductory Astronomy Newton and Gravity

  2. 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

  3. 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

  4. 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

  5. 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:

  6. 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!!

  7. Kepler and Newton • Planet of mass orbits Sun at radius with speed • Force Sun applies to planet is thus • Kepler says • Find

  8. 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

  9. 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:

  10. 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

  11. 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.

  12. 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

  13. Example: Low-Earth Orbit • ISS orbits at an altitude so has orbital radius • Period given by

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