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Physics 152: Gravity

 

Lecture Notes

Discovering Gravity: Galileo, Newton, Kepler   PDF

Galileo analyzes a cannonballís trajectory, Newton imagines the cannon on a very high mountain shooting the cannonball into orbit, and sees the analogy to the Moonís motion, which leads him to conjecture that the gravitational force extends to the moon and beyond, with strength proportional to the inverse-square of the distance. Analyzing Kepler's Laws of planetary motion indicates that a similar gravitational force keeps the planets in their orbit, suggesting a Universal Law of Gravitation. We give an (optional) calculus-based proof that the planetsí orbits are in fact ellipses. 

Visualizing Gravity: the Gravitational Field  PDF

Finding the gravitational attraction form a single mass, a pair of masses, a ring, a hollow sphere and finally a solid sphere, both inside and out.  How does gravity change on going down a mine?

Working with Gravity: Potential Energy  PDF

How potential energy relates to the gravitational field, near the earthís surface and far away.  Potential energy and escape velocity.  Potential and kinetic energies in circular orbits.

Elliptic Orbits: Paths to the Planets  PDF

The interesting orbits are ellipses, or sequences of pieces of ellipses.  Some simple properties of the ellipse make it possible to understand these orbits well. We briefly discuss other (hyperbolic) orbits, and also the important role of the slingshot in actually reaching the outer planets.

Binary Stars and Tides  PDF

More gravitational phenomena: pairs of stars orbiting a common center; how a close gravitational source can distort a planet.

General Relativity†† PDF

The Principle of Equivalence: a uniformly accelerating frame of reference is equivalent to a gravitational field.  How it necessarily follows that a gravitational field deflects light, and that a clock on the surface of a big planet runs slow.

 

Flashlets, etc.

Newtonís Mountain

Animation of Newtonís Classic Thought Experiment: shooting a cannonball horizontally from an imaginary mountaintop above the atmosphere,with sufficient speed, the ball goes into orbit.

Keplerís Laws Flashlet

Create your own planetary orbit with the click of a mouse, and see Keplerís Laws in action.

Shoot Mars Flashlet

How good is your aim at getting a spaceship to Mars?

Jupiter Slingshot Flashlet ††

Using Jupiterís gravity to get way out there: read the instructions, then go tofull screen.

General Planetary Spreadsheet

This Excel spreadsheet will calculate planetary orbits over a wide range of initial conditions, and will work for gravitational forces that are not inverse square, producing some strange looking orbits.  Convenient numbers, such as GM = 8, correspond to mini solar systems with one-kilogram planets orbiting stars weighing only a hundred million tons or so, but the geometry of the orbits doesnít depend on the scale, so we can gain intuition about real planetary systems.

 

For Students: Fact Sheet, Homework Problems, Study Guide

 

Gravity Fact SheetPDF

 

Gravity Homework ProblemsPDF

 

Gravity: the Essentials †††PDF

 

 

 

Next topic: Fluids