Potential Energy Orbital Motion PHYS116 A1 102714 Lecture

Potential Energy, Orbital Motion PHYS-116 A-1, 10/27/14, Lecture 29 Momchil Velkovsky

Gravitational potential energy

Energy Superposition Principle

Escape Speed • You move a ball of mass m away from a sphere of mass M. (a) Does the gravitational potential energy of the system of ball and sphere increase or decrease? (b) Is positive work or negative work done by the gravitational force between the ball and the sphere?

Compared to the Earth, Planet X has twice the mass and twice the radius. This means that compared to the amount of energy required to move an object from the Earth’s surface to infinity, the amount of energy required to move that same object from Planet X’s surface to infinity is • • • A. 4 times as much. B. twice as much. C. the same. D. 1/2 as much. E. 1/4 as much.

Satellite motion

Consider satellite orbits • Several images of things in orbit to consider are shown below.

Kepler’s laws for planetary motion • Each planet moves in an elliptical orbit with the sun at one focus. • A line connecting the sun to a given planet sweeps out equal areas in equal times. • The periods of the planets are proportional to the 3/2 powers of the major axis lengths in their orbits.

Orbital questions Halley’s comet distance from the Sun: At perihelion 8. 75 x 107 km, at aphelion- 5. 26 x 109 km. What is a, e, T?

General Relativity

General Relativity

General Relativity Effects • Perihelion of Mercury • Deflection of light

General Relativity Effects • Gravitational Lensing

Time Effects • Time is also curved! In Special relativity: Spacetime • Time goes slower for us than at a satellite : GPS correction

Reading for next time • Chapter 14