1. Consider a satellite of mass 1000 kg moving in a circular orbit 5000 km above the earth's surface
a. Find its period, energy, and speed. Graph Veff vs r, and plot the orbit (r vs 0).
b. Now instantly double its velocity. Describe the motion (Is it bounded?, what is its distance of closest approach? What is its maximum distance?). Graph Veff, and include energy on this graph. Plot the orbit
2. [analytical and software plot] Halley's comet has an eccentricity of 0.967 and a perihelion distance of 89 x 106 km. Calculate the aphelion distance, the speeds at perihelion and aphelion, and the time period of the orbit. Draw the path of the comet.
3. (a) If the Sun suddenly loses half its mass, show that the Earth's orbit will be a parabola (and so the Earth will escape to infinity).
(b) If the Sun's mass suddenly doubles, what will be the Earth's orbital period?