University:
California State University, Northridge
Course:
PHYS 100A | General Physics I
Academic year:

2024
Views:

159

Pages:

2
Author:

moinault8kd

Circular Orbits In this section we assume that the central body of mass (or moving uniformly). And the second body of mass is the earth and is fixed is a small artificial satellite. The Earth's mass Sputnik I on the other hand weighed 83.6 kg. So its gravitational pull on the Earth can probably be neglected. (This is certainly not true for its effect on world history or American politics). We will also assume that the satellite moves on a circular orbit. and that earth is at the center of this orbit. Let be the radius of the circular orbit. The distance traveled after a time is given by Hence, The area swept in a time is given by Kepler's second law implies that this area is proportional to . It follows that for some constant angular velocity . Thus we have the rule: Satellites on circular orbits must move at a constant angular velocity. In polar coordinates we have then and therefore (4) can thus be written as or simply as (6) If is the period of this motion then substituting this into (6) we get (7) this is of course Kepler's third law in the special case of circular orbits. The expression is called the geocentric gravitational constant. Its value is