Final answer:
A 500kg satellite in geosynchronous orbit has its orbital radius extended to approximately 42,164 km from the center of the Earth.
Step-by-step explanation:
The question asks for details about placing a 500kg satellite into a geosynchronous orbit around the Earth. A geosynchronous orbit has a special characteristic where the orbital period of the satellite matches the Earth's rotation period, which is 24 hours. This means the satellite will appear stationary relative to a point on the Earth's equator.
For part a, the radius of a geosynchronous orbit is approximately 42,164 km from the center of the Earth, which includes the Earth's radius. Hence, the satellite is about 35,786 km above the Earth's surface.
Part b involves calculating the gravitational potential energy (U) of the satellite on Earth's surface. This can be found using U = -G * (M * m) / r, where G is the gravitational constant, M is Earth's mass, m is the satellite's mass, and r is the Earth's radius.
Part c looks for the total energy of the satellite in geosynchronous orbit, which is the sum of its kinetic energy (KE) and gravitational potential energy (U). The total energy in a stable orbit is always negative, indicating a bound system.
Finally, part d asks how much work is done to place the satellite in orbit. This work is essentially the difference in the satellite's total energy between its position on the Earth's surface and in its geosynchronous orbit.