# Gravitation, orbit, escape velocity

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**Satellite in geostationary orbit of the Earth**A 465 kg satellite is in geostationary orbit around the Earth.

- What is the radius of its circular orbit? What is its altitude?
- What is the satellite's speed?
- What is the gravitational potential energy of the satellite when it is still attached to its launch rocket at the Earth's surface? What is the potential energy in orbit?
- Concept: what is the difference between $E_{p}=mgh$ and $E_{p}=-G\frac{m_{1}m_{2}}{r}$? Why is one positive and one negative?
- What is the total mechanical energy of the satellite once it is in orbit?
- Concept: which of the following sets of energies could represent the kinetic energy, gravitational potential energy, and total mechanical energy of a satellite in a stable circular orbit? (Proof: for an object in stable circular orbit, $E_{p}=-2E_{k}$)
a) $E_{k} = 30000J, E_{p} = -30000J, E_{mech} = 0J$

b) $E_{k} = 30000J, E_{p} = -60000J, E_{mech} = -30000J$

c) $E_{k} = 60000J, E_{p} = -30000J, E_{mech} = 30000J$

d) $E_{k} = 60000J, E_{p} = 30000J, E_{mech} = 90000J$

- How much work must be done on the satellite to launch it into geostationary orbit?
- What speed does the satellite need at the surface of the Earth from its launch to reach the geostationary orbit?
- In orbit, how much additional energy does the satellite need to escape the Earth's gravity?
- What is the escape velocity from the surface of the Earth?