Moving from a 320 km circular Low Earth Orbit (LEO) to a Geosynchronous Earth Orbit (GEO) using an elliptical orbit uses a delta V of 2.439 km/s.

Circularizing the orbit at GEO uses a delta V of 1.785 km/s. All the plane changes are included in these two burns. Reversing the course and going from GEO to LEO would require the same to delta V?s.

We have an Orbital Transfer Vehicle (OTV). It is a single stage chemical rocket with a specific impulse of 2.900 km/s. It has a mass of 14,500 kg, the mass of propellant is 14,000 kg.

(a) The OTV?s first use is to take a spacecraft to GEO, grab another spacecraft that has the same mass, and return that spacecraft to LEO so it can be repaired. When it finishes its burn at LEO it has used all of its fuel. How much mass can the OTV take to and from GEO?

(b) How much spacecraft mass can it take up, release the spacecraft, then return empty, i.e. no spacecraft coming down?

Hint: use this equation

Where ?vis the change in velocity, M ₀ is the initial mass, and M _b is the mass at burnout.

Av = Is * In(Mo/Mb)