# Getting from LEO to a station in geostationary orbit and docking with it using a Hohmann transfer?

How long would it take for a spacecraft with a mass of 30,000 kg, to go from LEO to reach and match the speed of a space station in geostationary orbit so it could dock with the station, using a Hohmann transfer orbit?

LEO speed 7.8 km/s, 160 km above the Earth GEO speed 3 km/s, height of 36,000 km ESA Space Transportation page

Thrust of the craft's engine 45 kN, modeled on the CSM. Wikipedia-Apollo CSM

Are there any other parameters I should include? If any of the information doesn't make sense please let me know.

• For a rough approximation: There's a Hohmann transfer calculator here that will give you the required delta-v (which affects the burn time); the transfer trajectory is one-half of an orbit with perigee in LEO and apogee at GEO, so compute the orbital period and divide by two to get the transfer time. Since the thrust is pretty low, the burn time will be significant; the idealized instant-impulse Hohmann transfer doesn't apply, but it'll be close to correct. – Russell Borogove May 24 '19 at 20:42

The time in transfer will be a good approximation - replacing the long burns with impulsive.

LEO altitude 160 km + 6,371km Earth average radius, so periapsis of the transfer orbit is 6531km from Earth center.

$$T=2 \pi \sqrt{a^3 \over GM}$$