# Calculate Delta-V for a Hohmann transfer to a higher orbit

I am wondering if anybody can help me with calculating Delta-V in Kerbal Space program?

I have a ship in circularized 100 km orbit around planet Kerbin. Planet's radius is 600 km (standard gravitational parameter μ = 3.5316000×1012 m3s-2). I want to perform a Hohmann transfer to a target orbit of 400 km above surface, i.e. 1000 km radius to planet's center of gravity (orbit's focus).

Can anybody please explain how can I calculate Delta-V cost of a Hohmann transfer orbit raising maneuver?

• Is the fact that you need this for a game relevant at all to your question? KSP uses instantaneous impulse, right? So $\Delta v = \sqrt{\frac{\mu}{r_1}} \left( \sqrt{\frac{2 r_2}{r_1+r_2}} - 1 \right) + \sqrt{\frac{\mu}{r_2}} \left( 1 - \sqrt{\frac{2 r_1}{r_1+r_2}}\,\,\right)$ as explained in Hohmann transfer Wiki. – TildalWave Jun 2 '14 at 19:38

## 1 Answer

KSP also offers a nav computer that lets you plot a course and then gives you the relevant markers (and burn w/time estimate) to achieve what you want. If you want to do this to change your orbit I recommend the in game tool, but if you are trying to familiarize yourself with the math then that's a different issue.

To use the game nav tool:

Switch to map view and locate your periapsis (the point on your orbit closest to the orbiting body). Click that mark on your orbit and add a prograde burn until your apoapsis is raised to the desired altitude. When your ship arrives at your periapsis start the designated prograde burn and stop thrusting when your real apoapsis matches that of your projected apoapsis. Do the same process at your apoapsis increasing your periapsis to the desired altitude. Then perform the required prograde burn and you've just increased your orbit.

Remember to burn with SAS on and if you over burn you can quickly retrograde burn to decrease your apoapsis/periapsis in case you increase either value too much.