What is the equations for the delta-v needed for an altitude change.

[goldenpeach]

Hi!

As the tittle say,I would want to know the equation that tell you how much delta-v is needed to change the periasis/apoasis of an orbit.

Also,what is the equation that tell you what will be your speed at a given altitude of your orbit?

Thank you for reading and thank you in advance for answering!

Edited September 26, 2013 by goldenpeach

[Ralathon]

Hohmann transfer orbits give the basic equations for apoasis/periapsis changes.

To calculate velocity as a function of altitude you can simply rewrite the vis-viva equation.

[goldenpeach]

Thank you for the answer,but I don't understand wich equation of your link for the Hohmann transfer orbit I must use.

Also,thank you for the vis-visa equation!

[Meithan]

Assuming you're thrusting at periapsis or apoapsis of your current orbit (or that your initial orbit is circular), you can simply subtract the speeds in each orbit computed with the vis-viva equation.

The vis-viva equation gives you the current orbital speed when you're at a distance r from the center of the planet/moon and on an orbit with semi-major axis a (which is simply the average of your periapsis and apoapsis distances, a=(rpe+rap)/2):

where μ=GM is the "gravitational parameter" of the planet (M its mass, G the gravitational constant) -- it's listed in the KSP wiki article for each celestial body in the game.

If your orbit is circular, then a=r, so you get the simpler equation:

Example

Suppose we're in a 100 km orbit aroun Kerbin and we want to perform a burn so that our apoapsis climbs to the keosynchronous altitude, 2868.75 km.

First, it's important to convert those altitudes into distances from the center of Kerbin. Just add 600 km. So the radius of the initial orbit is 700 km and the target apoapsis distance is 3468.75 km. Also, you need them in meters, so multiply by 1000.

1) Compute the orbital speed in the 100 km orbit

For Kerbin μ=3.5316000x10^12, so:

2) Compute the speed you would have on the transfer orbit at the point you're doing the burn.

The transfer orbit has the same 100 km periapsis (700 km radius), but an apoapsis altitude of 2868.75 km (3468.75 radius). So its semi-major axis is:

So, plugging in the vis-visa, with r the radius of your initial orbit:

3) Finally, just subtract these two speeds to determine the required delta-v for the maneuver.

You can then repeat the analysis to calculate the delta-v for circularization once you reach the apoapsis of the transfer orbit.

Edited September 27, 2013 by Meithan

[goldenpeach]

Thank you very much for the answer and the exemple!

PS:because the reputation systeme don't work at the time of writing,I say in thie post that I give you a reputation point,for the clear answer and the usefu exemple!