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Important equations about orbital mechanics and rockets


Rjhere
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So I want to learn, I want to learn different equations to calculate important things about orbits and rockets etc...

I already know three equations:

DV = Isp * g0 * In (m0 / m1)

Twr = F (rocket) / (m * g0)

and velocity of a circular orbit:

SQRRoot(SGP / r (radius of earth + height of orbit))

These are the equations I know beforehand, do I need to know more? I would know all this if I had gone into astrophysics, but I have already chosen my path (Automatition, electrical engineer... bachelor later maybe...?), although I have been interested in these things all my life. Maybe I'll be able to take a major in astrophysics afterall... Don't know, as the Norwegian school system sucks...

Anyway, write down equations you think I should know!!!

Thanks in advance!

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If we are looking at very basic orbital motion, by analogy with circular orbit, there are formulae for periapsis and apoapss velocities of elliptic orbit. To get the notation consistent, you know:

vc = Sqrt(GM/rc)

Where vc is velocity of circular orbit, GM is gravitational parameter (Mass times gravitational constant), and rc is radius of circular orbit, which is planet's orbit + orbit's height. So lets say that instead you have an orbit with two different heights, yielding ra as the apoapsis distance and rp for periapsis. Just like circular orbit, that's planet's radius + corresponding height. In that case, the two velocities are given by the following.

va = Sqrt(rp/ra) * Sqrt(GM/a)

vp = Sqrt(ra/rp) * Sqrt(GM/a)

Where a is the semimajor axis, a = (ra + rp)/2

Using these, you should be able to compute Hohmann transfer, which is elliptical orbit connecting two other orbits (often circular ones). So you can do the math, for example, on how much fuel it will take to transfer from Kerbin's orbit to Duna's. These tend to work pretty close in the real world too. They aren't exactly right, unfortunately, but any reasonable approximation can be made.

One more useful thing to know is how much delta-V you need to go from surface to a low orbit. Since potential energy change is usually minimal, as a rough estimate, you can simply use velocity of circular orbit when there is no atmosphere. You'll need just a touch more to fight gravity, so have some reserves. If, however, there is atmosphere, you need one more formula to estimate extra velocity required to fight through it. This assumes that thrust of your engines is about 2x the weight of your ship. This is what you need to ascent at terminal velocity and what you should be aiming for. The extra delta-V is given by this formula.

v = 4gH / vt.

Here, g is surface gravity, H is scale height, and vt is the terminal velocity at whatever altitude you are taking off from. For planets in KSP, all 3 of these are available for every planet in the system. For real world applications, you have to be able to estimate vt, which will be very different for different rockets.

This last one is for very rough estimates. So keep it in mind if you are going to use it in KSP to estimate fuel needed on a lander.

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