Orbit calculator in Real Solar System

[DrLicor]

Hey guys,

 

I don't know if this was discussed earlyer, but I found a way to calculate orbits in real solar system.

For me it was a real pain in the butt to find premade calculation for orbit.

You can easily find the geostationary/geosychronous orbit of earth, but it get's a bit tricky for the rest of the planets.

So I watched some YouTube videos and came to the conclusion that is't pretty simple.

You can basically do this with every planet you want, even in the stock solar system.

 

The only data you need for the formule are:

- The mass of the planet in Kilograms. We call it M^e

- The orbital time in seconds.     We call it T

- The radius of the planet.     We call it r

- Gravital Constant, this is always:

• for KSP 1.1.3:      6,67*10^-11
• for KSP 1.2:         6,67408*10^-11

If you miss one, you can solve it, in my case it was the radius.

The formula goes as follows:

 

Now you have the radius cube from the middle of your craft(doesn't effect the calculation) to the middle of the earth.

To get the actual radius, you need to cube root your outcome, goes as follows:

 

If you fill this formula in, you'll get the altitude you want.

 

I have set this up in excel for myself.

You can just fill your data in and you have your answer, very simple:

Earth's mass is 5,972*10²⁴ kg

Radius is 6371km

Orbital time is 60(seconds)*60(minutes)*24(hours)=86400 seconds

 

For the ones who want it in excel like me, put this in: =((((G)*(M^e)*((T)^2)/(4*π()^2))^(1/3))-r.

((([G]*[M^e]*([T]^2))/(4*π^2))^(1/3))-[r]. .

I will put the excel file in the comments, if someone wants it.

 

Sorry for my bad English

 

Greetings,

DrLicor

Edited October 24, 2016 by DrLicor

[Snark]

Great general tips for any planetary body in KSP, whether it's stock, RSS, or something else. 

Moving to Tutorials.

[DrLicor]

KSP 1.2 comes with a new input for G:

* Now always use g0 = 9.80665 and G (big G) = 6.67408e-11 for gravitational constants.

 It doesn't change a lot, but it's just for optimizing your calculation. 

Edited October 12, 2016 by DrLicor

[John Cochran]

Actually you don't need the value of either G or M. What you really want is the product of G and M. Why am I making that distinction? Because in real life, we know the product far more accurately than we know either G or M. For instance, Earth's standard gravitational parameter is 398600.4418 plus or minus 0.0008 km^2/s^2 which is accurate to about 1 part in 500000000. But we only know G to within about 1 part in 7000. And because of the uncertainty in knowing G, we also only know the mass of the earth to within 1 part in 7000. 

[DrLicor]

4 hours ago, John Cochran said:

Actually you don't need the value of either G or M. What you really want is the product of G and M. Why am I making that distinction? Because in real life, we know the product far more accurately than we know either G or M. For instance, Earth's standard gravitational parameter is 398600.4418 plus or minus 0.0008 km^2/s^2 which is accurate to about 1 part in 500000000. But we only know G to within about 1 part in 7000. And because of the uncertainty in knowing G, we also only know the mass of the earth to within 1 part in 7000. 

True, but in KSP G is the value as stated and when you fill everything into excel or some calculation, the answer will be 100% accurate to KSP, but indeed, in real life you want better parameters. Thanks for your info

[Serpens Solidus]

You forgot to square pi in the pics.

[DrLicor]

On 14-10-2016 at 4:38 PM, Serpens Solidus said:

You forgot to square pi in the pics.

Pi doesn't need to be squared, afaik. But I do see a mistake in the excel formula, needs to be this: 

((([G]*[M^e]*([T]^2))/(4*π^2))^(1/3))-[r]. .

 

Edited October 24, 2016 by DrLicor

[Serpens Solidus]

I does need to be squared
https://en.wikipedia.org/wiki/Orbital_period#Small_body_orbiting_a_central_body

[DrLicor]

46 minutes ago, Serpens Solidus said:

I does need to be squared
https://en.wikipedia.org/wiki/Orbital_period#Small_body_orbiting_a_central_body

I snap, don't know why I haven't see that. Thanks!