Calculating geostationary orbits

[Sokar408]

http://wiki.kerbalspaceprogram.com/wiki/Geosynchronous_Orbit_(Math)

Here it is explained how to do that. However I can't seem to figure the gravitational constant out, as I can't find, particularly then; m3/(kg*s2) part. I can't figure out what the s2 part is, or where to find it, anyone care to point out the obvious for me?

And yes I know I can find the answers on the wiki for every planet, I'm just the sorta of hopeless person who likes to do manual labor xD

Edited November 14, 2013 by Sokar408

[FenrirWolf]

I'm not sure I understand what the trouble is. The gravitational constant is just that: a constant number that you shouldn't have to worry about "finding."

[andrewas]

The m3/(kg*s2) part is the units of the gravitational constant. Length cubed over mass times time squared. So just plug 6.67384*10^-11 into the formula.

[Jason Patterson]

Those are the units of that particular constant. meters cubed per (kilogram second squared). It's not a variable, it's just units, in just the same way that light goes 300M m/s <-- meters per second

[Sokar408]

The m3/(kg*s2) part is the units of the gravitational constant. Length cubed over mass times time squared. So just plug 6.67384*10^-11 into the formula.

I normally consider myself pretty decent at math, and maybe its because I'm trying to deal with it in English, but what the hell is time then?

[Jason Patterson]

t is the period of the orbit. In this case, the length of the day in seconds. Sometimes a capital T is used for period.

ETA:

To be clear, you don't put ANYTHING in for G other than 6.67x10-11 when you do the math. Units are just units.

[Sokar408]

So in order to use the formular:

G = 6,68384*10^(1/-11) = 5,421468692 (Constant, no matter for which planet)

M1 = 5,2915793*10^22 = 5,29158E+22 (for Kerbin)

t = 24*60*60 = 86400 (for Kerbin)

Rp = 600000 (for Kerbin)

With these numbers, a = 37.854.407.546

That number does not look correct by any stretch of the imagination. Also what unit is "a" listened in? Meters? Why are these things not clearly labeled I wonder

[purpletarget]

t = 24*60*60 = 86400 (for Kerbin)

Kerbin's day is only 6 hours long.

Units in KSP are metric...so yes, you'll want to use meters

[Sokar408]

Kerbin's day is only 6 hours long.

Units in KSP are metric...so yes, you'll want to use meters

t modified to: 6*60*60 = 21600

a is now = 15,022,169,700

Now the according to wiki a should be = 2,868,750

So there is still something going wrong. Here is the equation as I have plugged it into excel:

=(((C4*D4*E4^2)/(4*(PI()^2)))^(1/3))-F4

C4 = G

D4 = M1

E4 = t

F4 = Rp

Anyone see my mistake?

[Jason Patterson]

So in order to use the formular:

G = 6,68384*10^(1/-11) = 5,421468692 (Constant, no matter for which planet)

M1 = 5,2915793*10^22 = 5,29158E+22 (for Kerbin)

t = 24*60*60 = 86400 (for Kerbin)

Rp = 600000 (for Kerbin)

With these numbers, a = 37.854.407.546

That number does not look correct by any stretch of the imagination. Also what unit is "a" listened in? Meters? Why are these things not clearly labeled I wonder

It's not, because your value for G is wrong, but you have the right idea of how to use it.

6.67x10^-11 = 0.0000000000667 (0.---ten zeroes-----667)

[Sokar408]

It's not, because your value for G is wrong, but you have the right idea of how to use it.

6.67x10^-11 = 0.0000000000667 (0.---ten zeroes-----667)

Oh wauw I have no idea what I tried to take the minus elenth root there. Now I'm getting

2,870,454.65 meters

Which isn't exactly what is listen on the wiki, but its only a 2 km fall off. Is the wiki wrong or can I do more to get it more accurate?

Also, is there anyway to accurated calculate the time of a day on a planetary body?

EDIT: Nevermind about the day calculation, a bit of thinking solved that one (circumference divided by rotational speed)

Edited November 14, 2013 by Sokar408

[Jason Patterson]

The difference is likely due to rounding. If you used my value for G it would probably explain all of the difference away (it's only 1 part in 1000, after all.)

The best that you can do is use the most precise values you can find and go with what you calculate. No synchronous orbit you choose is going to wind up working perfectly. Even real satellites have to use station keeping rockets to stay in place as a function of time. Your 2km difference will correspond to a few seconds of drifting each day for Kerbin, which may or may not be acceptable to you.

[Sokar408]

The difference is likely due to rounding. If you used my value for G it would probably explain all of the difference away (it's only 1 part in 1000, after all.)

The best that you can do is use the most precise values you can find and go with what you calculate. No synchronous orbit you choose is going to wind up working perfectly. Even real satellites have to use station keeping rockets to stay in place as a function of time. Your 2km difference will correspond to a few seconds of drifting each day for Kerbin, which may or may not be acceptable to you.

Well the thing is, my results is using all the more accurate data I could find (on the KSP wiki). The G that I'm using is calculated from the exact mass listened on that wiki.

Yours: 6.67x10^-11 = 0.0000000000667

Mine: 6,68384x10^-11 = 0.0000000000668384

So which is more accurate?

EDIT: Nevermind, again it is me making a typing mistake. Its 6,67384 and not 6,68384

Anyway thank you very much for your help man