Celestia Forums

How do i find geosynch orbit for an imaginary planet?
The question is: i have a planet with:
Radius 4935.8

... and want to have a satellite in a proper geostationary orbit around it. How do i find the semimajoraxis for the satellite?

-rthorvald

The radius is irrelevant: you need to know the rotation period (P) and the mass (M).
Then the required semimajor axis (a) is given by:

a^3 = G*M*P^2/(4*pi^2)

where all variables are in SI units and G = 6.67E-11.

Grant

rthorvald,

I don't know if this link that uses the planet Earth as the example will also help you ?

http://www.satcom.co.uk/print.asp?article=11

granthutchison wrote:you need to know the rotation period (P) and the mass (M).
Then the required semimajor axis (a) is given by:
a^3 = G*M*P^2/(4*pi^2)

Thanks. Though i can?t read that formula; regrettably, i haven?t learned the language

I can read and use it if you tell me what the symbol ^ means... (Sorry for stupid questions).

I got this off stargen.
The mass is 2.7E+24Kg
Rotationperiod (lenght of day) is 23.10 hours


-rthorvald

rthorvald wrote:I can read and use it if you tell me what the symbol ^ means... (Sorry for stupid questions).

It means "to the power" (but you could type it into a spreadsheet and get the answer even if you didn't know what it meant).
So:
a cubed = 6.67E-11*2.7E+24*(23.10*3600)*(23.10*3600)/(4*pi*pi)

a cubed = 3.155E+22m

a ~ 31600km

You can get the same result more easily if you use Earth-units: the rotation period is 0.965 Earth rotation periods; the mass is 0.452 Earth masses. So the synchronous radius for your planet (in multiples of Earth's synchronous radius) is:

a cubed = 0.965*0.965*0.452

a cubed = 0.421

a = 0.749

Since Earth's synchronous radius is 42164km, a = 42164*0.749 ~ 31600km.
Same result, different route.

Grant

Thank you for the help.
One of the very nice things about this forum - one actually get good answers to dumb questions.

-rthorvald
(which just learned that the ^sign is the same as a "2" superscript)

rthorvald wrote:(which just learned that the ^sign is the same as a "2" superscript) :-)

Not quite!
"^2" is the same as a 2 superscript (="squared"). But "^3" is the same as a 3 superscript (="cubed"), "^4" is a 4 superscript (= "to the power four"), and so on.

Grant

The radius is irrelevant: you need to know the rotation period (P) and the mass (M).

Well, since Celestia planets don't have mass, how do I create a sinchronous orbit? I tried using the formula, but the math just didn't work, specially because my fake planet lacks a precise mass number.
I'm not trying to be precise or anything, so I thought: wouldn't it work like a big disk does? If the satelite has an orbital period equal to the rotation of the planet, wouldn't it make it circle around the same point?
I'm just asking coz I spent this whole afternoon over a papersheet covered with 11 digit numbers and a lot of mistakes, and yet it does not work.
thanks anyway

Tanketai, you'll have to make up the mass for your imaginary planet...

Typical density values for planets in our solar system are about 5000 kg/m?? for rocky planets, 1300 kg/m?? for gas giants. You then use the formula:

M = (4/3)?€r???

Tanketai wrote: If the satelite has an orbital period equal to the rotation of the planet, wouldn't it make it circle around the same point?

Yes, it will. The RotationPeriod of the planet should be equal to the Period of the satellite.

But the RotationPeriod of both planets and satellites are noted in hours, while the Period of Planets are noted in years, and the Period of Satellites are noted in DAYS.

So, to set the satellite in geosynch, you will have convert the planet??s RotationPeriod (hours) into days for the satellite Period.

-rthorvald

the Period of Satellites are noted in DAYS.

Now it made sense. thanks, man, I got it right now.

(Da primeira vez eu tinha duas p??ginas de ra?­zes c??bicas, agora eu fiz meia conta de Regra de tr??s e deu certo)

There's a file I think it's called "BCelestia" that shows the information of mass, density and other informations. I think you can find this file in Developer Forum and in a topic I think it's called "...that reload files..."