Comm Sat Minimum Orbits

[WanderingKid]

EDIT: THIS MATH IS WRONG.  I don't know what's inaccurate in my math, but it's outright wrong.  I can't even get 500km satellites to work in a triangle and talk to each other.  I'll work on it when I get some time but if someone beats on this and figures out where I made the mistake, please let me know.

 

So I spent a bit trying to get myself figured out on what is the minimum altitude for a triangular comm sat system on Kerbin and sat down with all the math I needed.  Attempting to do that I realized I needed a picture.  While I was at it, I figured I'd make it pretty so I could share it.

A LKO Comm Sat network needs to roll at a minimum of 281 km orbital height.  Punch this up to 350k and you should be golden.  If you're not concerned with atmospheric distortion, anything above 200km will work.

The outer network (assuming MG-5s), to stay in comms with each other, can fly at most 3,799 km orbital height with 1 MG-5, 7,598 km with dual MG-5's.  This isn't to say they can't reach Kerbin with that giant ground based DSN, but to be able to relay to each other.

Hope this helps.

Edit: Almost forgot to add the actual final equation if you need it for another body.  Rp is the Radius of the Planet you're orbiting, Ra is the Radius of the planet + atmosphere (Ie: Kerbin is 600km radius, + 70km of atmo, so Rp = 600 and Ra = 670), Rs is the satellite's final orbital height.  Can't get the radical sign to show up so SqRt(3) is the square root of 3.

Rs = SqRt( ( (Ra * SqRt(3)) ^2 * SqRt(3)) /3 ) - Rp

For Max Network intercommunication, the equation is (Max Comm Distance = Mc)

Rs = SqRt( ( Mc^2 * SqRt(3)) /3) - Rp

Edited November 2, 2016 by WanderingKid
The math is bad, don't know why. Yet.

[OrbitalBuzzsaw]

Cool. I just chuck 'em in a 300k orbit to start, and adjust as nessecary

[EpicSpaceTroll139]

In my experience the signals can go through the atmosphere so I think you can take that out of the equation.

[COL.R.Neville]

2 sats at 2468750 with a lan of 270 and 90. pretty much covers everything. 

[paul23]

Uhhh Isn't kerbin radius 600 km? That's at least what the [url=http://wiki.kerbalspaceprogram.com/wiki/Kerbin]wiki[/url] states.

[Superfluous J]

3 minutes ago, paul23 said:

Uhhh Isn't kerbin radius 600 km? That's at least what the [url=http://wiki.kerbalspaceprogram.com/wiki/Kerbin]wiki[/url] states.

This is correct. Though you can keep the chart and just change the numbers. I do like the chart.

Although, in my experience satellite wandering will quickly cause one of the three satellite links to fail. That's not a huge deal, as the signal can take the long way around, but I find it's better to make the orbits a bit higher to account for drift and placement errors.

[WanderingKid]

5 hours ago, paul23 said:

Uhhh Isn't kerbin radius 600 km? That's at least what the [url=http://wiki.kerbalspaceprogram.com/wiki/Kerbin]wiki[/url] states.

Grrr, Yes, yes it is...  I misread it as diameter for some blinking reason.

So, edited first post.  Let's try that AGAIN!  (Thanks for catching it!)

[DrLicor]

2 hours ago, WanderingKid said:

Grrr, Yes, yes it is...  I misread it as diameter for some blinking reason.

So, edited first post.  Let's try that AGAIN!  (Thanks for catching it!)

Please correct me if I'm wrong, but I might have read something about they changed it to the real 10% of earth radius, so 637km. Anyway, great calculation. Very helpfull for when you're using RemoteTech, when you have to deal with signal delay.