Formula for spacing satellites?

[CheftonUTD]

I'm working on getting multiple satellites launched from a larger ship to be evenly spaced in their orbit.

I've worked out a method to get them spaced out nicely, but my maths isn't quite right and I end up short a satellite or two.

What I've been doing is:

Say I want 3 satellites in a 240k orbit.

I devide the 240k by 3 (for 3 satellites), giving me 80k.

I get the carrier ship into a 80k orbit (or 79k peri / 81k ap, to stop the ap/peri from moving about)

I launch a satellite every time my carrier it at its Ap, then get the satellite into its' 240k orbit.

They end up spaced perfectly but too close, eg in this situation the 3 satellites were 90* to each other with 1 more 'corner' left empty. When I followed my formula with 6 satellites I was left with 2 'empty' points.

If I want to keep doing it this way could someone fix my formula for me please?

[Faark]

You have to make sure your orbital period is 1/3rd (or other multiples for that method. 4/3 should work fine as well) of that of your target orbit. Lets imagine your target orbit would be kerbins geosynchronous orbit at 2 868.75 km. It has a period of 6h, just like kerbin. So if you drop a satellite there on the same spot every 2 hours (or 4h, aka dropping every 2/3rds) , they should align perfectly. So your carriers orbit has to pass the geosynchronous orbit while also requiring exactly 2 (or 4) hours to make a turn.

[Frederf]

Resonant orbits like Faark mentions is the way.

[rpayne88]

I typically deploy four comm sats at a time. When I do that, I drop one sat off at one orbit, place my periapse to half of my apoapse, and wait two orbits. That spaces me 90 degrees from the first sat. I don't know how you would do it with just three.

[CheftonUTD]

Ah that explains where I went wrong, thanks . Is there a way to work out orbital duration at specific orbits? Say if I calculate the circumference/radius/diameter of a potential orbit, is there a way to know what the speed or orbit time would be?

I typically deploy four comm sats at a time. When I do that, I drop one sat off at one orbit, place my periapse to half of my apoapse, and wait two orbits. That spaces me 90 degrees from the first sat. I don't know how you would do it with just three.

That sounds like a good idea, maybe I can play with the Ap/Pe ratio to adjust it for different angles of satellite spread.

[Arkalius]

The formula for orbital period is T = 2*Pi*(a^3 / (G * M))^(1/2)

G is the gravitational constant, M is the mass of the body you're orbiting, and a is the orbit's semi-major axis. The major axis of an ellipse is the line that passes through both foci of the ellipse and it's center. The semi-major axis is half that. In a circular orbit, it's just the orbital radius.

If you're going for a circular orbit, either decide the orbital period or altitude you want. The altitude (in a circular orbit) is the semi-major axis minus the radius of the planet. Then find the other value you don't have using the formula above.

Since you want to put 4 satellites equally spaced, you can divide the orbital period either by 1/4 or 3/4. Chances are you won't be able to get an orbit with the apoapsis you want that is 1/4 the period, so 3/4 works better. Taking that 3/4 period value, determine the semi major axis with the formula above (you'll have to do some algebra to solve for a). Now, you know the new semi-major axis you need for your shorter period orbit. Double it, then subtract your desired orbit radius from that value (ie your desired altitude plus the radius of the planet). Then, subtract the radius of the planet from that value, and that tells you the new periapsis you want. Get yourself into a circular orbit at that altitude. Then, expand the orbit so the apoapsis is at your final desired altitude. Release a craft every time you reach apoapsis and have it boost itself into a circular orbit. Your other craft will come around again on its own to do this again, but 90 degrees away from the first craft, because the orbital period is 3/4 the desired orbit.

Hopefully that explanation was clear enough for you.

[Scarecrow88]

There is a mod available that allows you to attach a small part to your craft that will give you the orbital period readout in real time. Think it is Engineer Redux, but someone will correct me if I'm wrong.

[Stone Blue]

There is a mod available that allows you to attach a small part to your craft that will give you the orbital period readout in real time. Think it is Engineer Redux, but someone will correct me if I'm wrong.

MechJeb also shows realtime Orbital Period...Just Engineer Redux goes one decimal point more, to tenths of seconds...lol

MechJeb shows basic Orbit and Vessel info, and Engineer Redux shows quite a bit more advanced Orbit and Vessel info, as well as adding Surface and Rendevous info.

Edited August 26, 2013 by Stone Blue