..Calculate a semi-synchronous orbit?

[rosenkranz]

Title says it all. For GPS sat nets a semi-synchronous orbit is recomended. How does one calculate that?

Specifically for Laythe

[UmbralRaptor]

This question is ambiguous -- are you looking for semi-major axis? Period? Something else? Assuming you want semi-major axis, try Kepler's 3rd law.

Specifically, the form T² == (µ/4À²)*a³ (4À²/µ)*a³

T -- period of the orbit (findable in the KSP wiki)

μ -- gravitational parameter of the parent body (also in the KSP wiki)

a -- semi-major axis of the orbit.

Solving for a:

a == ((µT²)/(4À²))^(1/3)

edit: I got the constant wrong in setting up the equation.

Edited April 24, 2013 by UmbralRaptor
formula error.

[rosenkranz]

My bad, i didn't mean to be unclear. I was looking to set up a GPS net around Laythe. So an orbit with half the period.

I did find a kepler calc online and was trying to test it against known values for Kerbin but couldn't get it to work out. I'll try out your link and see how that works. Thanks.

[K^2]

Raptor gave you correct formulae. Just keep in mind that for circular orbit r = a, so to get altitude just subtract planet's radius. (Look up equatorial radius on the KSP wiki)

[rosenkranz]

I'm trying to work that equation but the variable 'n' is not clear to me. What does that represent? I had thought maybe it was PI but that doesn't yield a good baseline for kerbin.

[K^2]

That's Pi. 3.1415... Yeah, it looks weird with standard fonts on these (and most other) forums.

If you didn't get good values for Kerbin, you probably made an algebraic mistake or used the wrong units somewhere. Check your work.

Edit: Oh, never mind. I should have looked at Raptor's post more carefully. He must have cross-multiplied wrong. a = ((µT²)/(4À²))^(1/3)

Try that.

Edited April 24, 2013 by K^2

[rosenkranz]

Yeah, that's what I figured out. in excel it looks like =((Gravitation*Time^2)/(4*PI()^2))^(1/3) which after subtracting kerbin's radius of 600,000m gets me a correct number. Now to figure out laythe. I may not be able to fit a semi-synchronous orbit in laythes SOI. I hadn't realized that laythes rotation was 14hr.

[rosenkranz]

Yes it can Now the real trick is I'll have 3 sat carriers coming into laythe at different times and likely different inclinations. Changing the inclinations I know how to do. However at that point spacing in orbit will be random. Do you know a technique to space them evenly?

Eventually the goal is to get the carriers separated 60 degrees apart and then incline each to 55 deg. Then it's time to deploy individual sats and space them out along those three orbits. Advise is defiantly welcome

[K^2]

You'll kind of have to do this by eye. There isn't a terribly precise method. But the basic principle is easy enough. Higher orbits lag behind lower orbits. So if your satellite is more than 60° ahead of the following one, raise it to a higher orbit, wait until it's at the right angle, and lower it again. If it's too close, lower it, then raise it back. Just keep in mind that raising/lowering will take up an extra half-revolution between burns. So you want to make sure that the difference is small, and that means you might have to wait for quite a few turns in between. By the way, it might be easier to do inclination change first.

P.S. Practice on Kerbin. You really don't want to put in all the effort of taking sats to Laythe only to find out that you don't have the fuel for all the corrections.

[UmbralRaptor]

Edit: Oh, never mind. I should have looked at Raptor's post more carefully. He must have cross-multiplied wrong. a = ((µT²)/(4À²))^(1/3)

More of misremembering the equation, than cross-multiplying wrong. I had 4À²/µ at the start when I should have had µ/4À².

[K^2]

Start with Virial theorem. Can't go wrong with that one. For circular orbit it tells you that v²/2 = µ/r. That's how I always check myself with these.

[rosenkranz]

Fuel shouldn't be a problem. The transfer stage has 4800dv, so it should get into laythe orbit with plenty to spare. Each sat also has 3000dv on there own so yeah, fuel shouldn't be an issue.

Once the fleet is headed out to Laythe (about 20 ships going) I'll launch some carriers into LKO randomly and practice the orbital spacing.

[TaranisElsu]

You will need to watch not only the spacing within an orbit, but also how the orbits are separated. For that, pay attention to the Longitude of the Ascending node -- both MechJeb and Flight Engineer give that information. Ref: http://en.wikipedia.org/wiki/Longitude_of_the_ascending_node

I'm not sure how to change the Longitude of the Ascending node without flattening out your orbit first, then burning normal at the appropriate longitude. I've been looking for information about that...

Edited April 26, 2013 by TaranisElsu
typo

[rosenkranz]

Well, the initial insertion orbit wants to be a 0 deg orbit. Once all three carriers are in this orbit, spacing them 60 degrees apart is next.

After than each carrier in turn, inclines it's orbit to 55 degrees. Each carrier has three probes. So each one deploys and spaces itself out 60.

Then each carrier (now empty) waits for an opportunity to land at the base on the surface and burns accordingly.