evenly spacing probes

[jwenting]

Been trying to build a constellation of geosynchronous (kerbosynchronous?) probes, but having a hard time spacing them nicely. They're all in the same orbit, but can't seem to get them at proper intervals of 60 degrees. With a lot of fiddling, repositioning, etc. etc. I've got them spaces between 40 and 80 degrees apart, but that's a pretty big spread, would love to get them closer.

How do the experts do it? Any trick?

[K^2]

Yes. The "trick" is called the Kepler's 3rd Law. T² = ka³ for some constant k, where T is the period of time required to complete the orbit and a is semi-major axis. You can compute the later by taking planet's radius + (periapsis + apoapsis)/2. For the synchronous orbit, T = sidereal day, which is 6 hours for Kerbin. So say you have second satellite too close behind the first one. They both complete a full rotation in 6 hours. That's 360° around Kerbin. In 6 hours and 1 minute the first satellite will move 361°. So if you make the second satellite's period 6 hours and 1 minute, you will increase the separation between them by 1° for one revolution. If you keep your periapsis at synchronous altitude of 2,868.7 km and raise apoapsis to 2,881.6 km, the period will be exactly 1 minute longer. Feel free to check that with the Kepler's 3rd above. Now, if you only need to move by 1°, you raise apoapsis to that altitude, wait for 1 full revolution, and bring apoapsis back down to circularize back at synchronous. If you need to move 5°, you can wait for five revolutions. Or you can re-compute the new altitude to go 5° in one turn.

Naturally, you can also catch up by lowering the periapsis. In either case, a few maneuvers like that, and you should have all your sats aligned. Shouldn't take much delta-V, either.

[jwenting]

was hoping to have an easy way to eyeball the insertion burns from LKO to GEO so they end up more or less in the right spot

[K^2]

Transfer orbit follows Kepler's 3rd same as any other. Compute the period of transfer orbit. Half of that is how long it will take your sat to reach synchronous orbit. Satellites in sync will shift forward 60° for every hour of transfer.

[GJames]

I found this out about a week back and posted it on another thread, so I've just pasted it here to save people from going and looking it up. Does sound like this could help you out a bit though.

I put a nuclear-powered probe carrier into orbit that was carrying five ion-powered probes. I raised the carrier's periapsis to geosynchronous altitude (2868.4km) and then moved it's apoapsis to 1225km. With a bit of tweaking this gave me an orbit with an orbital period of 4 hours. Obviously you'll want to put a few more probes into space than I have.

Then I released a probe at apoapsis and put it into a rough geostationary orbit with it's ion engine. I repeated this twice more, creating a network of three satellites each 120 degrees apart. I fine tuned the orbits to make sure that they stayed in roughly the same place for the next few months of in-game time. To get 6 of them on one orbit, just get the carrier to a orbit with a period of five hours instead of four.

The last equatorial probe leaving the carrier. The other two are going to be put onto a geosynchronus polar orbit using the same method, but where the carrier has an orbital period of three hours so they are placed 180 degrees apart. Just try and time it so your carrier's apoapsis isn't in the shadow of Kerbin, or ion drives will be useless. Best use a tiny engine instead, some of the circularization burns took 15 minutes...

I ended up with a network of three equatorial probes spaced at between 118-122 degrees apart, and two polar probes with a gap of 188 degrees due to sloppy burning and course correction.

EDIT: I used this KSP Calculator to determine how I could get an orbit with a period of exactly four hours: https://code.google.com/p/ksp-calculator/ It's fairly simple to use, but you need to use trial and error for getting the period right.

Edited July 7, 2013 by GJames

[SRV Ron]

Launch the first probe noting how you have flown it into place but don't place it geosynchronous orbit, place it in low orbit. Note the time of day when you raise it to geosynchronous orbit. Launch the next probe to the same low orbit. This time, do the insertion four hours later from the time you did the previous insertion. Do that for the next four launches. Fine tune when all are in place.

Note, due to rounding errors, it will be impossible to hold geosynchronous orbit for long periods of time.

[Kimberly]

If you use Flight Engineer, you don't need to use any fancy math:

Build one carrier that holds all the satellites you want to deploy into a particular orbit. Make sure it has plenty of fuel. Achieve your desired orbit, release satellite 1. Then, say you want to space the rest out 90 degrees, i.e. a quarter of an orbit: burn retrograde until your orbital period (as shown by the Flight Engineer) is 3/4ths of the orbital period of your desired orbit. (So if you want the satellites in geosychronous orbit, which means an orbital period of 6 hours, you burn retrograde until your orbital period is 6 * 0.75 = 4.5 hours.) Time-warp until you complete a full orbit, and then burn prograde again until you're in the proper orbit. Release satellite 2, which should be a quarter of an orbit away from the previous satellite. Rinse and repeat.

For fuel savings and greater accuracy, you can make smaller retrograde burns and complete more orbits. For example, if you wanted to space the probes out 90 degrees as in the previous example, you can burn retrograde until your orbital period is 7/8ths, then wait two full orbits before burning prograde again.

The advantage of this method is that the satellites don't need any propulsion mechanism of their own, saving weight. If you can tell your orbital period using Flight Engineer, you don't need to do any math besides basic fractions. The disadvantage is that it takes more time.

Like SRV Ron said, though, rounding errors will tend to make every satellite constellation drift apart eventually. It's usually not possible to reliably get a margin of error for your orbital period of less than 0.3 seconds. You can use HyperEdit to put your satellites into a truly perfect orbit they'll never drift out of (so long as you don't select the satellites, their orbits won't change due to rounding), if you don't mind cheating.

[purpletarget]

You can see the not so fancy math on how to calculate the time required for transfer here, late in the video, I think it's the last 10 minutes or so.

You also don't need mods. The maneuver nodes will allow you all the precision you need, and the time calculations. Once your first Sat is up, you can use it as the target for the next satellite. When you push the Ap of the new Sat up to the KSO altitude the intercept markers will show up. Shift your node around on the orbit to move the intercept, but unlike an RV, instead of matching the markers as close as possible, make them so they're 90 or 120 degrees or whatever you want, away from your original KSOSAT. Once you get there, circularize as close as you can.

Wash rinse repeat with the other sats as required.

[TMC_Sherpa]

It is probably poor form for me to dump a post here before I do the introduction thang but I'm a rebel like that sometimes.

Resonance orbits are beautiful things for putting multiple objects in sync and if you are lazy, like I am, doing the math(s) over and over gets old really fast. I will make my own thread but for right now I'll just leave this here http://www.ksp.interrutt.com. Pick a planet, the orbit you want and the resonance that will do the trick (3 sats try 5/6, 4 sats 7/8) and click the button. Send them up on a carrier like GJames suggested and release (and circularize) them at Apoapsis.

I'll make the page pretty and do a writeup later but spacing things in...er...space is a common question.

Good luck

Sherpa