Calculating Orbits for Spacing Satellite Constellations

[mikemcdonald83]

So I have used RemoteTech for a long time, but now that I'm trying out 1.2 I've decided to learn how to mathematically align my communication satellite constellations. Basically, if anyone can tell me if this is the "standard/not overly complicated" way of doing this, I'd really appreciate it. I tried searching the forums, and I apologize if I've missed other threads with this same topic. Also, this is my first topic, so sorry if it's offensive in any way.

My plan was to launch 3 ComSats into stationary orbits around Kerbin. 360 degrees / 3 satellites gives me a phase angle (angle between satellites) of 120 degrees. I am using Kerbal Engineer to see my phase angles and orbit periods. I launched my ComSat1 into a Keosynchronous orbit at 2863.3km with 0 inclination. Good to go. I launch my ComSat2 into the same orbit, but its phase angle is 220 degrees, where an optimal phase angle would be either 240 degrees or 120 degrees. 240 degrees was closer, so I decided to shoot for that.

Since I wanted to change the phase angle precisely without any guesswork, my goal was to make only 2 burns with ComSat2 to allow ComSat1 to catch up a bit (20 degrees.) Since 20 degrees is 5.55% of 360 degrees, I figured that if I made a single orbit 5.55% longer, the trailing satellite would catch up. 5.55% of 6 hours is ~18m53s. I burned ComSat2 until its period was 6h18m53s. I then completed exactly one orbit, and burned again to lower the Apoapsis back to 2863.3km with a period of ~6hrs.

To my great surprise, it actually worked. Whenever something goes well in this game I assume it was an accident, coincidence or over-complicated. Can someone please tell me I'm a good boy, or explain how to do it better or simpler? I really want to understand orbital mechanics better, and that's why I'm interested.

TIA

[DrLicor]

Hey welcome to the forums  , first you have to know that a day on kerbal isn't exact 6 hours. but anyway, the orbital time of the 3 sats have to be exact the same, thats whats the most important. The way you calculated your solution is indeed a right way to do it. I prefer to launch all the sats at once, get the last stage of my rocket in a orbit with an Ap of 2863.3km and an orbital time of 4 hours and launch every orbit 1 sat. This way they al have the same orbit, and the perfect angle. 

For calculating orbits and time I recently made a calculator, maybe you can understand the math behind it afterall:

Spoiler

 

 

[mikemcdonald83]

Thanks a lot for the info @DrLicor. That single launch idea is really cool. Plus it'll add the extra challenge of packing a whole constellation on my early-career rockets. I also copied your spreadsheet into docs. So I can use this to find the altitude for a given period. But, couldn't you also solve for T and get the period for a given altitude? It's been a long time since I've tried to factor anything, but this looks like a fun excuse.

[DrLicor]

You're welcome :), yep thats also possible. As long as you have all factors except for one, you can solve it. 

 

[DrLicor]

Since my math instinct got triggered I had to solve it haha:

The formula for time will be:

just get the root of t2 and you got your answer 

 

[Rodhern]

@mikemcdonald83 Yup, that is the way I would have done it too.

Just one tiny detail, I couldn't help notice that you approximated 20/360 * (6h*60min/h) = 20min by ~18m53s. I know it doesn't matter. It made me smile though.

[mikemcdonald83]

5 hours ago, Rodhern said:

@mikemcdonald83 Yup, that is the way I would have done it too.

Just one tiny detail, I couldn't help notice that you approximated 20/360 * (6h*60min/h) = 20min by ~18m53s. I know it doesn't matter. It made me smile though.

Oh yeah. haha. I think I actually used the 5h59m17s or thereabouts from the KER readout. I was at a 2863.3km circular orbit. So whatever that period is. Which now I can figure out thanks to @DrLicor.

[ansaman]

3 minutes ago, mikemcdonald83 said:

Oh yeah. haha. I think I actually used the 5h59m17s or thereabouts from the KER readout.

Unless I am mistaken (and I would love to be corrected) The effective day on Kerbin for a non-wandering synchronous satellite has been quoted as 5h 59m 9.4s. That is the best figure I could find.

[FancyMouse]

Yup - solar day and sidereal day difference

And this is a fantastic tool exactly for what OP wants (specifically multiple launch view) but with a better visual (and congratulations to OP finding the same solution independently!)

Edited September 29, 2016 by FancyMouse

[Cairol]

My technique for setting up a well distributed sat network is this:
If I want to deploy 3 satellites around a planet, I look up the orbital period of the desired orbit around that planet.
http://ryohpops.github.io/kspRemoteTechPlanner/

Let's say it's 3h for a 1500 km orbit. (don't mind my numbers here. I don't have realistic ones in front of me).
So I lauch a single vessel which carries ALL 3 satellites.
Then I enter my desired orbit, but with an orbital period of 1/3  (or 2/3) of the desired orbital period for my sats by establishing an excentric orbit,
with the AP at my desired distance and the PE so it results in the 1/3 period.
Then when I approach my AP, I deploy my first sat and circularize it's orbit at the AP.
Then I wait until I again approach my AP and deploy my second sat and circularize it's orbit, which has now exactly 120° phase angle to the first one,
as I have effectively spent 1/3 of the target orbital period going around the planet.
And on the 3rd pass of my AP, I deploy the 3rd sat and circularize it's orbit. So all 3 are now in pretty much perfect alignment, phase-angle-wise.
Last step is, to finetune the sats orbital period to the millisecond, so they won't go out of sync for ages.
The site above actually has a graph for this "Multiple Launch" approach, which provides the 1/3 period numbers and corresponding AP/PE.
Just in case you don't want to calculate them yourself.

Doing the same with multiple separate launches will be much more of a problem, when you want evenly distributed sats.

[Van Disaster]

Is there a reason for launching synchronous sats now? they weren't a good idea in RT unless you wanted one as a giant antenna for a ground station. And yeah, the orbit period itself doesn't matter as long as all sats on that orbit have the same period. If you're launching from a resonant orbit it also doesn't matter when you release them - you can drop the whole lot in one go at any point - what matters is when you circularize the sat.

[DrLicor]

@Van Disaster, indeed, despite it looks cool that they stay in the same orbit, it doesn't have a real advantage. Although, higher orbits can result in better precision, 1 sec delay on a 6hour orbit has a much smaller effect in comparison with a 2hour orbit. Also a higher orbit has better coverage, so other sats can have a higher altitude. 

Nevertheless, it doesn't have to be a geosychronous or geostationary orbit. I think people like it because it's special, just to see a sat hovering over the same spot for years. 

 

[Van Disaster]

4 hours ago, DrLicor said:

@Van Disaster, indeed, despite it looks cool that they stay in the same orbit, it doesn't have a real advantage. Although, higher orbits can result in better precision, 1 sec delay on a 6hour orbit has a much smaller effect in comparison with a 2hour orbit. Also a higher orbit has better coverage, so other sats can have a higher altitude.

The RT omnis wouldn't reach synchronous/stationary sats, so you needed relays in lower orbits anyway. The only reason for stationary sats would be if the ground station couldn't swap satellite, which would be a very odd idea. It matters to *us* because most satellite consumers have fixed dishes, but we can assume science teams aren't quite that limited.

Trying to work out intersecting eccentric orbits drives me nuts, there must be some tool for that...

Edited September 30, 2016 by Van Disaster

[mikemcdonald83]

6 hours ago, Van Disaster said:

Is there a reason for launching synchronous sats now? they weren't a good idea in RT unless you wanted one as a giant antenna for a ground station. And yeah, the orbit period itself doesn't matter as long as all sats on that orbit have the same period. If you're launching from a resonant orbit it also doesn't matter when you release them - you can drop the whole lot in one go at any point - what matters is when you circularize the sat.

No really good reason. It's at a good distance to reach the Kerbin moons with the new early relays. Also, with the other ground stations turned off, I have it set up to where there is only one relay directly over KSC, and the others have to act as relays. Still, it's all cosmetic and for fun setting it up. Thanks for all the tips, btw, everyone.

23 hours ago, FancyMouse said:

 

Yup - solar day and sidereal day difference

And this is a fantastic tool exactly for what OP wants (specifically multiple launch view) but with a better visual (and congratulations to OP finding the same solution independently!)

Also, this tool is amazing. I really wish I had known about this when I was trying to do all the darkness time calculations manually for RT.

Edited September 30, 2016 by mikemcdonald83
add

[StevenLawyer]

I created an easy to use free Excel spreadsheet for calculating even Satellite spacing.  Enjoy!

Satellite Spacing Calculator

[MonsterBenny]

Hey  @StevenLawyer, you found an old thread dating back in september 2016. ;)

 

This are my two tools - they run in the browser.

The first one is for  satellite spacing and the second one is for moving a satellite in synchronous orbit over a designated degree of longitude.

 

[Snark]

Moving to Gameplay Questions.