Orbital Periods/Syncronous Orbits

[StahnAileron]

Good day all.

I've been playing KSP for a bit over a month now. I started adding mods soon enough (like a week in). One of the gems I found was RemoteTech2. It adds a challenge to the game that mostly makes sense (I both lament and am grateful for the lack of directional requirements for antennas - i.e. Directional antennas don't have to be physically pointed at the target, unlike how solar panels should be facing the sun in the game.)

Anyway, beside the obvious communications challenge RM2 added, the other challenge is setting up a nice constellation of comsats. There are some of us who are kinda OCD about some things. I fall into that category a bit. I've made some of constellations to date, all eyeballed for spacing. 90 degree spacing was easy, but for my last constellation, I wanted LESS comsats in it - the minimum of 3 in KEO - so I needed 120 degree spacing. That's not as easy to eyeball.

I futzed around in KSP for a while instead of creating this new constellation. (I got horribly sidetracked by what eventually was found to be a memory leak bug in AGX...) I recently broke down and decided to create something to help me out with my constellation planning: A synchronous orbital period calculator.

It's just an Excel spreadsheet that take 2 of 3 inputs and spits out the relevant variable you're probably looking for:

- Input an orbit period and an apsis = gives you the other apsis height for the actual orbit

- Input both apses = gives you the orbital period (and Semi-major axis)

- Input just the period and you get at least the circular orbital height

The game and wiki gave me all the data required. Some browsing on Wikipedia gave me the relevant equations I needed. So now I know that a 4-hour sync orbit with KEO has an AP of 2868.75KM and a PERI of 1225.337KM. Now I can just lift one comsat to a given circular orbit and use my calculator to figure out the orbital apses I need to sync the subsequent comsats for even spacing. e.g. I lift one comsat and stick it in KEO (6 hour period). My next one is sent to circular orbit at 1225.337km. I set an "intercept/rendezvous" node with the first probe, burn, then adjust to make my APO = KEO height. I wait until the second orbital intersect and circularize. I am now 2 hours (120 degrees) ahead of the first comsat, give or take.

This post is to see if anyone else has any interest in this calculator. It's excel-only, so not in-game. (I currently have no plans to write an actual game plugin or anything.) If there is interest, I'll have some incentive to make actually complete the spreadsheet in full. I currently only have data for the Kerbin system (Kerbin, Mun, Mimas). I haven't gathered the data for other bodies yet. I also need to clean up and complete the "UI" section.

I figure if I wanted/needed something like this, there might be others who do as well. I can stick a copy of the current version on OneDrive for people to try out if they need to actually see what I'm talking about.

This little pseudo-project is also an excuse to brush up on my Excel skills.

Interest and feedback would be appreciated.

[sarbian]

I am quite sure you can find such speadsheet on the forum already. I had mine customized from one I found in a thread.

[Sigma88]

Scott manley made a video on how to put 3 satellites at 120 degrees apart

Basically you put all three in one vessel and put the vessel in an elliptical orbit around kerbin

With apoapsis at the synchronous altitude and with orbital period of 4 hr

Every time you reach apoapsis you release one satellite and circularize it's orbit

You end up with 3 satellites spaced equally

[hab136]

See also:

In-game RemoteTech Assist calculator: http://forum.kerbalspaceprogram.com/threads/95072

Visual RemoteTech Planner (web site): http://ryohpops.github.io/kspRemoteTechPlanner/

[Stone Blue]

Scott manley made a video on how to put 3 satellites at 120 degrees apart

Basically you put all three in one vessel and put the vessel in an elliptical orbit around kerbin

With apoapsis at the synchronous altitude and with orbital period of 4 hr

Every time you reach apoapsis you release one satellite and circularize it's orbit

You end up with 3 satellites spaced equally

I can't use this method, because my commsats always end up too big, and cant easily be stacked into one launch...lol

I HAVE tried it while trying to build a 24 sat GPS constellation, but couldnt get it to work then either, due to multiple launches...

[StahnAileron]

Scott manley made a video on how to put 3 satellites at 120 degrees apart

Basically you put all three in one vessel and put the vessel in an elliptical orbit around kerbin

With apoapsis at the synchronous altitude and with orbital period of 4 hr

Every time you reach apoapsis you release one satellite and circularize it's orbit

You end up with 3 satellites spaced equally

Yes, and not everyone will know what apo and peri to use right off the bat for a 4-hour spacing orbit. This calc I started is meant to figure that out for the user (for Kerbin or any other celestial body in KSP). You pick the body, enter the target altitude/apsis and the period you want; it tells you the other apsis you need to aim for. Or you can enter both Apses and it'll tell you the Period. (Just entering a period will give you the circular altitude.)

Also, what if a player wants something other than 3 satellites? Let's say 4 sats: they need to figure out the (peri)apsis for a 4.5-hour orbit. This calc will do that for him/her.

This will also help you if you're NOT or CAN'T do stationary orbits. Placing a constellation around say the Mun requires different numbers. Again, this calc will help there. You can first type I either the target Period or altitude for your constellation (for alt, just use the same value for the Apo and Peri). Using the resultant numbers plus the number of sats you want, you can figure out the parking/transition orbit for spacing the satellites around.

See also:

In-game RemoteTech Assist calculator: http://forum.kerbalspaceprogram.com/threads/95072

Visual RemoteTech Planner (web site): http://ryohpops.github.io/kspRemoteTechPlanner/

This is close to what I was looking for. It's pretty old/out-of-date though. The OTHER link, now THAT is NICE! It still doesn't tell you Orbital periods (or better yet, offset angles) for spacing. (Unless that's what the slide angle is?) I wish KSP had an Lat/Long angle overlay for planets while in map view for something like this. Still, that web planner is VERY useful, especially for some of the other stats it offers and the visualization. (I was thinking of doing a dV calc as well in the spreadsheet.)

Anyway, there are other features I intended to add if I did develop this further:

-Comparing the orbital altitude to both atmosphere alt (if applicable) and S.O.I. radius and warn if the resultant orbit crosses either one.

-dV costs from (circular) parking orbit to target (circular) orbit.

And a couple of other checks I can't recall right now...

@Stone Blue: For a multi-launch constellation (especially equatorial), you get the second (and later) satellite(s) into a lower parking orbit, preferably at the same altitude as the periapsis of the spacing orbit you need. From there, set up an intercept with the first satellite. Do the first burn. For the second burn, wait another orbit, then burn. You should now have the second correctly spaced from the first. Actual example:

Kerbin Geostationary orbit is 6 hours @ ~2,868,751 meters altitude. A 4-hour spacing orbit needs a periapsis of ~1,225,554 meters. (<<< found out using my calc, BTW ^_~) I already have one comsat in KEO.

For the second comsat, I would place it in a 1,225.554km parking orbit. I target Comsat 1 and plan an intercept maneuver to it (MechJeb is VERY useful for that).

I "intercept" Comsat 1 and wait one more full (4-hour) orbit later to circularize. Comsat 2 is now 2-hours (120 degrees) AHEAD of the first sat. The third sat does the same thing, but using Comsat 2 as the target. (You can use Comsat 1, but you'd have to wait 2 orbits...) In theory for Comsat 3 you could do a 2 hour transfer orbit... But the periapsis for a KEO-based spacing orbit is under Kerbins surface.

Now, if MechJeb had a "Match target orbit and offset" function... (Match the target's orbit and offset by some period/angle).

[dewin]

For RT2 placement in separate launches, I've found a reasonable way to adjust orbits to get appropriate spacing with MJ -- though all's you really need is a way to view orbital parameters (and phase angle to father) and a way to calculate resonant orbits.

After circularizing 3 satellites, they need to be 360/3 = 120 degrees apart. So we take one satellite, target the satellite that is "ahead" of it, and compare phase angles. Let's say it's currently 150.

150-120=30, which means we are 30 degrees behind. To fix this, we need a faster orbit. Enter resonant orbits.

If we set up a burn that gets us into a 360-30/360 resonant orbit (330/360), we will orbit 360 degrees in the time it takes our target to orbit 330. Circularize after one orbit (e.g at next Ap) and... We'll be about 120 degrees separated.

Not enough dV for that? Well, you could also do a 345/360 orbit (360-(30/2)) and circularize after 2 passes, or 350/360 after 3 and so on.

This works if you're too far ahead as well, just circularize at Pe instead.

After spacing all of your satellites properly, go back to each one and get them all to have the same semi-major axis. This translates to the same orbital period, and is far more important to reduce drift than having a perfectly circular orbit.

Edited April 30, 2015 by dewin
Make some edits now that I have a real keyboard and not a phone keyboard.

[StahnAileron]

That's sounds more dV intensive than needed. Though it is a good way to correct spacing if you decide to add more sats to a constellation. (Like adding a fourth comsat to a properly spaced 3-sat system.) Otherwise, you need more parameters than readily and easily accessible (I think). Pre-planning the orbital insertions of subsequent comsats I think is better overall rather than adjusting at the final orbit. Also less time, I think. I'd rather have a direct insertion to final orbit and angle offset rather than using sync'ed spacing orbits, but no one's made an in-game plugin for that yet, AFAIK. (Like a MechJeb function.)

[dewin]

That's sounds more dV intensive than needed. Though it is a good way to correct spacing if you decide to add more sats to a constellation. (Like adding a fourth comsat to a properly spaced 3-sat system.) Otherwise, you need more parameters than readily and easily accessible (I think). Pre-planning the orbital insertions of subsequent comsats I think is better overall rather than adjusting at the final orbit. Also less time, I think. I'd rather have a direct insertion to final orbit and angle offset rather than using sync'ed spacing orbits, but no one's made an in-game plugin for that yet, AFAIK. (Like a MechJeb function.)

Yes, it is more dV intensive -- and normally I've used other means (e.g. the single launch vehicle in resonant orbit with timed releases method), or only used my method after getting satellites 'approximately' right. It does work though, and it's also a viable method for correcting an existing constellation that's drifted.

I'd love to be able to have something that can do the equivalent math to do it as part of the overall ascent/entry process though, and it wouldn't be too difficult to adapt my current method. Assuming a Kerbin constellation:

1. Start with satellite #1 launched normally and in the target orbit
   
2. Launch satellite #2 into orbital/suborbital trajectory with correct Ap.
   
3. Determine what the phase angle between #1 and #2 will be when satellite #2 reaches Ap and construct the appropriate resonant orbit, burning at Ap. This is dV you would be using to circularize anyways, so it's not wasted. (If your launch timing is such that your spacing is already perfect, you'll end up with 360/360 = a normal circular orbit at the appropriate time.)
   
4. Circularize at next Ap
   

Time launches to error on the side of being "behind" your target position rather than being "ahead" for the most efficient results.

For constellations around other planets or moons, follow the same process with all burns at Pe instead of Ap.

[StahnAileron]

See, what we need is JUST #3. Target your first comsat. Call some function like "RT2 Constellation Launch" and input offset angle to the taget. It calculates the launch profile (or tells you "Insufficent dV for targeted orbit") AND the launch window.

Another function like "RT2 Constellation Transfer" would let you do the same thing, but from a parking orbit. 90% of the functionality is in MechJeb. The only other calculations I can see needed is the offset angles.

[Freeman Dyson]

Finally those trig lessons make sense For a triangle of sides a,b,c and angles opposite those sides A,B,C : a/(sin(A))= b/(sin() = c/(sin©)

So if our circular orbit is 2500km then we add kerbin's radius 600km this gives us one of the two short sides at 3100km now if we choose to have 3 satellites then the angles between each will be 120deg as we know triangle angles add up to 180deg so the remaining two angles must total 60deg. Seeing as all the satellites are at the same altitude we can infer that this is an isosceles triangle and the two angles are equal therefore the corresponding angle to our side must be 30deg (half of 60deg). So our satellite spacing, the side of the triangle opposite 120deg, can be found using: Spacing = (3100/sin(30))*(sin(120))

This can be simplified for all 3 satellite constellations, with the a circular orbit and equal inclination, to: Spacing/sin(120) = (Altitude + 600km)/sin(30) (rearrange as required)

" " " " " " 4 " " " " " " " " " " " Spacing/1 = (Altitude + 600km)/sin(40) (sin(90) = 1)

" " " " " " 5 " " " " " " " " " " " Spacing/sin(72) = (Altitude + 600km)/sin(54)

" " " " " " 6 " " " " " " " " " " " Spacing = Altitude + 600km (all the triangles here are equilateral with sides of the same length so the sin maths is not needed)