Help me position my commsats more accurately

[tengu-mai]

Hi.  I am trying to achieve the following:

• 8 relay satellites, each in a Kerbin polar orbit (90 degree inclination)
• 4 different orbital paths, 2 sats per path.  Each path is 45 degrees rotated (LAN)
• In each path, the 2 sats are opposite each other (e.g. 1 at north pole, 1 at south pole)
• I don't care about altitude, provided they all use the same.

I can get pretty close by doing the following:

• Set my altitude to 1581.76 (semi-geosynchronous)
• Launch all 8 sats at intervals of 44 minutes, 53 seconds (one eighth of a sidereal day)
• Launch the first four sats at 90 deg inclination
• Launch the second four sats at -90 deg inclination

This gets me really really close, but my (main) problem is that the launch pad is not exactly on the equator, so the sats launched northbound achieve a slightly different orbit than the ones launched southbound.  Is there an easy way to compensate for this?  How close might I get if I calculate the duration needed to fly to the equator, then add half of it to my launch time in one direction, and subtract half of it from my launch time in the other direction?

 

Edited March 2, 2020 by tengu-mai

[AHHans]

8 hours ago, tengu-mai said:

This gets me really really close, but my (main) problem is that the launch pad is not exactly on the equator, so the sats launched northbound achieve a slightly different orbit than the ones launched southbound. 

Are you using a script to launch the satellites? Because I'm sure that I couldn't do a manual launch precise enough for the tiny distance of the launchpad from the equator to matter.

I would use one of the following three approaches to this issue:

• Just don't care about the tiny difference in orbit. (Well, yes, but it is what I would do. )
• Adjust the orbit of one of the satellites to the orbit of the other once in space.
• Launch both satellites on the same booster into an elliptical transfer orbit - with a convenient resonance to the target orbit - and detach them so that they are at the correct phase angle.

8 hours ago, tengu-mai said:

How close might I get if I calculate the duration needed to fly to the equator, then add half of it to my launch time in one direction, and subtract half of it from my launch time in the other direction?

If you can do your launches precise enough, then adjusting the launch times should give you the needed correction. To get the value of the correction, you can also look at the angle the that orbits of the two satellites have to each other and convert that into a difference in launch time.

[Zhetaan]

@AHHans's suggestions are all good ones, and I will add that, considering the amount of effort that you're putting into it, you can also build a mobile launcher into a rover and simply drive to the equator.

For my part, my preference would be to get them to the same orbit in space and then make my adjustments once there, thus eliminating the persistent imperfections of the planet and my launch location.

[DeadJohn]

Interesting exercise. I assume you are trying it just for the challenge, because being a little off in the orbits probably won't make any difference for communications. What's your goal for these satellites?

My suggestion is to include RCS on your satellites. Get close during your launch, then fine tune your orbit later.

My preference is to make few rings, and use 3 satellites in a triangle per ring. All 3 satellites go up in one launch to simplify coordination. Include RCS in the satellite design. Raise Ap to geosync height, set Pe to get an orbital period of 2/3 day (4 hours in stock). Release 1 satellite each time you pass Ap then use satellite RCS to adjust its orbital period from 2/3 day to exactly 1 day. One ring at the equator with an optional ring in polar orbit provides 100% coverage for Kerbin, but it could also be done without an eq ring and 2 polar rings offset 90 degrees from each other.

Edited March 2, 2020 by DeadJohn

[tengu-mai]

On 3/2/2020 at 5:25 AM, Zhetaan said:

You can also build a mobile launcher into a rover and simply drive to the equator.

Mind blown.  This never occurred to me as remotely possible.  Wow.

[tengu-mai]

On 3/2/2020 at 2:14 AM, AHHans said:

I would use one of the following three approaches to this issue:

• Just don't care about the tiny difference in orbit. (Well, yes, but it is what I would do. )
• Adjust the orbit of one of the satellites to the orbit of the other once in space.
• Launch both satellites on the same booster into an elliptical transfer orbit - with a convenient resonance to the target orbit - and detach them so that they are at the correct phase angle.

Firstly: thanks for the helpful suggestions!  I was inspired to attempt this by an animation on the kerbal wiki.

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Just don't care about the tiny difference in orbit.

It must be nice to be so unencumbered by OCD.

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Launch both satellites on the same booster into an elliptical transfer orbit - with a convenient resonance to the target orbit - and detach them so that they are at the correct phase angle.

Yes, this is pretty much what I expected/was afraid of.   This sounds like precisely the correct answer, and one which is likely to have some challenging math to go along with it.  I've never calculated Hohmann transfers before.

In fact, I have absolutely no history in astronomy or astrodynamics, so here are a couple more basic questions.   

• If I understand correctly, each of my polar-orbiting satellites is orbiting along a right ascension line.  Is that correct?
• Does the KSP user interface display the information required for me to determine the hour-offset of my satellite so that I can insure two different satellites are proceeding along the same right ascension?

 

 

On 3/2/2020 at 9:07 AM, DeadJohn said:

Raise Ap to geosync height, set Pe to get an orbital period of 2/3 day (4 hours in stock). Release 1 satellite each time you pass Ap then use satellite RCS to adjust its orbital period from 2/3 day to exactly 1 day. 

This is an excellent suggestion!  Very practical and sounds like it should be effective.

[AHHans]

3 hours ago, tengu-mai said:

• If I understand correctly, each of my polar-orbiting satellites is orbiting along a right ascension line.  Is that correct?
• Does the KSP user interface display the information required for me to determine the hour-offset of my satellite so that I can insure two different satellites are proceeding along the same right ascension?

Not sure what you mean with "right ascension line", the value used in KSP for the orientation is the longitude of the ascending node or LAN. This is displayed in the "Advanced Orbital Info" tab in the "Maneuver Mode" in the bottom left of the UI. So (together with the inclination) you can check if two satellites are orbiting in the same plane. AFAIK it does not directly tell you when you have to launch another satellite to get it into the same plane. (Most people just eyeball it and then adjust in orbit.)

[Zhetaan]

7 hours ago, tengu-mai said:

If I understand correctly, each of my polar-orbiting satellites is orbiting along a right ascension line.  Is that correct?

 

3 hours ago, AHHans said:

Not sure what you mean with "right ascension line", the value used in KSP for the orientation is the longitude of the ascending node or LAN.

They are close but not equivalent.  A line of right ascension is the celestial equivalent to lines of longitude, and thus there is a relationship to longitude in the same sense as the longitude of ascending node.  However, right ascension is specifically defined for celestial observations made from Earth (it uses a particular point in Earth's sky as a sort of 'east pole' and would need a different definition for observations made from different places) and is more useful for locating fixed points in the sky as seen by an observer on the ground, whereas longitude of ascending node is specific to objects in orbit of something and is determined without respect to an observer's location.

In other words, one uses right ascension to locate a point on the face of the sky, and one uses longitude of ascending node to locate an orbit, which is not a point.  In this case, an object in polar orbit will always have one of two right ascensions:  when travelling from the north to the south pole, it will have one value, and when travelling from the south to the north pole, it will have the supplement to that value.

 

[AHHans]

18 minutes ago, Zhetaan said:

They are close but not equivalent.  A line of right ascension is the celestial equivalent to lines of longitude,

Ah, O.K. I didn't make that connection. And, yes, a 100% polar orbit (i.e. with an inclination of exactly 90 deg) will travel along two lines of RA.

I also think that IRL the longitude of an ascending node is typically given in right ascension. (Btw. I'm not sure how you meant that one comment, but the ascending node of an orbit is a point.)  AFAIK in KSP instead of using the vernal equinox, the reference direction for longitude (or RA) is the direction of one of the coordinate axes of the underlying Cartesian coordinate system - and the line from Kerbin to the sun at the start of a game. So in case you were worrying: the LAN of an orbit will stay constant  while Kerbin orbits around the sun, even if the direction from there to the sun changes. Which is as you would expect of an orbit in two-body gravity.

[DeadJohn]

9 hours ago, tengu-mai said:

Quote

Launch both satellites on the same booster into an elliptical transfer orbit - with a convenient resonance to the target orbit - and detach them so that they are at the correct phase angle.

Yes, this is pretty much what I expected/was afraid of.   This sounds like precisely the correct answer, and one which is likely to have some challenging math to go along with it.  I've never calculated Hohmann transfers before.

[snipped for brevity]

 

On 3/2/2020 at 12:07 PM, DeadJohn said:

Raise Ap to geosync height, set Pe to get an orbital period of 2/3 day (4 hours in stock). Release 1 satellite each time you pass Ap then use satellite RCS to adjust its orbital period from 2/3 day to exactly 1 day. 

This is an excellent suggestion!  Very practical and sounds like it should be effective.

The resonance orbit that AHHans mentioned, and that you feared had challenging math, is sort of the same thing that I described.

I strongly recommend 3 relay satellites in a ring instead of 2. If the satellites are high enough (geosync is more than adequate) the members of a ring always have lines of sight to each other. In terms of KSP gameplay, typical difficulty settings let a single equatorial ring cover 100% of Kerbin, but if you dial up difficulty a second polar ring may be needed when you're landed at the poles.