Deep Space Relay Networks

[Hotel26]

This tutorial, Setting Up A Commnet System, suggests placing 6 satellites into a 4Gm Kerbolar orbit, 12 into 25Gm and, optionally, 24 into a 50Gm orbit.

 

To do this in a finite amount of time requires launching them all individually at specific time intervals.  I've calculated the following:

 

To launch 6 Comm Sats to a 4Gm orbit, launch each with 13.48 day separation.

To launch 12 Comm Sats to a 25Gm orbit, launch each with a 59.30 day separation.

To launch 24 Comm Sats to a 50Gm orbit (optional), launch each with a 20.69 day separation.

 

The 3 formulae used in this computation are:

 

1.   v = sqrt(G * M / R)
2.   p = 2 * PI * R / v / (6 * 3600)
3.   dt = 1 / (N * (1 / p1 - 1 / p2))

 

where:

•   v is orbital speed
•   G is grav:6.67408e-11
•   M is mass of Kerbol: 1.7565459E28
•   R is orbital altitude
•   p is orbital period (days)
•   PI is pi
•   dt is launch separation (days)
•   N is number of satellites to occupy an orbital altitude
•   p1 is orbital period of Kerbin (days)
•   p2 is orbital period of the target orbit (days)

 

Note:

•   dt for inner orbits will be negative which merely indicates the satellites will arrive in counter-revolutionary order
•   1/p is angular speed expressed as radians/day and subtracting the speed of the target frame of reference from the launch frame of reference is the insight that makes this achieve a full orbit with even spacing (your mileage may vary depending on how timely your launches are)

 

I plan once arriving at apoapsis to not worry too much about the orbital parameters or spacing but to have the exact same orbital period for all sats in the orbit.  This will keep them locked in their relative positions over a very long duration.

 

If you're more picky about getting exact spacing, this tutorial, https://wiki.kerbalspaceprogram.com/wiki/Tutorial:Ideal_Orbits_for_Communication_Satellites, particularly the treatment of the Law of Cosines, is quite fascinating.  It's most relevant to low altitude orbits, e.g. spacing N space stations around a body.

 

[All of the above may have been covered elsewhere but I haven't seen it/didn't find it and I've just had to create all this from scratch; so I hope it's useful to someone else.  Please let me know if you find any errors, as I have not executed this yet.]

Edited June 10, 2023 by Hotel26

[JoeNapalm]

Very nice!

Meanwhile, I've thrown some lifters and sats together from scrap left over from that trailer park Jeb landed on, squinted a bit at the Tracking Station display, then lobbed some antennas into space.

Seems to be working okay so far.

-Jn-

[suicidejunkie]

If you're really picky about your orbital periods, you can deploy a satellite constellation at 5km geosynchronous.  Deploying them is quite inexpensive and scenic, particularly if you've added clouds and scatterer and such.

[Snark]

The scheme laid out in the OP seems awfully fancy, but is it really necessary?

I've never done anything even vaguely like that.  I just put one long-range relay sat in high polar orbit around each planet.  Then put whatever low-altitude, short-range comsats are needed around a given planet for covering its surface.

The high-polar interplanetary relays take care of communicating across the solar system, do so very efficiently and reliably, are super simple to set up, and don't need to follow any carefully constrained orbital parameters (basically, any high orbit will do).

What's the rationale for the much-fancier approach?  (Other than just being a challenge for its own sake, for those who are so inclined, that is.) 

[Tyko]

14 minutes ago, Snark said:

The scheme laid out in the OP seems awfully fancy, but is it really necessary?

I've never done anything even vaguely like that.  I just put one long-range relay sat in high polar orbit around each planet.  Then put whatever low-altitude, short-range comsats are needed around a given planet for covering its surface.

The high-polar interplanetary relays take care of communicating across the solar system, do so very efficiently and reliably, are super simple to set up, and don't need to follow any carefully constrained orbital parameters (basically, any high orbit will do).

What's the rationale for the much-fancier approach?  (Other than just being a challenge for its own sake, for those who are so inclined, that is.) 

Agreed. You need 4 sats - One high power interplanetary relay in high polar orbit and 3 lower power relays on the equatorial plane, same altitude, set at 120 degree intervals.

If you want to be REALLY thorough you could have 3 high polar in the same plane at 120 degree intervals - this would ensure coverage of craters at the poles and those brief moments when a single high polar relay might by occluded by the planet it's orbiting.

Edited July 13, 2018 by Tyko

[JoeNapalm]

11 minutes ago, Tyko said:

Agreed. You need 4 sats - One high power interplanetary relay in high polar orbit and 3 lower power relays on the equatorial plane, same altitude, set at 120 degree intervals.

If you want to be REALLY thorough you could have 3 high polar in the same plane at 120 degree intervals - this would ensure coverage of craters at the poles and those brief moments when a single high polar relay might by occluded by the planet it's orbiting.

I typically just do two -- yeah, three is probably optimal, but two in opposite syncopated high polar orbits generally gives me "good enough" coverage...and I'm sending at least one for mapping, anyway.

If actual lives depended on it, I'd go with three equitorial and three polar, but that rapidly ends up to more sats than I'm interested in sending.

-Jn-

[Tyko]

Totally agree...you can really get away with one for most missions. I include an interplanetary relay on my initial survey sat and with a little planning you can land anywhere on the planet with just that. You just have to wait until that high orbit relay sat has a field of view onto the landing site.

If I'm planning a bunch of landings I'll send a single launch with 3 satellites and place them in an equatorial equilateral   triangle and then I have 99%(ish) coverage.

[Snark]

4 minutes ago, Tyko said:

Totally agree...you can really get away with one for most missions. I include an interplanetary relay on my initial survey sat and with a little planning you can land anywhere on the planet with just that. You just have to wait until that high orbit relay sat has a field of view onto the landing site.

I usually just go with one surface-relay satellite.  I put it in a very eccentric orbit with a low Pe over the midnight line, and a high Ap over the noon line.

That way, the relay spends the large majority of its time loitering over the planet's daylight side, which is perfect because I always land in daytime; I never do significant planetary surface exploration at night.  So I only need relay coverage over the daylight side, because at nighttime I shut down anyway.

Of course, such an orbit is a temporary arrangement, because as the planet orbits around the sun, the Ap will gradually migrate around until it's on the night side.  But unless I'm setting up a permanent surface colony that will last for at least one solar orbit of the planet (which I very rarely do), it's not an issue:  the orbit orientation stays good for a period of weeks or months (unless it's at Moho), which is usually longer than my surface operations last anyway.

[Srpadget]

I go with 3 equatorial relays (typically using RA2s) spaced ~120° apart around a planet and each of its moons for ground coverage, and 2 long-range (RA15 or RA100 depending on the planet) ~180° degrees apart in high polar orbit.  It seems to work plenty well enough (actually it's generally overkill). It's not a really big effort--typically I do that using 1 launch with 2 long-range relays and another that packs 6 of the smaller relays into a single fairing (planet plus 1 moon).  Certainly seems less hassle to me than that constellation of 18 to 42 solar-orbiting relays.

Edited July 14, 2018 by Srpadget
Edited to fix spelling/punctuation errors

[Hotel26]

And I quote from my original citation:

Constellations

Each system needs its own constellation.

Kerbol

A set of six evenly space relays at around 4,000,000km. A set of twelve evenly spaced relays at around 25,000,000km. A set of 24 evenly spaced satellites at around 50,000,000km. Use RA-100 relays. These relays are for connecting with deep space probes. You may omit the third ring but deep space coverage in the outer system may be a bit spotty.

(For satellites around a planet, the orbits are small and deploying 3 or 4 at once using the harmonic resonance method is entirely feasible.  But not for Kerbolar orbits...)

I'll take it under advisement, however, that the above may be just not necessary.

Edited July 14, 2018 by Hotel26

[StarStreak2109]

Mmmh, still you don't explain, why you need so many sats.

I do it this way:

• Three CommSats in kerbal-stationary orbit, spaced at 120° intervals for covering the Kerbin system.
• One Longrange CommSat (LRCS) in an excentric polar orbit (PE at 100km, AP just shy of the SoI boundary) for interplanetary communication.
• Optionally: Two LRCS sats, one trailing and the other leading outside of the Kerbin SoI, but at the same orbital altitude as Kerbin, to ensure a commlink from interplanetary vessels at all times.

As required, this may be repeated around other worlds as well, whereas it is not necessary to place the sats in stationary orbits.

[MisterKerman]

Are relays basically an unpleasable pain in the bum in regards to a single celestial body? I set up 3 evenly spaced relays and within a mission or three they were totally buggered and clustering. I couldn't manage matching their orbits any better than I had to avoid velocity difference. I don't have numbers handy but they were like, god damn perfect basically.

 

Edit: I regret the last word in my post because I know in my heart that was why... Do you guys nail it every single time you set a relay system up? Do they stay perfect for you?

Edited July 15, 2018 by MisterKerman

[LordFerret]

9 hours ago, MisterKerman said:

Are relays basically an unpleasable pain in the bum in regards to a single celestial body? I set up 3 evenly spaced relays and within a mission or three they were totally buggered and clustering. I couldn't manage matching their orbits any better than I had to avoid velocity difference. I don't have numbers handy but they were like, god damn perfect basically.

 

Edit: I regret the last word in my post because I know in my heart that was why... Do you guys nail it every single time you set a relay system up? Do they stay perfect for you?

I don't find them a pain, just tedious and time-consuming. I set up 3-per constellations as well, around planets, moons, whatever. I use Ion propulsion systems, with solar and/or RTG, and battery backup power solutions (sufficient enough for science data/mapping transmissions and dark-side passages). Without regard to the orbit chosen, polar, equatorial, etc, I put all 3 on the same plane with matched orbits (circularized as perfect as possible). Over the years there is some drift, but for me it's nominal and easily corrected thanks to the onboard propulsion system.

 

[MisterKerman]

7 hours ago, LordFerret said:

I don't find them a pain

I should try much harder to match up my orbits. I got it real real close though. I'll try for exact using rcs perhaps or maybe a 99% thrust-limited engine.

Way too science-broke to even think about ion propulsion right now until I gut the Mun.

[Hotel26]

14 minutes ago, MisterKerman said:

I should try much harder to match up my orbits.

With KER installed, there is a read-out on orbital period down to the millseconds.  The orbits don't have to match perfectly (geometrically), but if you use RCS or ions (especially thrust-limited for the final tweak) and you note the orbital period of your lead satellite and then you tune the followers to have the same orbital period right down to the millisecond or as near as you can get...  you will have done the job as well as it can be done.

[MisterKerman]

53 minutes ago, Hotel26 said:

With KER installed...

I don't mod but I wouldn't mind one specifically for logistics like DV while engineering spacecraft in the VAB. I'm sick of trial and error because generally it's only good for specific payloads on a specific mission or lighter payloads than the loads your lifter was used for prior.

It's a little time consuming for something that the game ought to just let you know.

Edited July 16, 2018 by MisterKerman

[Hotel26]

2 hours ago, MisterKerman said:

I don't mod

I understand your sentiments most precisely.

My ten year-old questioned me about this a few years ago when I first installed MechJeb because my household had a strict no-modding policy (mainly about Minecraft)...  When/if one outgrows MechJeb (which has been a great teacher!), KER is the natural replacement umbilical for information.  I had to make an exception for KSP mods because the KSP biological culture is mod-rich but I try to limit the number.  I have a shortlist of essential exceptions: KER and KAC are the prime examples.  Both are informational.  KER also has a straight-line distance stat that can be used with Law of Cosines [2nd citation in OP] to establish exact spacing in an orbit (if one wanted to be that precise) [although the same number appears in the Map View in stock].

The rationale with orbital period is that all participants return to the same position/speed at the same moment and this is what "freezes" drift.  And it's directly and easily adjustable.

Edited July 16, 2018 by Hotel26