Calculating Satellite Altitude for RemoteTech

[rogerwilco]

So I found the RemoteTech addon and I really think it is fantastic. It really makes you think a little harder about Why your are doing a particular mission rather than How.

The first step in RemoteTech is to launch an array of satellites from which you can relay mission controls instructions, so you retain control of your craft.

From their tutorial, they recommend placing 3 satellites in an orbit of around 1000Km.

So whilst I could take this at face value and just do as they say, I wanted to understand why they had chosen this value, and I wanted to understand how to calculate what you would need for different configurations or numbers of satellites, so that I can create networks around other planets without resorting to someone's youtube channel for instance.

What you want in a relay satellite configuration is for each neighbor satellite to be able to see each other, so if you have 3 satellites, each satellite must be able to see the other two. This also means that they can see every longitude on the body they are orbiting. I visualized this as a triangle bounding a circle, and wondered how to calculate what the altitude of the satellites must be in order for this to be accurate.

Whilst I am no maths guru, I can at least do a little trig. I have come up with a value which is that if you can get a satellite orbiting at 51Km off Kerbin (ignoring the mountains and atmosphere) then that would actually do the job.

My question is, am I incorrect in this? If so, why? And if not, why has the tutorial chosen such a large distance between satellites? Bearing in mind the further orbit you have the stronger (more power/mass/cost/sci level) requirement of the antennas.

If I am correct that 51Km is just fine with 3 sats, can I just plop them all in a nice and tidy 80Km orbit and save myself the cost, power, dV to push them higher?

Or am I totally wrong and need tearing a new one by the maths capable here.

Just trying to learn to fish rather than asking what orbit I should be at! Many thanks you helpful KSPers!

Here are my workings:

Edited February 27, 2015 by rogerwilco

[IllicitMedic]

I just put 3 in GSO. 1 above KSC and the others positioned as to where they all 3 have constant line of site with each other much like your picture only at GSO altitude. Each GSO sat has 1 omni (5mn range) and 3 of the small dishes. The dishes point at the GSO sats to the flanks and the 3rd to the active vessel, the omni creates connections with all my ships in the Kerbin orbit and the 3rd dish connects any ship around the 2 moons.

When I'm ready to go outside the Kerbin system I just put 2 more sats up (1 dish, the biggest and one omni (5mn range) about halfway to the Mun on each side of Kerbin. 5 sats total and the entire solar system is covered. The large dish will cover the entire system. The large dish will point at active vessel and the omni will maintain connection with the GSO sats. Out of connection time on inter planetary missions are usually zero unless behind a planet which is normally no longer then minutes.

Edited February 27, 2015 by IllicitMedic

[mudkest]

I'm not a big math person either, but I did manage to figure out somehow that the minimum orbit height for a 3-sat network to be able to see each other is the same as the planets radius(cant remember how is the result was easier to remember then how I worked it out). So for Kerbin with a 600km (equatorial) radius you'd have to put the satalites in a 600km orbit equaly spaced for them to see each other. Off course the placement has to be spot-on for that, getting a larger orbit gives you a bigger room of error to work with.

No need to remember any math when you want to put up a new 3-sat network, just look up the planets size(which you can do in game) add 10-20% and you have a nice orbit target

[Rhomphaia]

The square of the hypotenuse is the sum of the squares of the other two sides.

you seem to have gotten that confused for square root, the radius of your orbit has to be a minimum of 1200 km (600 above sea level)

[ColourOfFire]

I just put three in Kerbistationary orbit in an equilateral triangle. Altitude is 2868km and a bit, never had any problems with them getting out of alignment or whatever. I always give my comsats a docking port so I can attach modules with bigger dishes for interplanetary missions later.

[rogerwilco]

Thanks for your help guys, I think the first number I came up with was:

sin(θ) = Opposite / Hypotenuse

sin(30) = 600 / Hypotenuse

0.5 = 600 / Hypotenuse

Hypotenuse = 600 / 0.5

Hypotenuse = 1200

So the orbit altitude is 600Km.

The square of the hypotenuse is the sum of the squares of the other two sides.

you seem to have gotten that confused for square root, the radius of your orbit has to be a minimum of 1200 km (600 above sea level)

Thanks Rhomphaia, when I did as you said and corrected that mistake it came out at 1199.9, so I assume my half radio distance (line of sight distance from satellite to satellite) is correct.

With a line of sight distance (x2) resulting in 2078.46Km, this is under the Communitron 16 range so I can avoid adding a 32.

I will go about setting this up and see if I can make this work.

Thanks chaps!

- - - Updated - - -

I just put three in Kerbistationary orbit in an equilateral triangle. Altitude is 2868km and a bit, never had any problems with them getting out of alignment or whatever. I always give my comsats a docking port so I can attach modules with bigger dishes for interplanetary missions later.

Good idea about the docking port!

[match]

I think you will find that while the solution of 600 km solves the equation, it does not fully resolve the issue. At 600 km, the line between satellites tangents the planet. LOS will be obstructed.

While it is good to brush off those trig skills, do take a moment to consider the issue from a min max view. You have found the minimum altitude capable of a three satellite deployment (>600 km). The next step is to rework it from the other end... What is the maximum altitude that three satellites could operate? (Using Communitron 16s, like the first example.)

From there you will find that the difference needed in dv is minor, so the final choice of altitude may be based on personal choice.

I use a 90 minute orbital period ~775 km, iirc. I normally launch all three at once to a 125 km orbit and insert on successive orbits (30 miutes apart). I only put omnidirectionals on these and they serve as the inner relay, but you can easily add dishes for LD comms if desired.

[RCgothic]

Yup, if you insert into 600 km altitude you will need to get the spacing and orbital period exactly right or your satellites will drift behind the planet with respect each other and even then you'll often get obscured by mountains. This is a mistake I first made when starting out with remote tech. I put too much trust into the solution of the equations without adjusting for practical experience. 700 km altitude gives you much more phase error to work with, and allows you to spot angular drift over time and correct it before you lose contact between sats.

[jlcarneiro]

I agree, it seems that rogerwilco has confused "square of the catheti" with "square root of the catheti".

What mudkest says is the rule of thumb: the minimum altitude is equal to the radius of the planet/moon. Although, I think those margin of 10% or 20% is insufficient: using a Communotron 32 at 1000km makes your network much more stable.

What I DON'T KNOW is: to get the same (big) margin of error, what should be the altitude on each planet/moon? 2 times the radius? Or this would be too exagerated in some cases (Minmus, for example)?

[Van Disaster]

I tend to put one in stationary orbit above KSC, and then set up enough low level sats in polar orbits ( 300ish km for Kerbin ) to let me use the low power omni antennae - setting those networks up is a bit of a chore though. For other planets I'll use a couple of interplanetary relays in elliptical orbits and then low level planetary relays again. The only place you probably need a geostationary sat is over KSC, and even then that's mostly convenience.

Having said all that I threw RT out of my current game, it wasn't actually adding gameplay... well it was, but it was turning into a job. One of the antenna modes where it takes the size of both antenna into account when attempting a connection may make it a bit less hassle.

Edited March 1, 2015 by Van Disaster

[Stone Blue]

Not being a math person, AND not being a person who just wants to totally copy other people without knowing the HOWs and WHYs, I found a good approach for those who find jumping straight into the math alone to be intimidating, try using THIS, AND then the math, to help understand the HOWs and WHYs:

http://ryohpops.github.io/kspRemoteTechPlanner/

[RCgothic]

You don't need geostationary sats. You just need at least one visible from KSC at all times, which you get with a 3-sat constellation in equatorial orbit above minimum altitude for line of sight pretty much by default.

The other approach you could take is 'How do I enclose maximum volume', which you get by finding the altitude at which the sats are at maximum range from each other, and then minus a small bit.

[Mighty1]

Not being a math person, AND not being a person who just wants to totally copy other people without knowing the HOWs and WHYs, I found a good approach for those who find jumping straight into the math alone to be intimidating, try using THIS, AND then the math, to help understand the HOWs and WHYs:

http://ryohpops.github.io/kspRemoteTechPlanner/

This is just beautiful. I did that using word, drawing circles and lines. This is a much more elegant solution. Thank you.