Satellites Network Placement

[brusura]

Hi

I have a specific question about placing 3 satellites around a planet at 120° ( or arbitray angle and number of satellites )

My idea is to start in an circle orbit with all 3 satellites, then boost the apoapsis of 2nd and 3rd satellites to two specific heights, so when at periapsis I can circularize again the orbit having 2nd satellite at 120° ahead of 1fst and 3rd at 240° ahead.

Is there a formula that give me the apo I need to raise to move at a desired degree ahead?

 

Thanks

[Streetwind]

There is; you can do it via orbital periods.

If your orbital period is 6 hours, that equals 360 minutes. Thus, traversing one degree of the orbital path takes one minute. If you change your orbit to be 5 hours 59 minutes long, you will advance 1° forward relative to your old position for each orbit. If you change it to be 6 hours 10 minutes long, you will fall 10° behind per orbit. And so on. You can solve this for any given base period, but the 360 minute example just lines up so nicely with 360 degrees

Orbital periods can be calculated. I will refer you to Wikipedia here, which has the relevant math.

[Vive_moi]

Hi,

Usually for my circular CommSat Network, I use one launcher with all the sats. I put it on a circular parking orbit a bit above or below the destination orbit at the convenience and the fuel economy. Then I push the sats one by one to their orbital position.

I put the first one anywhere on the destination orbit.

Then I take the second one and set the first as target.

I set a maneuver to have an (and only one) intersection with the first one's orbit and a closest approach at " OrbitDiameter*sin(Pi/NbSat) " and a second maneuver to circularize. (Note the maneuver might be further orbit ahead, depending of the orbital speed and height difference.)

 

For example, for a Kerbin 700km circular orbit and 3 sats network, my parking orbit would be 600-650km and the closest approach must be set at ((600+700)*2)*sin(Pi/3) = 2251.66km.

I hope this was almost comprehensible.

See you,

Vive_moi

Edited July 20, 2016 by Vive_moi

[brusura]

5 hours ago, Streetwind said:

There is; you can do it via orbital periods.

If your orbital period is 6 hours, that equals 360 minutes. Thus, traversing one degree of the orbital path takes one minute. If you change your orbit to be 5 hours 59 minutes long, you will advance 1° forward relative to your old position for each orbit. If you change it to be 6 hours 10 minutes long, you will fall 10° behind per orbit. And so on. You can solve this for any given base period, but the 360 minute example just lines up so nicely with 360 degrees

Orbital periods can be calculated. I will refer you to Wikipedia here, which has the relevant math.

This is what I thought and did some calculation in the excel file but in the field I always move too ahead or too behind.... there's must be something wrong in my math surely....  here is the file if you want to take a look at it : http://s000.tinyupload.com/index.php?file_id=03089097859948083140

EDIT: I think I have to correctly apply the equation in the link you gave me

EDIT2: with formulas from wiki , I have to still try in game http://s000.tinyupload.com/index.php?file_id=13562692573534272466

@Vive_moi Your method is interesting too , I dont get how the formula works but it's just a matter of plugin the data, I'll have to try it

Edited July 20, 2016 by brusura

[Vive_moi]

Hi again,

See you

Vm

[brusura]

Wow thanks , I hope to study that in the weekend

Have a nice day

[Spricigo]

 

5 hours ago, Streetwind said:

There is; you can do it via orbital periods.

.... 

This. 

Easely done when orbital period is nicely displayed  (mechjeb,  KER,  etc). After launching the first satellite just burn progade until you orbital period equal to 4/3 of satellite orbital period and one orbit later you will be back 120° behind the previous  satellite. 

 

[Zhetaan]

@brusura:

@Streetwind's excellent example is the special case where one minute of orbital period corresponds to one degree of separation.  That's easy to calculate, and so would be the common multiples and divisors (a three-hour orbital period is adjusted by one degree every thirty seconds, for example).  For an arbitrary angle in any orbital period, you would use fractions of a circle normalised against the orbital period, meaning that you would increase your orbital period by an amount that corresponds to the angle of separation you want to have.  For an arbitrary number of satellites, assuming that they are equally spaced, the formula reduces to (n + 1) / n of your current orbital period, where n is the number of satellites you want to launch.

According to our well-known friend Kepler, T² / a³ = k where:

T = orbital period (in seconds)
a = semi-major axis of the orbit (in metres)
k = constant of proportionality (in unholy Kraken-units of square seconds per cubic metre)

The semi-major axis of a circular orbit is just the orbital radius, but don't forget to add Kerbin's radius (600,000 m) to the Pe display in map mode, as map mode only counts altitude from sea level.  The general solution to find semi-major axis from map mode information is (1 / 2) * (Ap + Pe + d_Kerbin), or the diameter of whatever you're orbiting if not Kerbin.  The constant is equal to 4π² / μ, where μ is the standard gravitational parameter for the body you're orbiting.  For Kerbin, μ is equal to about 3.531644 * 10¹², so k is about 1.117848 * 10^-11.

Now I'm going to show you why you don't need to know most of that.  Let's assume you already know your orbital period.  Maybe you have a mod that tells you the period.  Maybe you figure it out from map mode (time to the next apsis subtracted from time to the apsis after that, times 2).  Maybe you just want to call it time T.  I like T, myself, though I am known to take coffee quite often, too.  Let's also assume that your orbit is not necessarily circular, but that you will always do your staggering at the periapsis.

To stagger the next satellite by an arbitrary angle (in degrees), you need to multiply T by 1 + (angle / 360) to space it out behind, or 1 - (angle / 360) to space it out ahead.  Be careful with that spacing ahead when you're in low orbit; you may reenter instead.  I assume you will always want to stagger satellites behind.  If you want to space four sats evenly about the orbit, then they will need to be 90 degrees apart.  T * (1 + [90 / 360]) = T * (1 + [1 / 4]) = T * (5 / 4).

For n equally spaced sats, it would be T * (1 + [(360 / n) / 360]) = T * (1 + [1 / n]) = T * ([n + 1] / n) which proves what I mentioned earlier about the spacing being (n + 1) / n for n equally spaced satellites.  In any case, the ratio of orbital periods (T₂ / T₁) will be some form of (360 + angle) / 360 or (n + 1) / n.  Remember how I mentioned you could figure out the orbital period from map mode?  You don't really need to do that:  you don't even need to know the actual orbital period unless you want to check your result or the period is the target (as in a synchronous orbit); you only need the ratio of new to old.

Anyway, to find the new apoapsis for an arbitrary spacing orbit, note that the constant k from Kepler's equation is constant for all orbits about the same primary.  This means that we can set (T₁² / a₁³) = (T₂² / a₂³), where the left side is your current orbit and the right is your new orbit.

This unsightly soup magibraically simplifies to (desired semi-major axis) = (current semi-major axis) * (ratio of desired to current orbital period)^(2/3).  The desired semi-major axis is equal to the current plus half of the amount you want to raise the apoapsis, and the ratio is what we originally wanted to use to modify our orbital periods: (360 + angle) / 360 or (n + 1) / n.

For an example:  A synchronous circular orbit (six-hour period) is at 2863.33 km, so the semi-major axis will be that plus 600 km, or 3463.33 km.  Let's say we want to space six sats equally at that orbit.  The ratio of orbital periods, then, is 7 / 6, and that to the two-thirds power is about 1.10823.  All told, our new semi-major axis will be 3838.17 km (if you check it with Kepler's law, you'll see that this value does give an orbital period of approximately seven hours). Subtract the current semi-major axis (= 374.84 km), multiply by 2 (= 749.68 km), add our apoapsis altitude (the original orbit altitude in this case, because it was circular) and the result is the apoapsis you want, or 3613.01 km.

In your case, you want to space three sats equally, so your ratio is (3 / 2).  That to the two-thirds power is about 1.31037.  Multiply that by your semi-major axis and the rest is simple arithmetic.

Performing the burn on time is your problem. 

Edited July 20, 2016 by Zhetaan

[FancyMouse]

And there's even a tool for people like me who knows how it works but too lazy to fire up a calculator. The "multiple launch view" in that page is doing exactly what @Zhetaan just talked about.

[brusura]

Thanks guys you have been all very kind and helpful

[carlorizzante]

My approach to setup a network of comm satellites is pretty simple but it served me well.

Once I decided the altitude at which the 3 or 4 satellites will be positioned, I pack them all on a single ship/rocket (mother ship) and take off.

I position the mother ship in an orbit that satisfies two requisites:

1. The apoapsis has to equal the altitude to which I will position the 3 or 4 satellites.
2. The orbital period has to be a module of the orbital period the satellites will have, for example 1/3 for three satellites, 1/4 for four sats (see below).

Let's assume I decided to position 3 satellites, evenly spaced, and their final orbital period will be 6 hours. That equals to 2,863.33 km altitude.

To achieve my goal I first position the mother ship in an orbit that has an apoapsis of 2,863.33 km altitude, and then I trim the periapsis so that the orbital period will be 1/3 of the final orbit of the satellites, which means that the mother ship will reach apoapsis every 2 hours.

At each pass to apoapsis I detach one satellite, I take control of it, and I circularize its orbit straight away. Then I switch back to the mother ship, preparing the next satellite.

The net result is that I will be able to detach each satellite at 2 hours interval from one another. That spaces them evenly across an orbit of 6 hours.

# Few tips.

Do not forget to activate the antennas before detaching a satellite. Limit the decoupler force, and pay attention that the engine of the satellite will not push the mother ship or it will change its orbit (to avoid that I orient the mother ship radially). Do not use RCS to rotate the satellite because their trusts affect orbit.

Hope that will help