Making a perfect launch (or gib maths pls)

[rokkit_scientist]

Hello everyone,

So I just got back in the game for the first time since early access (0.24 or so), as expected I'm loving the bejeezus out of it. I'm using Realism Overhaul with Real Solar System because reasons.

I've already gotten back on track, mostly. I can reliably design a rocket to achieve orbit etc. However, there is something that has been bugging me A LOT, and that is that most of my launches are "unplanned". While I can put a satellite on a GEO, no problem, I'm having trouble planning my launches so that I can do things efficiently. For instance, I have devised a mission to put three satellites in GEO. The first one got up no problems, though I forgot to add fuel to its RCS tank and it's pretty much just floating now, lol. My question now is, is there some "magic" math formula or whatever I can rely on so that I can plan where my satellites go? For instance, I want these three satellites to be precisely 120 degrees apart from each other (+/- 1 or 2 degrees). How would I go about planning and executing that? I realize I can use the longitudes to gauge where they need to be, but how would I go about planning my maneuvers so that they end up where I want them to?

This is especially problematic with RO because delta-v and engine ignitions are VERY precious things, so I can`t just make 5-6 burns to adjust my orbits most of the time.

Any help is appreciated.

[r_rolo1]

Well, I do not play with RSS, but I think I can give you some advice.

The period of a geostationary orbit is 24h ( duh ), so the best way of dealing with the 3 sat positioning in GEO would be to launch the three of them in one launch, put them all in a orbit with a period of 24/3 = 8 hours and that has the Apoapsis at the geostationary height ( around 36000 km , IIRC ) and then separate one at the time for the circularization burn every time you get to the Apoapsis of that 8h orbit. But given that you already launched the first one ...

Well, Give me some moments for doing the math ( or that someone that knows it to chime in )

P.S. Do you have a preference about the parking orbit altitude ? It makes a diference

Edited October 26, 2015 by r_rolo1

[Krux']

The period of a geostationary orbit is 24h ( duh )

Well, if he wants to get it precise he should shoot for ~23 hours, 56 minutes (plus a couple seconds) for his orbital period. Earth's sidereal day isn't an exact 24 hours, hence leap years. (this was dumb, and super wrong)

It's obviously pretty insignificant, but when I'm setting up my satellite network I try to get it as close as possible. Once you get close you can start doing your maneuvering using your RCS, which don't require ignitions, and shouldn't be too strong to overshoot your target orbit changes.

Edited October 26, 2015 by Krux'

[r_rolo1]

Well, leap years have nothing to do with sideral day lenght, besides the fact that the Earth orbital period is not a perfect multiple of it ( if it was , there would not be a need for them )

[paul23]

Still for geosats you use the sidereal day.

Secondly: in reality a few dozen small rocket burns always happen to align a gps satellite. (Which are btw are not on geostationary orbits).

[rokkit_scientist]

Well, I do not play with RSS, but I think I can give you some advice.

The period of a geostationary orbit is 24h ( duh ), so the best way of dealing with the 3 sat positioning in GEO would be to launch the three of them in one launch, put them all in a orbit with a period of 24/3 = 8 hours and that has the Apoapsis at the geostationary height ( around 36000 km , IIRC ) and then separate one at the time for the circularization burn every time you get to the Apoapsis of that 8h orbit. But given that you already launched the first one ...

Well, Give me some moments for doing the math ( or that someone that knows it to chime in )

P.S. Do you have a preference about the parking orbit altitude ? It makes a diference

First, thanks for the input

The problem though is that putting 3 satellites into a parking orbit, each with their own boosting stages in RSS is no easy task. Off the top of my head that's about a 12 ton payload right there :S

That said, that seems like a pretty smart way to go about it and I might tackle that, if anything for the pure challenge

As for the parking orbit preference, I don't really have one. So far I've been experimenting with launching directly to GTO, but that creates more problems than solves, especially when it comes to satellite constellations.

Also, I'm considering scrapping the first one and starting over, so your idea is not entirely out of consideration

[paul23]

Is there a particular reason you can't use 4 satellites? You have a full 90 degrees "spare" then, so you only need to have each satellite correct within 22.5 degrees.

[Tank Buddy]

Using orbital periods is probably your best bet. I don't want to think it out now, but a clever use of the periods of geosynchronous, low Earth, and transfer orbits will allow you to place satellites with relative accuracy.

Hint: For every minute that passes, an object in geosynchronous orbit will move 4 degrees.

[GoSlash27]

RokkitScientist,

I don't use RSS, but the technique would be the same.

Basically you use a resonant parking orbit to interface with the geosynchronous orbit so that they act like a set of gears. You use period instead of radius, but otherwise the concept is the same.

If you have an orbit with 24hr period and wish to precisely space 3 sats on it, you would use an elliptical orbit with a period of 16 hours and an apogee equal to the altitude of the geosynchronous orbit. In sidereal space, the resonant orbit makes a full rotation in 16 hours, but the GSO only makes 2/3 of a rotation.

When your sat gets to apogee the first time, it's at an arbitrary longitude "zero". Next time around, it's advanced 1/3. Then 2/3 and finally back to 0.

For the math, we worry about semimajor axis (or average radius) and period. We have to flip back and forth between them.

μ=GM where

G= the universal gravitation constant; approx. 6.674x10^-11

M= Earth's mass in kilograms; approx. 5.972x10^24

to find an orbit's period by it's radius or SMA

p= 2*pi*sqrt(r^3/μ) where

pi= approx. 3.142

r= the orbit's radius in meters

and conversely

r= cuberoot( μ(p/(2pi)^2)

It's important to remember that if you stretch an orbit to be elliptical, the apogee is just as much higher than the SMA as the perigee is below it such that

r=(Pe+Ap)/2

So for the process,

1) Place a control module on KSC grounds pointed up so it can track sats as they pass overhead.

2) Place the vehicle into a temporary parking orbit with a convenient orbital period. I like to use 101,306m for the stock game because it passes overhead KSC precisely once every 36 minutes. You will have to pick a different parking orbit for RSS.

3) figure out the transit time from this parking orbit to the GSO altitude. This is 1/2 the period of the SMA of the transfer orbit.

4) Figure out how far the Earth will rotate in that time.

5) Since it has a convenient orbital period, it's easy to convert longitude to time. Figure out the latitude of the burn, then convert to time.

6) Burn at the required time to set GSO apogee.

7) Upon arrival at apogee

7a) if a single sat, burn to circularize at GSO

7b) if multiple sats on a single bus, burn to establish resonant orbit perigee and kick off/ circularize first sat.

8) at apogee, kick off and circularize second sat and so on

9) after all sats deployed, at apogee burn retrograde to deorbit bus.

Now... if you're doing individual launches, you would orbit the first and then target it on the next launch to get an intercept. At apogee, you would raise the perigee to the resonant perigee and circularize on the next pass.

Voila; perfectly- spaced sats!

HTHs,

-Slashy

Edited October 26, 2015 by GoSlash27

[regex]

How would I go about planning and executing that? I realize I can use the longitudes to gauge where they need to be, but how would I go about planning my maneuvers so that they end up where I want them to?

The same way you would from a rendezvous from a lower orbit. Notice that the maneuver node shows closest approach to the target in rendezvous mode. Now you can plan where your circularization burn will happen to place the next satellite in its correct position. You need 2 burns to accomplish this (Hohmann transfer + circularization) and it can be done quite early in RP-0 with the second-gen Agena engine (2 ignitions). If you're feeling froggy about that, pick up the RD-58 with five restarts, no problem. Once circularized, adjust your orbit to 23 hours, 56 minutes, 5 seconds (I think?) using RCS.

A good early Vostok replica will bring roughly 5 tons to LEO, which, combined with the American Agena engine, will do the trick just fine for three single launches. Use target mode during launch and make sure to match relative inclination with Engineer.

Edited October 26, 2015 by regex