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Keostationary Orbit Above a Specific Point


RayLuxeYacht
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I have a contract to put a satellite into orbit above a specific point on Kerbin.  I can get a keostationary orbit easily, but I can't figure out how (even to approach) ensuring I'm above a specific spot when I get keostationary.  I have looked through the forum and the closest advice I've seen is to establish a circular orbit a bit higher than keostationary and burn retrograde a bit ahead of where you want to be.  Even so, I can't figure out how to position the ship so I wind up in the right place after the burn.  I don't use Mech Jeb (yet), I want to build skill and understanding in plain vanilla, then add mods.  Nothing against mods, and I do understand how using them can help one understand as opposed to relying on them as a "crutch."  So...what should I be thinking about?  Although I'm not at all mathophobic, I feel like I should be able to "seat of the pants" this.

~~~~~EDIT~~~~

Just want to say thanks.  Yes, make an orbit slightly smaller (if you want to catch up to the spot) or slightly bigger (if you want the spot to catch up to you), get into position, then adjust orbit.  I did have to time warp 18 days (I made a few false starts and had to correct) but ultimately go it done.

Edited by RayLuxeYacht
Gratitude.
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It's not hard to do it stock... What I do is to first find the position on Kerbin... there should be a marker. I get myself into a keostationary, orbit around to the AP, then burn retrograde for a little bit. This will bring your PE in closer, and allow you to orbit faster than Kerbin is actually turning. At this point I'll start time advancing, and watching the position I'm supposed to over, until it gets close enough for the contract to say I'm in position (It will start blinking). The go back to the AP and re-circularize the orbit, and done.

I hope this made sense

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I actually figured this out with only a little bit of math, but this was for Eve in a modded game and not Kerbin. The logic is similar, though.

Kerbin rotates every six hours, approximately. The exact number is in the Wiki. Also in the Wiki is the altitude you want for a stationary orbit. So from low Kerbin orbit, figure out how long your craft will rise from the start of your manoeuvre to stationary altitude; the projected Kerbin AP should have a "time to" value, but subtract the time before your manouevre from that.

Divide six hours into that "time-to" value to get a percentage, and multiply that by 360 degrees to get some angle value. Aim your projected Kerbin AP that many degrees counter-clockwise from your target on the ground right before you start your burn. This will likely mean many postponements of your burn until you get close enough.

Then close your stationary orbit at AP. If you hit the altitude just right, you could try burning retrograde in surface mode until you get 0 m/s. You can fiddle with the orbit from there.

Duna Stationary Side-Note: You want to be 0 m/s in target mode with Ike as the target, rather than 0 m/s in surface mode, if you want to attempt a stationary orbit at Duna. Or Duna's moon Ike will eat your satellite sooner or later.

 

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To do it by the seat of your pants, yes, you have to go for a different-sized orbit and wait for a while and let your positions line up. The more comfortable you are about it, the bigger the difference you can use between your initial and destination orbit -- and the faster you can get things to align. If your initial orbit is circular, one little tip is to eyeball how much of an angular change there is between your ship and your target during one orbit. Your final position will be correct if your current angle is one quarter of that number when you start your burn to match the final orbit.

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15 hours ago, RayLuxeYacht said:

Yes, make an orbit slightly smaller (if you want to catch up to the spot) or slightly bigger (if you want the spot to catch up to you), get into position, then adjust orbit.  I did have to time warp 18 days (I made a few false starts and had to correct) but ultimately go it done.

A very rough method: when low orbit, to put a satellite above KSC start burn to prograde above the crater. Western or eastern rim, depends on TWR. The satellite reaches an apoapsis above KSC, then circularize.

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I tend to work this sort of thing through backwards.  You want to end up above an arbitrary point and stay there.  The easy way to do this is going to be in two burns from a circular orbit, one to put apoapsis at the right height, then the other to circularize.  Probably the easiest visual marker's going to be the point you want to end up over.  This means you'll do x + .5 orbits, while the body rotates y + .5 times.

For Kerbin, let's see how that looks for x=2, y=1:

Let p be the orbital period for the transfer orbit in seconds

2.5 * p = 1.5 * 21549.425

p = 12929.655

Plug the orbital period and apoapsis into an orbital calculator and you'll have your initial orbit.

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KSP really doesn't give you enough information or reference points.  But -- The TL;DR version is that you need to start with a circular orbit at 864.3 km, and then when you're directly above the target, burn to geosynchronous orbit height - after 2.5 orbit or 1.5 days you then need to circularise - and you'll be directly over the target again.

You need maths to figure this out.

KSP really doesn't give you enough information or reference points but we do have both of these points - the point directly above the target and the point where geosynchronous is.

YZDiZHR.png

We need to find the initial orbit where we can burn and (eventually) reach the target orbit, with the transfer burn being done directly above the target.

There's a lot more - but here's some maths if you're interested in how I determined the altitude to start from -- https://www.dropbox.com/s/ibtrhq7kya728on/geosynchronous.pdf?dl=0

 

Edited by bigcalm
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