Kerbostationary Orbit Study

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Kerbostationary Orbit Study

Post by BGraves on Tue Mar 19, 2013 11:09 pm

The following is a copy of a report that was submitted March 11, 2013.

Kerbostationary Orbit Study
By BGraves

For my first study at the university, I decided to determine the altitude and velocity of a stationary orbit around the planet Kerbin, henceforth referred to as a Kerbostationary Orbit, or KO, and also to determine an estimate for the delta v required to get to this orbit. In order to determine the altitude of this orbit, I used this equation:

RKO = (G x M x P^2/(4 x pi^2) )^(1/3)-RKP

Where RKO is the altitude of the KO, G is the gravitational constant, M is the mass of the planet Kerbin, P is the length of a sidereal day (One rotation relative to the distant stars) on Kerbin, and RKP is the radius of the planet Kerbin.

This is the final calculation:
((6.61×10^(-11)×5.2915793×10^22×21600×21600)/(4 pi^2))^(1/3)-600000
~2 857 630 m

Now armed with the altitude, I could determine the velocity and delta v experimentally. I took a rocket of my own design, a rocket I named the "LH- Pioneer", and I brought it up to an orbit at the altitude I had calculated, and made the orbit as circular as I could. I recorded the speed, and I indeed discovered that my calculations were likely correct, to within a reasonable margin of error. While I was unable to be completely sure of my calculation (As I could never had gotten a perfectly circular orbit) I did indeed discover that where my craft, which was close to my calculated altitude, seemed to remain above the large desert of Kerbin. I simulated the flight for ~73 days before the desert had disappeared past the horizon of Kerbin. This means that it would take approximately 280 days for my craft to have been above every segment of the equator.

FINAL RESULTS:
RKO~2857.63 km
VKO~1010
Delta V~4250

Note: The delta v calculation is not very exact, as some problems with my orbit stabilization led to my delta v estimates to be higher than they should be. I am unsure how much the numbers have been affected, so allow for deviation when using these guidelines in designing of rockets.

BGraves
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Re: Kerbostationary Orbit Study

Post by jb2512 on Tue Mar 19, 2013 11:13 pm

Well done!!

I searched a lot for the Kerbostationary Orbit and I finally found it.

jb2512,
kerbonaut

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Re: Kerbostationary Orbit Study

Post by BGraves on Tue Mar 19, 2013 11:26 pm

jb2512 wrote:Well done!!

I searched a lot for the Kerbostationary Orbit and I finally found it.

jb2512,
kerbonaut


Why yes, but my calculation still needs to be proved more... rigorously. You might notice my new mission available in the kerbonaut thread.
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Re: Kerbostationary Orbit Study

Post by FriedMünCake on Wed Mar 20, 2013 2:39 pm

As a formal request, The Planetology Division would like to know the requirements for an equatorial geostationary orbit around Eve or Jool.

You may use the Kerbonautical Division if you require them in this assignment.

Best of luck

Doctor Francis Kerman
Planetologist - Planetology Division - University of Kerbol
BSE - Mathematics
Ph. D - Planetology.
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Re: Kerbostationary Orbit Study

Post by BGraves on Wed Mar 20, 2013 7:39 pm

Sure, I can calculate it for Eve. However, I'm not sure if the Jool calculation is possible, or even why you would need a geostationary orbit around an object with no surface features.

I'll find those values immediately.

EDIT: I'll put the values here as I find them.

EO (Evesynchronus Orbit) ~ 10 293 100 meters

JO (Joolsynchronus Orbit) ~ 14 943 100 meters

Note: The accuracy of these measurements seems inversely proportional to the size and mass of the celestial body. Actual values may differ by 50 km for EO, and 100 km for JO.
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Re: Kerbostationary Orbit Study

Post by Majormarks on Sun Mar 24, 2013 10:18 am

BGraves wrote:
Why yes, but my calculation still needs to be proved more... rigorously. You might notice my new mission available in the kerbonaut thread.

I saw this and decided to have a crack at it. Maybe I've just restated what's in the OP, but it was an interesting hour or so of maths.

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Re: Kerbostationary Orbit Study

Post by BGraves on Fri Mar 29, 2013 3:14 pm

Majormarks wrote:
I saw this and decided to have a crack at it. Maybe I've just restated what's in the OP, but it was an interesting hour or so of maths.

*snip*

Great step-by-step work there. However, recently the data submitted by MoShY as part of the verification isn't very promising for the validity of my equation. MoShY managed an extremely accurate and circular orbit at an altitude very close to the one I calculated, but he found that the ground below still moved from the point of view of the satellite, and couldn't even keep sight of the target area for more than thirty days before it disappeared over the horizon. Currently I have no explanation for this, other than "Kerbal Space Program isn't real life".
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