Kerbostationary Orbit Study
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Kerbostationary Orbit Study
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:
R_{KO} = (G x M x P^2/(4 x pi^2) )^(1/3)R_{KP}
Where R_{KO} 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 R_{KP} 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:
R_{KO}~2857.63 km
V_{KO}~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
Physics Division
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:
R_{KO} = (G x M x P^2/(4 x pi^2) )^(1/3)R_{KP}
Where R_{KO} 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 R_{KP} 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:
R_{KO}~2857.63 km
V_{KO}~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
Physics Division
BGraves Ensign
 Posts : 32
Join date : 20130319
Location : Canada
Re: Kerbostationary Orbit Study
Well done!!
I searched a lot for the Kerbostationary Orbit and I finally found it.
jb2512,
kerbonaut
I searched a lot for the Kerbostationary Orbit and I finally found it.
jb2512,
kerbonaut
jb2512 Ensign
 Posts : 31
Join date : 20130319
Age : 20
Location : Canada
Re: Kerbostationary Orbit Study
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.
BGraves Ensign
 Posts : 32
Join date : 20130319
Location : Canada
Re: Kerbostationary Orbit Study
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.
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.
FriedMünCake Ensign
 Posts : 16
Join date : 20130319
Location : Britain. In my laboratory (Aka My House)
Re: Kerbostationary Orbit Study
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.
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.
BGraves Ensign
 Posts : 32
Join date : 20130319
Location : Canada
Re: Kerbostationary Orbit Study
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.
Majormarks Ensign
 Posts : 10
Join date : 20130319
Age : 23
Location : Britain
Re: Kerbostationary Orbit Study
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 stepbystep 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".
BGraves Ensign
 Posts : 32
Join date : 20130319
Location : Canada
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