Kerbol Gravitational Parameter

[Black Haired Guy]

With the release of .17 we are all very excited to begin our interplanetary journeys. But the usual trial and error method doesnt work too well...and will usually involve sending kerbals off into space for 40 days (at least) before knowing the failure of our mission.

So we bust out some Hohmann Transfers!

Using the numbers from ksp wiki, I did my calculations for an Eve transfer (large gravity 'target', low delta V requirement) and I obtained a 854 hour flight or 35.6 days. Thats not too bad.

But checking the Grav. parameter of Kerbol by deriving the orbital velocities of known Kerbin, Eve, and Duna gave an error. Everything orbits faster than it should. But it doesnt.

So I reversed the math to solve the grav parameter of Kerbol (Ill call it 'u'). a/v^2=1/u or v^2/a=u

For all 3 of the innermost planets I arrived nearly at the value of 1.18E9 instead of the given 1.679E9. Theres still was some disagreement to those 3 values but the approximation was close enough.

My new Hohmann Transfer time was calculated to now be 42 days. Thats a 19% error! Which is bad for spaceflight!

A quick check with a mechjeb probe revealed time to periapsis (of 9,833,000km, Eves Semimajor axis) to be 42 days and 4 hours.

This would also mean that Kerbol is less massive than once previously thought.

My big question is...am I the first to realize this or has this already been noted?

[softweir]

It may be the orbits of the planets weren't calculated at all precisely. After all, they run on rails, not by gravity! Then again, it might well be that Kerbol's "mass" has been adjusted slightly, or even that the wiki is simply incorrect.

[vexx32]

Hmm. Maybe we should double-check that their orbits obey the laws of physics haha.

[Nadrek]

maltesh put together a spreadsheet of celestial body orbits that might be useful for this:

http://kerbalspaceprogram.com/forum/showthread.php/21251-17-Planet-information?p=272764&viewfull=1#post272764

[D0SBoots]

I made a hacked up ship and flew into several close, nearly circular orbits around the sun. (These were separate runs, because the kraken got me after each one.) Here's my raw data:

<table><tr><td></td><td>Apoapsis</td><td>Periapsis</td><td>Velocity</td><td>Altitude @given velocity</td><td>Half-orbit time</td></tr>

<tr><td>Orbit 1</td><td>1499999195 m</td><td>1499997471 m</td><td>25797.2 m/s</td><td>1499998333 m</td><td>214501 s</td></tr>

<tr><td>Orbit 2</td><td>50110046 m</td><td>50109778 m</td><td>61326.8 m/s</td><td>50109912 m</td><td>15968 s</td></tr>

<tr><td>Orbit 3</td><td>10090841 m</td><td>10090173 m</td><td>65688.35 m/s</td><td>10090438 m</td><td>12993 s</td></tr>

</table>

Running the numbers, Kerbol's radius has to be 261595+-10 km. I figured it's probably a round number, so I used 261600km in the rest of my calculations.

I used velocity and semi-major axis for calculating the gravitational parameter, because there's much less error in those numbers than in the period. Based on that, I get mu = 1.172334+-.000001 * 10^18 m^3/s^2.

I'm going to go update the wiki now.