Maths help.

[uncle natzer]

I'm really starting to get into the really nerdy side of this game but I'm have problems figuring out some of the maths, mainly the Orbital Period. I cannot figure out where I am messing up. I'm using an altitude of 2,863,330m because I know the period should be 6hrs but I cannot get 21,600 seconds for the life of me. Radius of Kerbin is 600,000m and the Gravitational Parameter I've gotten is 3530.461, both of those I pulled from the wiki. 681,835,704 is the answer I keep getting.

This is the webpage I've gotten the formula from, https://en.wikipedia.org/wiki/Orbital_period.

If anyone can help me by breaking down the maths so I can figure out what I'm doing wrong that would be amazing. 

[manaiaK]

In the game, the tracking station gives the gravitational parameter for Kerbin as 3.532 x 10¹² m³s^-2, which is 10⁹ greater than your value.  That could be it.

Edited December 1, 2015 by manaiaK

[GoSlash27]

You rang?

The velocity of an orbit is sqrt (GM/r). The period of an orbit is circumference/v, or 2pir/sqrt(GM/r).

Rearranging that, we get p=2pir*sqrt(r/GM)

p=2pi*sqrt(r^3/GM)

Rearranging for r as a function of p

p/2pi= sqrt (r^3/GM)

(p/2pi)^2= r^3/GM

GM(p/2pi)^2= r^3

cuberoot(GM(p/2pi)^2)= r

so plugging in the values...

cuberoot((6.67384x10^-11)(5.29158x10^22)(21,600/2(3.14159))^2)= r

cuberoot((3.53156x10^12)(3.43775x10^3)^2)=r

cuberoot(4.17364x10^19)=r

3.46874x10^6=r

Altitude= r-600,000

Altitude= 2,868,740m

 

Hit me up if you have any questions!

Best,

-Slashy

Edited December 1, 2015 by GoSlash27

[rockbloodystar]

10^9 would be km cubes compared with m cubes.

 

somewhere the units are inconsistent, always pays to double check.