How to calculate T from a and G

[SmarterThanMe]

G'day All. It's been a while since I did any interesting maths. So I think I've stuffed something.

I'm trying to make a spreadsheet function to a (the semimajor axis) from T (orbital period in seconds, the input variable) and G (gravitational parameter).

I'm certain that I'm calculating G correctly (because I've borrowed from the KSP Battery Calculator, which definitely gets it right. But otherwise, I think I'm stuffing it.

I start with:

T=2À(a

3

G)

1/2

Then moving a out:

T/2À=(a

3

G)

1/2

(T/2À)

2

=a

3

G

T

2

/4À

2

=a

3

G

(T

2

/4À

2

)/G=a

3

((T

2

/4À

2

)/G)

1/3

=a

I think all my maths is right there (although I could be wrong). This gives me a spreadsheet formula of

=(((G8^2)/(4*(PI()^2)))/C6)^(1/3)

...where G8 is the time variable, and C6 is G.

Where am I going wrong?

[SmarterThanMe]

BTW, I apologise for my dodgy formatting... Trust me, my literal back of napkin notes for this are far worse.

[TythosEternal]

Period = 2 pi sqrt(a^3 / mu)

So...

((Period / (2 pi))^2) mu)^(1/3) = a

Basically, you need to divide by the gravitational parameter in the original expression... Keep in mind it has units of length-cubed-over-time-squared.

[Claw]

Also, a lot of people mess up orbital distances and forget that they are from the center of the planet. Not the height above the terrain. I believe Kerbin Radius = 600km.

Cheers,

~Claw

[SmarterThanMe]

Period = 2 pi sqrt(a^3 / mu)

Wait. It's ﾗμ NOT /μ? Argh. Well that explains a lot (for example, why my physics marks weren't crash hot at the end of high school).

Edited August 23, 2014 by SmarterThanMe