Re: conplaneteering
| From: | Cian Ross <cian@...> |
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| Date: | Sunday, February 13, 2005, 5:25 |
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On Friday 11 February 2005 03:02 pm, Mark J. Reed wrote:
> I'm trying to calculate the orbital period of an Earth-sized planet at
> 15 AUs out from a star that's about 7.5 times the mass of the Sun. I'm
> guestimating around 50 years, but Kepler's laws don't seem to be much
> help when looking for absolutes; you need a known quantity within the
> same solar system to compare against. Can anyone point me at the
> correct formulae?
>
> Thanks.
Working from Szebehely and Mark, _Adventures in Celestial Mechanics_,
with their statement of Kepler's Law and a few constants from one of
the appendices:
a^3 = GM T^2 / 4pi^2
a = semi-major axis
M = mass of primary
T = orbit period
Rearrange to:
T^2 = 4pi^2 a^3 / GM
T = sqrt(4pi^2 (15 AU)^3 / (1.5 GMsol)
T = 2pi sqrt((15 * 1.496e11 m)^3 / (1.5 * 1.327e20 m^3/sec^2)
T = 2pi sqrt(1.130e37 m^3 / (1.991e20 m^3/sec^2))
T = 2pi sqrt(5.676e16 sec^2)
T = 2.382e8 sec = ~2757 Terra-days = ~7.55 Terra-years
CKR
cian@cox-internet.com
http://crlh.tzo.org/~cian/CR/conlang
Noimma loku:wiapoiemonar. (I think therefore I conlang.)