> Since I'm curious about orbit periods, can any of you physics wizards
> suggest a calculation to determine orbit period around a planet given
> distance and mass of central planet (or star?)
>
> joe University of Missouri - Columbia
> [email removed] [phone removed]
Pulling out my handy copy of "Golstein's Tome of Mystical Classical
Mechanics," we find that tha appropriate expression is:
T = 2*pi*a^(3/2)*(m/k)^(1/2)
(This is the essence of the Third Law of Kepler The Mystical.)
Here, a is the semi-major axis of the orbit (i.e. radius, if you assume
a spherical orbit). m is the "reduced mass" of the two-body system:
m = m(1)*m(2)/(m(1)+m(2))
If ,say, m(1)>>m(2) this reduces to the approximation m=m(1). (This will
be the case when you consider the typical spacecraft orbiting a planet.)
Finally, k is the force constant of the potential; in the case of gravity
we have k = G*m(1)*m(2), where G =6.67E-11 Nm^2/kg^2 (I think...)
Putting this all together, then, we have:
T^2 = (4*pi^2*a^3)/(G*m(1))
Now, as to units...assuming a in km, M in earth masses (Me = 5.976E+24 kg),
we obtain:
T^2 = (0.99E-4)*a^3/M with time T in seconds
= (1E-4)*a^3/M (approximating)
So, for example, orbiting Earth (M=1) at an altitude of 100km (a=6440)
we get T=5184 s = 1.44 h. This assumes I did my math right, but I did
double check by calculating the Earth's period around the sun (with
a back-of-the-envelope calculation, I got .95 years...that seems good
enough to me...)
- ---Marty "Wow! My first post to the TML in years" Jarrio
- ---gt4534b@prism.gatech.edu