Tuesday 17 January 2012

astrophysics - Calculating Orbital Period

I was using this formula to calculate the orbital period of a satellite in days:




T = sqrt[(4*pi^2)*R^3/GM-center]




Where R^3 is the radius of the orbit, or distance of the semi-major axis, G is the gravitational universal constant, and M-center is the mass of the object being orbited.



I'm attempting to calculate the orbital period for a planet that has a diameter of 5,124 kilometers, or 804,500,000/157 meters, and a mass of 5.526*10^13 Kilograms.



The star, which substitutes M-center, has a mass of 3.978*10^30 Kilograms. The length of the semi-major axis is 2.3AU, or 3.44*10^11 meters.



When substituted, I get:




T = sqrt[(4*pi^2)*(3.44*10^11)^3/(6.674*10^-11)*(3.978*10^30)




I simplified this too:




T = sqrt[(1.607094708736*10^33)/(6.674*10^-11)*(5.5616^13)




Which further simplifies too:




T = sqrt(1.607094708736*10^33)/(2.656092*10^20)




Something definitely seems wrong at this point. But, this comes out to:




T = sqrt(6.0505988073304689747192491826337340724643574093066053*10^12)



T = 2.459796*10^6




I find it hard to believe that it takes a planet that long to orbit around a star that is only 2.3AU away from it. Obviously, I am doing something very wrong, but I simply do not know where.



Somewhere, I am missing something.

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