(a) What is the radius of said orbit? (b) What parameters are conserved throughout the orbit? Calculate one of them

Question

A satellite is inserted into a circular Earth orbit with period = 8 hours.

Answer to part a) r = 20,307 km

Answer to part b) specific energy = -9.8142 km^2/s^2 & specific angular momentum = 89, 969 km^2/s

Answer 1

A) You can use Kepler's Law and the R_orb and T_orb for the moon in order to find the R for the satellite using

T² = kR³. You can solve for k using the moon data and then solve for R using that k (It is a constant for all orbits around the earth. Or you can use the fact that R is proportional to T^2/3

Or you can solve for R by equating the gravitational force to the centripetal force. GM_em/R² = 4π²Rm/T² and solve for R

B) The specific energy and specific angular momentum mean the E/m and L/m respectively. v = 2πR/T and E/m = -E_K/m = -(1/2)v² (Virial equation for orbit says U + K = E) and the L/m = Rv You should use MKS throughout and convert at the end. The units given as solutions have km in them, so energy will not be Joules/kg for specific energy.

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