Question

Two satellites are in circular orbits around the earth. the orbit for satellite a is at a height of 540. km above the earth's surface, while that for satellite b is at a height of 890. km. find the orbital speed for satellite a and satellite

b.

Answer 1

Answer: Va = 7,625 m/s Vb = 7,404 m/s Given: A = 486,000 m B = 901,000 m G = 6.67428E-11 m^3/kg-s^2 M = 5.9736E+24 kg r = 6,371,000 m Recall that you need the actual orbital distance from the *center* of the Earth, giving radius plus altitude: rA = 6,857,000 m rB = 7,272,000 m Equation: V = SQRT { GM / r } Solve for A Va = SQRT { [ (6.67428E-11 m^3/kg-s^2) * (5.9736E+24 kg) ] / (6,857,000 m) } Va = SQRT { [ 3.9869 m^3/s^2 ] / (6,857,000 m) } Va = SQRT { 58,144,202 m^2/s^2 } Va = 7,625 m/s Solve for B Vb = SQRT { [ (6.67428E-11 m^3/kg-s^2) * (5.9736E+24 kg) ] / (7,272,000 m) } Vb = SQRT { [ 3.9869 m^3/s^2 ] / (7,272,000 m) } Vb = SQRT { 54,826,016 m^2/s^2 } Vb = 7,404 m/s