(10%) Problem 9: A satellite m 500 kg orbits the earth at a distance d = 242 km,

Question

(10%) Problem 9: A satellite m 500 kg orbits the earth at a distance d = 242 km, above the surface of the planet. The radius of the earth 1s = 6.38 × 106 m and the gravitational constant G = 6.67x 10 1 1 N m4kg2 and the Earth's mass is m,-5.98 × 10-4 kg What is the speed of the satellite in m/s? Grade Sumi Deductions Potential sin) cotan asinO tan0 It acos() Submissions Attempts ren (L%, per atte cos) *1 23 detailed vie atan)acotan() sinhO cosh tanh) cotanh() °Degrees Radians END BACKSPACE DELCLEAR Submit Hint Hints: 1 % deduction per hint. Hints remaining: 5 Feedback: 1% deduction per feedback. Submission History Answer Hints Feedback

Explanation / Answer

Speed of a satellite in a orbit of radius is v =sqrt(G*M/R)

G is the universal gravitational constant

M is the mass of the earth

R is the radius of the orbit = (2.42*10^5)+(6.38*10^6) = 6.62*10^6 m

then V = sqrt(G*M/R) = sqrt(6.67*10^-11*5.98*10^24/(6.62*10^6)) = 7762 m/sec = 7.76 km/sec

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