QUESTION 16 The Moon which has mass of about 7.35 x 1022 kilograms, and it orbit

Question

QUESTION 16 The Moon which has mass of about 7.35 x 1022 kilograms, and it orbits the Earth with an average orbital distance of 384,400 kilometers. Calculate the following for the the magnitude of the average gravitational force exerted by the Earth on the Moon two decimals) Newtons (use scientific notation and round the coefficient to m/s (use scientific notation and round the coefficient to two decimals) the magnitude of the acceleration due to Earth's gravity at Moon's orbit the orbital velocity of the Moon the orbital period of the Moon the escape velocity from Earth's gravity for a spacecraft launched from the Moon's orbit km/s (round your answer to two decimals) days (round your answer to the nearest integer) km/s (round your answer to two decimals) Earth's mean radius is RE" 637 x 106 m; Earth's mass is ME . 5.97x 1024kg

Explanation / Answer

F = G M m / r^2

F = (6.67 x 10^-11) (5.97 x 10^24) (7.35 x 10^22) / (384400 x 10^3)^2

F = 1.98 x 10^20 Newtons ....Ans

a = F / m_moon = 2.70 x 10^-3 m/s^2 .....Ans

a = v^2 / r

v = sart(2.70 x 10^-3 x 384400 x 10^3) = 1018 m/s

Or 1.02 km/s ............Ans

T = 2 pi r / v = 2372641.5 sec

T (days ) = 27.5 days ......Ans

TE = - G M m / 2 r  

m v^2 /2 = G M m / 2 r

v = sqrt( G M_earth / r )

v =1.02 km/s ...Ans

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