In an attempt to land on the surface of the moon, an unfortunate astronaut (m =

Question

In an attempt to land on the surface of the moon, an unfortunate astronaut (m = 70 kg) miscalculates and misses. At closest approach he is 100 m above the surface and traveling tangentially at 3 km/s. The mass of the moon is 7.35×10^22 kg and the moon has a radius of 1.7×10^6 m.

a.   Is he captured by the moon’s gravity field? If not, how much excess energy does he possess?

b. How much slower would he need to be traveling to be captured into a closed orbit?

c. How much slower would he need to be traveling to be captured into a circular orbit?

d. Suppose that instead of the normal lunar mass, the moon suddenly had the mass of 100 suns! (This would be bad for us on Earth...) If the astronaut is 1.75m long, what is the difference between the lunar gravitation force on his feet and the force on his head (assume his feet point towards the moon)? Keep as many decimals as you can when running these calculations, else you’ll be confused!

Explanation / Answer

Force on astronaut due to Moon's gravity is

F= GMm/R^2 = 6.67*10-11* 7.35×10^22*70/(1.7×10^6)^2 = 118.7 N

Force on Man is m*v^2/R = 70*9*10^6/(1.7*10^6) = 370.58 N

No, He is not captured by Moon's Gravity,

Excess Energy Possesed is 370.58 N-118.7 N = 251.88 N

c. for a circular orbit, m*v^2/R = 70*v^2/(1.7*10^6) = 118.7

So, v = 1.697 Km/s

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