A free-fall experiment is performed on a newly discovered spherical planetoid (\

Question

A free-fall experiment is performed on a newly discovered spherical planetoid ("planet X"), where an 80 kg astronaut dropped a rock from a height of 216 cm and its falling time was electronically measured to be 1.0392 sec. The planet's circumference was determined to be 36.74 x 10 m by geometrical metheds. The astronaut is fully aware that h = 1/2 g t^2. Determine the following: The weight of the astronaut on the planet's surface: The mass M of planet X: A satellite's orbital speed v_orb near planet X's surface: A satellite's orbital period T near planet X's surface: The altitude h of a geo-synchronous satellite orbiting planet X if its rotational period is 0.7 S days:

Explanation / Answer

a)

W = mg

g = 2h/t^2 = 2*2.16/1.0392^2 = 4 m/s2

W = 80*4 = 320 N

b)

g = GM/R^2

M = gR^2/G = 4*(36.74*10^6/2*pi)^2/6.67*10^-11

M = 20.525*10^23 Kg

C)

R = 5.85*10^6 m = circumference/ 2pi

V = sqrt (GM/R), V = sqrt (6.6*10^-11*20.525*10^23/5.85*10^6)

V = 4812 m/s

d)

T = 2*pi* Sqrt (R^3/GM), given R and M is also Known

e)

T = 2*pi* Sqrt ((R+h)^3/GM)

0.75*24*3600 = 2*pi* Sqrt ((R+h)^3/GM),

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