1. A space capsule of mass 5070 kg orbits Mars with a period of 328 minutes. An
ID: 3278990 • Letter: 1
Question
1.
A space capsule of mass 5070 kg orbits Mars with a period of 328 minutes. An astronaut is riding in the space capsule. The astronaut weighs 750 N on earth.
Note: The computer solution uses the constants:
G=6.6742E-11 N-m2/kg2
mass of Mars = 6.42E+23 kg
radius of Mars = 3400 km
Format Check
4.44 pts.98%
Format Check
4.44 pts.98%
Format Check
4.44 pts.98%
(include units with answer)
Format Check
4.44 pts.98%
2% try penalty
Hints: 1,0 # tries: 0 B. What is the altitude of the space capsule?
(include units with answer)
Format Check
4.44 pts.98%
2% try penalty
Hints: 1,0 # tries: 0 C. What is the speed of the space capsule?
(include units with answer)
Format Check
4.44 pts.98%
2% try penalty
Hints: 1,0 # tries: 0 D. What is the normal acceleration of the space capsule?
(include units with answer)
Explanation / Answer
given
mass of mars, M = 6.42*10^23 kg
radius of mars, R = 3400,000 m
G = 6.6742*10^-11
mass of capsule, m = 5070 kg
Time period, T = 328 min
weight of astronaut on earth W = 750 N
a. Angular velocity , w = 2*pi/T = 2*pi/328*60 = 3.19267*10^-4 rad/s
b. altitude = h
now radius of orbit of capsule = r
then centripital acceleration = gravitational acceleratioon
w^2*r = GM/r^2
r = cuberoot(GM/w^2) = 7489.467 km
so altitude, h = r - R = 4089.467 km
c. speed of capsule, v = wr = 2391.139 m/s
d. Normal acceleration = w^2*r = 0.763 m/s/s
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