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Pd96 Pd96
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5 years ago
Mass   Radius   Orbital radius   Orbital period
Moon A   4.0 × 1020 kg   unknown   2.0 × 108 m   4.0 × 106 s
Moon B   1.5 × 1020 kg   2.0 × 105 m   3.0 × 108 m   unknown

Mithra is an unknown planet that has two moons, A and B, in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the mass of Mithra? (G = 6.67 × 10-11 N ∙ m2/kg2)
A) 1 × 1022 kg
B) 3 × 1022 kg
C) 1 × 1023 kg
D) 3 × 1023 kg
E) 1 × 1024 kg
Textbook 

College Physics


Edition: 1st
Authors:
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HotMathHotMath
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5 years ago
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More solutions for this book are available here
D

for moon A ::

orbital radius = r = 2 x 108 m

orbital time = T = 4 x 106 sec

Orbital speed is given as :

V = 2\pir /T = 2 (3.14) (2 x 108 ) / (4 x 106 ) = 314 m/s

let the mass of mithra = M

orbital speed is also given as

V = sqrt (GM/r)

314 = sqrt (6.67 x 10-11M / (2 x 108))

M = 2.95 x 1023 kg
1

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Anonymous
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