Chapter 8: Q.14 (page 199)

A satellite orbiting the moon very near the surface has a period of $110$ min. What is free-fall acceleration on the surface of the moon?

Short Answer

Expert verified

$g_{m o o n} = 1.58 m / s^{2}$

Step by step solution

Given information

Given in the question that, A satellite orbiting the moon very near the surface has a period of $110$ min.

Period of

Given:

$T_{sat} = 110 \min$

$T_{sat} = 110 \min \times \frac{60 s}{1 \min}$

$T_{sat} = 6600 s$

Step 3:A satellite is orbiting the moon

When a satellite is orbiting the moon at a constant speed, the only force that is acting on it is the gravitational force from the moon.

$\sum F = m g_{m o o n} = m a_{r}$

$m ̸ g_{moon} = m ̸ a_{r}$

$g_{moon} = \frac{v_{s a t}^{2}}{r}$

$g_{moon} = \frac{v_{sat}^{2}}{1.74 \times 10^{6}}$ (2)

$v_{sat} = \frac{2 π r}{T}$

$v_{sat} = \frac{2 π \times 1.74 \times 10^{6}}{6600}$
$v_{s a t} = 1.66 \times 10^{3} m / s (2)$

From (1) and(2)

$g_{moon} = \frac{{[1.66 \times 10^{3}]}^{2}}{1.74 \times 10^{6}}$

$g_{m o o n} = 1.58 m / s^{2}$

Final answer

The free-fall acceleration on the surface of the moon is

$g_{m o o n} = 1.58 m / s^{2}$

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A satellite orbiting the moon very near the surface has a period of $110$ min. What is free-fall acceleration on the surface of the moon?

Short Answer

Step by step solution

Given information

Period of

Step 3:A satellite is orbiting the moon

Final answer

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A satellite orbiting the moon very near the surface has a period of 110min. What is free-fall acceleration on the surface of the moon?

Short Answer

Step by step solution

Given information

Period of

Step 3:A satellite is orbiting the moon

Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Famous Physicists

Oscillations

Conservation of Energy and Momentum

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Kinematics Physics

Study anywhere. Anytime. Across all devices.

A satellite orbiting the moon very near the surface has a period of $110$ min. What is free-fall acceleration on the surface of the moon?