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Q. 77

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 334

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Short Answer

A satellite follows the elliptical orbit shown in FIGURE P12.77. The only force on the satellite is the gravitational attraction of the planet. The satellite’s speed at point a is 8000 m/s.
a. Does the satellite experience any torque about the center of the planet? Explain. b. What is the satellite’s speed at point b? c. What is the satellite’s speed at point c?

a) Satellite will not experience any torque at the center of the planet.

b) Speed at point b is 2000 m/sec

c) Speed at point c is 4000m/sec

See the step by step solution

Step by Step Solution

Part(a) Step1: Given information

A satellite is orbiting the planet in elliptical orbit.

It is experiences the gravitational force of attraction.

The speed of the satellite at point a, is 8000 m/sec.

Part(a) Step2: Explanation

The torque is calculated as

torque = Force x perpendicular distance

As gravitation force is parallel to position of satellite, so it will not generate any Torque.

Part(b) Step 1: Given information

A satellite is orbiting the planet in elliptical orbit.

It is experiences the gravitational force of attraction.

The speed of the satellite at point a, is 8000 m/sec.

Part(b) Step 2: Explanation

From the given diagram we can find the ra and rb

and

From the law of conservation of momentum, we get

La = Lb

La and Lb are angular momentum

Substitute values in equation (1) and solve for vb

Part(c) Step 1: Given information

A satellite is orbiting the planet in elliptical orbit.

It is experiences the gravitational force of attraction.

The speed of the satellite at point a, is 8000 m/sec.

Part(c) Step2: Explanation

First find the value of rc from the figure

use the trigonometric ratio

From the momentum conservation on point b and c

Substitute values in equation (2) and solve

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