Q. 77

Expert-verifiedFound in: Page 334

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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

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.

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.

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.

From the given diagram we can find the r_{a} and r_{b}

and

From the law of conservation of momentum, we get

L_{a} = L_{b}

L_{a} and L_{b} are angular momentum

Substitute values in equation (1) and solve for v_{b}

_{}

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.

First find the value of r_{c} 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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