Q. 63

Expert-verifiedFound in: Page 356

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A 55,000 kg space capsule is in a 28,000-km-diameter circular orbit around the moon. A brief but intense firing of its engine in the forward direction suddenly decreases its speed by 50%. Thiscauses the space capsule to go into an elliptical orbit. What are the space capsule’s (a) maximum and (b) minimum distances from the center of the moon in its new orbit?Hint: You will need to use two conservation laws.

a) Maximum distance from center is 14000 km

b) Minimum distance from center is 2000 km

Mass of the capsule, m_{Capsule}=55,000 kg

Diameter of the orbit, D=28000km=28000 x 10^{3}mDecreases in speed, is 50%

Given that the velocity decreases to half.

By conservation of angular momentum, at that instance, the capsule is at maximum distance from the moon.

So if we can say in the new orbit, the maximum distance from the center of the moon is equal to the radius of the orbit

So,

Max distance is 14000 km.

Mass of the capsule, m_{Capsule}=55,000 kgDiameter of the orbit, D=28000km=28000 x 10^{3}mDecreases in speed, is 50%

The velocity of the satellite in orbit can be calculated by

Where

M = mass of the moon,

G = gravitational constant and

r = orbital radius.

Substitute values and calculate velocity as

The velocity of the satellite at apogee

Now use momentum conservation

Now use energy conservation

Minimum distance is 2000 km.

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