Q. 19

Expert-verifiedFound in: Page 354

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A proposed space elevator would consist of a cable stretching from the earth’s surface to a satellite, orbiting far in space, that would keep the cable taut. A motorized climber could slowly carry rockets to the top, where they could be launched away from the earth using much less energy. What would be the escape speed for a craft launched from a space elevator at a height of ? Ignore the earth’s rotation.

The escape speed for the craft would be

The craft is launched at a height of

The expression for escape velocity is given by :

Where, 'v' is escape velocity.

'G' is the universal gravitational constant.

'M' is the mass of the earth.

'R' is the radius, here 'R' is (R + h).

Substituting the values of G, M, R, h in the above equation. And solving for 'V' we get :

The escape speed for the craft would be

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