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Example G.5: Acceleration due to Gravity at a Height

Example:

The acceleration due to gravity at a height h above the surface of the Earth is 50% of the value at the Earth's surface. Find the value of h.

Given: radius of the Earth R = 6400 km.

Solution:

Equation (G.6), reproduced below for convenience, may be directly used.

Here gh /g = 0.5. Therefore h/R = (1/0.707) - 1 = 0.414, and h = 2651 km.

Note: Equation (G.7) is applicable only when h is negligible compared to the radius of the Earth.

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