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Question
Suppose we go 200 km above and below the surface of the Earth, what are the g values at these two points? In which case, is the value of g small?
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Solution
d = 200 km = 200 × 103 m
RE = 6371 × 103 m
h = 200 km = 200 × 103 m
Variation of g’ with depth
g’ = `"g" (1 - "d"/"R"_"E")`
= `"g" (1 - (200 xx 10^3)/(6371 xx 10^3))`
= g (1 − 0.0314)
= g (0.9686)
g’ = 0.96 g
Variation of g’ with altitude
g’ = `"g" (1 - (2"h")/"R"_"E")`
= `"g" (1 - (2 xx 200 xx 10^3)/(6371 xx 10^3))`
= g (1 − 2(0.0314))
= g (0.9372)
g’ = 0.94 g
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