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ilovebeaches ilovebeaches
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11 years ago
The acceleration due to gravity, g, is constant at sea level on the Earth's surface. However, the acceleration decreases as an object moves away from the surface due to the increase in distance from the center of the Earth. Derive an expression for the acceleration due to gravity at a distance h above the surface of the Earth, gh. Express the equation in terms of the radius of the Earth RE, g and h.
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#1
11 years ago
Fg = FG
mg = (Gm1m2)/h^2

g = (Gm)/h^2
wrote...
#2
11 years ago
The formula for the acceleration due to gravity "g" at the surface of the Earth is;
g = GM/R^2

The formula for the acceleration due to gravity at a height "h" above the Earth's surface is;
g' = GM/(R+h)^2

The first eq. can be used to express GM in terms of g and substituted in the second eq;
From first eq;
GM = gR^2

Sub. into second eq;
g' = gR^2/(R+h)^2
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