Earth's gravitational field strength

AI Thread Summary
To determine the altitude where Earth's gravitational field strength is two-thirds and one-third of its surface value, the radius of Earth (6.371 x 10^3 km) must be used in calculations. The gravitational force formula F = GMm/r^2 is relevant, but the mass of the second object is not needed as it cancels out. The acceleration due to gravity at the surface is 9.8 m/s², which can be adjusted for the desired gravitational strength at the specified altitudes. The key is to set the radius equal to the Earth's radius plus the altitude and solve for the altitude. Understanding these relationships is crucial for solving the problem accurately.
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Homework Statement


(a) Find the altitude above the Earth's surface where Earth's gravitational field strength would be two-thirds of its value at the surface. Assume re = 6.371 multiplied by 10^3 km.
wrong check mark km
(b) Find the altitude above the Earth's surface where Earth's gravitational field strength would be one-third of its value at the surface.
wrong check mark km

[Hint: First find the radius for each situation; then recall that the altitude is the distance from the surface to a point above the surface. Use proportional reasoning.]

Homework Equations


F = GMm/r^2

The Attempt at a Solution


I have tried it and I am either calculating wrong or setting it up wrong... or both. One problem I see with the formula is that it doesn't have the mass of the second object.. so I don't know what to do there.
 
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you do not need to know the mass of the second object. F=ma and the masses of the second object cancel out. a=9.8m/s^2 on Earth and at the point above the Earth a=9.8/3 let r=radius of Earth + altitude. then plug in and solve for a.
 
Sorry but that still isn't helping me. Are you just using the F=ma formula?
 
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