Compute the value of g at a height of 4RE above the surface of the earth, given that the mass and radius of the earth (RE) have their usual values.*1 point0.39 m/s^20.42 m/s^20.49 m/s^23.90 m/s^2
Question
Compute the value of g at a height of 4RE above the surface of the earth, given that the mass and radius of the earth (RE) have their usual values.*1 point0.39 m/s^20.42 m/s^20.49 m/s^23.90 m/s^2
Solution
The formula for gravitational force is:
g = GM/r^2
where:
- G is the gravitational constant (6.674 * 10^-11 m^3 kg^-1 s^-2),
- M is the mass of the Earth (5.972 * 10^24 kg),
- r is the distance from the center of the Earth.
In this case, the height above the Earth's surface is 4RE, so the distance from the center of the Earth is 5RE (since RE is the radius of the Earth).
So, we substitute these values into the formula:
g = (6.674 * 10^-11 m^3 kg^-1 s^-2 * 5.972 * 10^24 kg) / (5 * 6.371 * 10^6 m)^2
After calculating the above expression, we get the value of g to be approximately 0.39 m/s^2.
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