(a) Calculate how much work is required to launch a spacecraft of mass m from the surface of the earth (mass mE, radius RE) and
place it in a circular low earth orbit, that is, an orbit whose altitude above the earth's surface is much less than RE. (As an example, the International Space Station is in low earth orbit at an altitude of about 400km, much less than RE = 6370km .) Ignore the kinetic energy that the spacecraft has on the ground due to the earth’s rotation.
(b) Calculate the minimum amount of additional work required to move the space craft from low earth orbit to a very great distance from the earth. Ignore the gravitational effects of the sun, the moon, and the other planets.
(c) Justify the statement "In terms of energy, low earth orbit is halfway to the edge of the universe.
(b) Calculate the minimum amount of additional work required to move the space craft from low earth orbit to a very great distance from the earth. Ignore the gravitational effects of the sun, the moon, and the other planets.
(c) Justify the statement "In terms of energy, low earth orbit is halfway to the edge of the universe.
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The acceleration due to gravity is g = 9.81 m/s^2
We have to find
(a) Magnitude of the gravitational force exerted on the raindrop by earth
(b)Magnitude of the gravitational force exerted on the earth by the raindrop
(a) The formula to calculate the magnitude of the gravitational force exerted on the raindrop by the earth is
Substituting the values, the gravitational force exerted on the raindrop by the earth is
(b) According to Newton's third law,
If F' is the gravitational force exerted on the earth by the raindrop, then
Here, the negative sign indicates that both forces act in opposite direction.
The gravitational force exerted on the earth by the raindrop is
And the magnitude of the gravitational force exerted on the earth by the raindrop is
Thus, the magnitude of both forces is equal.