Question

(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.

Answer 1

Answer:

(a) The Work need to   place spacecraft into low orbit is$Gmm_{E} /2R_{E}$

(b) Additional Work need to  place the spacecraft far away from the earth is

$Gmm_{E} /2R_{E}$.

(c) From part(a) and part(b) we observe the Both quantities are equal.

Explanation:

Explanation is in the following attachments