(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 400 km, much less than RE = 6370 km.) 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 spacecraft 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.”
(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
400 km, much less than RE = 6370 km.) 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 spacecraft 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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