A satellite is to be launched to orbit round the Earth. In which of the following directions of launching would the energy required be the least?
(Note: The Earth rotates from West to East.) Ans: A
A: due east from a point on the equator
B: due west from a point on the equator
C: due north or south from a point on the equator
D: from the North pole or the South pole
-Is the gravitational potential energy the same at any point on the surface of the Earth? (Because they needed the same amount of work to move from infinity to their position)
-As the orbit can vary and involve different energy after launching, how to decide the least launching energy?
-Although A,B,C has the highest total energy (their KE from circular motion is highest by v=wr), I don't think whoever contains the highest energy at this moment represents a lower launching energy. Work done after launching is needed and it depends on the orbit.(Direction, speed, radius etc.)
- 天同Lv 74 年前最愛解答
Answers to your three questions:
1. Yes. Assume the earth is a perfect sphere, then objects at any point on the earth surface are all at the same distance from the earth centre. Hence, they possess the same gravitational potential energy.
2. A stable orbit is one with constant height from earth surface. When a satellite is in a stable orbit, its total energy doesn't change.
What you have said is the situation BEFORE the satellite enters into orbit. During such period, its kinetic energy is decreasing, with the gain in gravitational potential energy.
3. Not quite understand what you ask. Once a satellite enters into a given stable orbit, its total energy is fixed. This is irrespective the launching point.
It is only that a satellite launched along the equator could take advantage of the rotational motion of the earth. In case the satellite is planned to enter into a polar orbit, launching at the equator won't help much.