本题目来源于试卷: Fields D.1 Gravitational Fields & Potential ，类别为 IB物理学
[问答题]
A satellite of mass g+:5n*0l w cxskw8 bt+l43uo f* hrfud5ox ci*d v*lqtn4) r;v$m$ is launched from the surface and placed in an orbit around a planet of mass $M$ and radius $R$. The height of its orbit from the surface of the planet is ℎh.
The initial speed of the satellite is equal to $\frac{4}{5}v_{esc}$.
The planet has no atmosphere.
1.Define gravitational potential energy
2.(1)Show that the initial total energy of the satellite is given by $-\frac{9GMm}{25R}$.
(2)The satellite is placed in an orbit with orbital radius $r$.
Determine the expression for the total energy of the satellite in its orbit in terms of $G$,$M$,$m$ and $r$.
(3)Use your answers to parts b(i) and b(ii) to determine the height of orbit above the surface of the planet in terms of $R$.
3.The satellite ejects excess fuel opposite to its direction of motion. Suggest the effect of this change on the average orbital radius of the satellite.
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