Question
Write a short note on gravitational potential.
✓
Answer
The gravitational potential energy of the system of Earth and any mass m at a distance r from the centre of the Earth is given by,
$\begin{aligned} U & =-\frac{ GMm }{ r } \\ & =\left(-\frac{ GM }{ r }\right) m \end{aligned}$
$=\left[\left( V _{ E }\right)_{ r }\right] m$
The factor $-\frac{ GM }{ r }=\left( V _{ E }\right)_r$ is defined as the gravitational potential of Earth at distance r from its centre.
As the potential depends only upon mass of the Earth and location of the object, it is same for any mass m bound to the Earth.
$\begin{aligned} U & =-\frac{ GMm }{ r } \\ & =\left(-\frac{ GM }{ r }\right) m \end{aligned}$
$=\left[\left( V _{ E }\right)_{ r }\right] m$
The factor $-\frac{ GM }{ r }=\left( V _{ E }\right)_r$ is defined as the gravitational potential of Earth at distance r from its centre.
As the potential depends only upon mass of the Earth and location of the object, it is same for any mass m bound to the Earth.
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