Gravitational potential energy
Gravitational potential energy is the energy stored due to the position of an object in a gravitational field.
Gravitational potential energy is negative when it is defined to be zero at infinity, since for two masses at a finite separation the potential energy is less than zero.
The formula for gravitational potential energy between two masses $m_1$ and $m_2$ separated by a distance $r$ is: $$E_p = -G \frac{m_1 m_2}{r}$$ where:
Consider a satellite of mass $1500 \, \text{kg}$ orbiting Earth at a distance of $7000 \, \text{km}$ from its center. Calculate its gravitational potential energy.
Solution
Substituting the given values:
$$E_p = -G \frac{M_{\text{Earth}} \cdot m_{\text{satellite}}}{r}$$
$$E_p = -\frac{6.67 \times 10^{-11} \times 6.0 \times 10^{24} \times 1500}{7.0 \times 10^6}$$
$$ \approx -8.57 \times 10^{10} \, \text{J}$$
Gravitational potential
Gravitational potential ($V_g$) is the work done per unit mass to bring a small test mass from infinity to a point in a gravitational field.
It is given by:
$$V_g = -G \frac{M}{r}$$
where:
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