Gravitational Potential Energy

Question

What is the gravitational potential energy of a mass m at a distance r from the center of Earth (mass M)?

RankGuru · Accepted Answer

1. **Definition**: The GPE of a point mass $m$ at distance $r$ is the work done by internal gravitational force to bring it from infinity to $r$.
2. **Integral Origin**: $U = \int_{\infty}^r \frac{GMm}{x^2} dx = [-GMm / x]_{\infty}^r$.
3. **Formula**: $U = -\frac{GMm}{r}$.
4. **Key Features**:
   - The negative sign signifies the **attractive** (bound) nature of the field.
   - Energy is zero at infinity ($r=\infty$).
   - As $r 	o 0$, energy becomes more negative (lower).

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Gravitational Potential Energy

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