Gravitational Potential

Question

The gravitational potential at a point due to Earth is -62.5 MJ/kg. What is the gravitational field intensity at that point if the point is at a distance of 10⁷ m from Earth's center?

RankGuru · Accepted Answer

1. **Potential vs Field**: For spheres, $|V| = \frac{GM}{r}$ and $E = \frac{GM}{r^2}$.
2. **Direct Relation**: $E = \frac{|V|}{r}$.
3. **Apply Data**:
   - $|V| = 62.5 	imes 10^6 	ext{ J/kg}$.
   - $r = 10^7$ m.
4. **Calculation**:
   - $E = \frac{62.5 	imes 10^6}{10^7} = 6.25 	ext{ N/kg}$.
5. **Note**: Gravitational field intensity has units of acceleration (m/s$^2$), which is also expressed as N/kg.

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