Gravitational Potential Energy
Gravitational Potential Energy
- Multiply potential (energy per kilogram) by the mass, and you get the potential energy of that mass.
- Use this instead of when the distance changes enough for g to change.
Energy of a mass in the field
Symbols
- = gravitational potential energy of the mass (J)
- = gravitational constant (N m² kg⁻²)
- = mass making the field (kg)
- = mass placed in the field (kg)
- = distance from the centre of M (m)
- Since φ is the energy per kilogram, multiply it by the mass m. This gives the equation shown above (9702/42/M/J/22 Q1(a)(ii)).
- It is negative for the same reason potential is: zero at infinity, less than zero everywhere else.
Your turn9702-style
Find the gravitational potential energy of a 250 kg spacecraft when it is 2.0 × 10⁷ m from the centre of Mars (mass 6.4 × 10²³ kg).
Show worked answer
- Multiply by the mass of Mars.
- Multiply this by the 250 kg spacecraft mass.
- Divide by the distance from the centre and keep the minus sign.
Answer: −5.3 × 10⁸ J.
Why mgh is not enough
- For a small height change, use the local equation below. This assumes that g is constant.
- You may choose any height as the zero level. The ground is a common choice, but it does not have to be zero.
- For a large distance change, g changes. Use the full gravitational equation, with zero potential energy at infinity.