Gravitational Field, Potential and Potential Energy
Field E = F/m = GM/r2, potential V = -GM/r and potential energy U = -GMm/r, all measured with zero at ∞.
What is Gravitational Field, Potential and Potential Energy?
Field E = F/m = GM/r2, potential V = -GM/r and potential energy U = -GMm/r, all measured with zero at ∞.
Key formula / rule: V = -GM/r; U = mV = -GMm/r.
Key points
- Compute gravitational potential and potential energy for a system of masses.
- Derive the field from the potential using E = -dV/dr.
Common exam trap
Dropping the negative sign in potential or potential energy.
Definitions
- Term
Gravitational Field, Potential and Potential Energy
- Meaning
Field E = F/m = GM/r2, potential V = -GM/r and potential energy U = -GMm/r, all measured with zero at ∞.
- Term
Gravitational Field, Potential and Potential Energy — explanation
- Meaning
The negative sign records that gravity is attractive and that work must be done to move a mass to ∞. Field is a vector, potential a scalar, which makes potential the easier route for many-body problems.
Learning objectives
Compute gravitational potential and potential energy for a system of masses.
Derive the field from the potential using E = -dV/dr.
Formulae
- Key point
V = -GM/r; U = mV = -GMm/r.
- Key point
E = -dV/dr; field is a vector, potential is a scalar.
- Key point
Near the surface U = mgh is the small-height approximation.
Prerequisites
PHY-U2-GRAV-T1-S1-C1
PHY-U1-WEP-T1-S2-C1
Common mistakes
Dropping the negative sign in potential or potential energy.
Adding potentials as vectors.
Keywords
Gravitational
Field
Potential
Potential
Energy
Practice preview
What is the SI unit of gravitational potential?…
easy
Which of the following statements correctly describes the relationship between gravitational field (E) and gravitational potential (V)?…
easy
How much work is required to move a mass 'm' from the surface of the Earth (radius R) to an infinite distance? (Assume Earth's mass is M).…
medium