PhysicsChapter 1: Gravitation
Gravitational Potential Energy
Gravitational potential energy is the energy associated with the position of masses in a gravitational field.
Definition
Gravitational potential energy is the energy associated with the position of masses in a gravitational field. For masses `M` and `m` separated by `r`: U = −GMm/r when zero energy is chosen at infinity.
Why Negative?
Since: **V = Um** and: **V = −GM/r** therefore: **U = −GMm/r** At infinity: **U = 0 At any finite distance: U < 0** A bound object must gain energy to reach infinity with zero final speed.
Change in Potential Energy
Moving from `r₁` to `r₂`: **ΔU = U₂ − U₁ ΔU = −GMm/r₂ + GMm/r₁**
Formula / Key Relation
**U = −GMm/r**
Exam preparation
Exam Focus
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Review the key facts, formulas and checks before you move on.Gravitational Potential Energy
Sticky Notes · Quick Revision
Near surface small h:
- `ΔU≈mgh`
- General:
- `U=-GMm/r`
60-second revision
- Bound gravitational systems have negative U relative to infinity.
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