Gravitational potential
The gravitational potential energy per unit mass at a point in a gravitational field, measured in J/kg or m²/s². Denoted Φ, it is related to gravitational field strength by g = −dΦ/dr. For a point mass M, Φ = −GM/r (negative because the field is attractive and potential is defined as zero at infinity). Gravitational potential is a scalar (unlike field strength, which is a vector).
Formula
Φ = −GM/r (J/kg)
Real World
GPS satellites must account for the difference in gravitational potential between orbit and Earth's surface — clocks run faster in the weaker field at altitude, requiring a relativistic correction.
Exam Focus
Gravitational potential is always negative; if your answer is positive you have an error — the negative sign reflects the attractive nature of gravity.
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