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Lesson 5.2 • Competency 5.1Complete Lesson
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Gravitational Potential and Potential Energy

Definition of gravitational potential V, negative potential sign convention, potential energy U = -GMm/r, work done in gravitational field, equipotential surfaces, and potential gradients.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • Define gravitational potential V at a point as the external work done per unit mass in bringing a test mass from infinity to that point without acceleration.
  • Deduce and apply V = -GM/r and U = -GMm/r, explaining why gravitational potential is intrinsically negative relative to infinity.
  • Calculate work done moving masses between points in gravitational fields (W = m ΔV) and describe properties of equipotential surfaces.

Core Theory & Concepts

Because gravity is a conservative force, a potential energy and scalar potential can be associated with every point in space. Since gravity is always attractive, bringing a mass from infinity requires negative work by an external agent, making gravitational potential everywhere negative.

Gravitational Potential

Scalar potential at distance r from spherical mass M: V = -GM/r. SI unit is J kg⁻¹.

V = -\frac{GM}{r}

Gravitational Potential Energy

Total interaction energy of two masses separated by r: U = -GMm/r. Near surface: ΔU ≈ mgh.

U = -\frac{GMm}{r}

Field Intensity as Potential Gradient

Gravitational field strength equals the negative spatial derivative of potential: g = -dV/dr.

g = -\frac{dV}{dr}

Common Misconceptions

Misconception

Gravitational potential energy is always given by U = mgh at any distance from Earth.

Physical Clarification:U = mgh is a linear approximation valid ONLY when height h is negligible compared to Earth’s radius R (h << R). For large distances, the exact formula U = -GMm/r must be used.

Syllabus Topic Outline

Competency 5.1
  • 1Work done by gravitational force and conservative field nature
  • 2Gravitational potential V = -GM/r with zero reference at infinity
  • 3Gravitational potential energy of two-mass system U = -GMm/r
  • 4Relationship between field intensity and potential gradient: g = -dV/dr
  • 5Equipotential surfaces: concentric spheres, perpendicularity to field lines
  • 6Work done moving a mass along and across equipotential surfaces