IB Physics • Gravitational potential • HL mastery
Gravitational Potential — from V to orbital energy
A focused route for the part of gravitation that is easiest to confuse: potential versus potential energy, negative values, potential differences, escape, orbits and the link between V and g.
V = −GM/rEₚ = mVΔV and workHarder HL synthesis
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Build the potential map
Keep the quantity, unit, sign and reference point visible before substituting.
Gravitational potential VV = −GM/r
Energy per unit mass. Unit J kg⁻¹. It belongs to a position in a field.
Energy per unit mass. Unit J kg⁻¹. It belongs to a position in a field.
Gravitational potential energy EₚEₚ = mV = −GMm/r
Energy of the two-body system. Unit J. It depends on the test mass.
Energy of the two-body system. Unit J. It depends on the test mass.
Reference: zero potential is normally chosen at infinity. A bound position therefore has negative V and negative Eₚ. Moving outward makes both less negative and increases them.
WANTED: identify V, Eₚ, ΔV, work, escape speed or orbital energy.
RADIUS: use centre-to-centre r. Convert altitude with r = R + h.
SIGN: preserve the negative sign until the physical interpretation is complete.
CHECK: J kg⁻¹ means potential; J means energy; a positive outward change is usually an energy input.
Potential is a position map
A test mass placed at the same point has the same V, whatever its own mass.
Potential difference becomes energy
Units make the relationship visible: J kg⁻¹ × kg = J.
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Potential and potential difference
Potential is a scalar. Add contributions algebraically, and use differences for energy transfers.
V = −GM/rFor several spherical or point sources: Vtotal = Σ(−GMᵢ/rᵢ)
Potential difference: ΔV = V₂ − V₁. For a mass m, ΔEₚ = mΔV. If the object moves slowly, the external work equals ΔEₚ.
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Energy, escape and circular orbits
These questions combine potential with kinetic energy and conservation laws.
Escapevₑ = √(−2V)
At infinity, final total energy is zero.
At infinity, final total energy is zero.
Circular orbitK = −Eₚ/2
Total energy E = Eₚ/2 = −GMm/(2r).
Total energy E = Eₚ/2 = −GMm/(2r).
Field linkg = |V|/r
For a spherical source outside the surface.
For a spherical source outside the surface.
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Hard HL potential synthesis
These are intentionally beyond routine substitution. Show the symbolic relationship first.
Hard-question protocol: state the reference, define r, write the energy equation, then decide whether the requested quantity is a scalar potential, a change, or a total orbit energy.
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Mastery summary
Explain every sign and every radius aloud before you count a question as secure.
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Keep going. Work through the course in order.