Key Equations

Gravitational Fields - OCR A-Level Physics

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Newton's law of gravitation
$$F = \frac{GMm}{r^2}$$
  • Where:
    • $F$ = N
    • $G$ = 6.67 \times \(10^{-11}\) N \(m^{2}\) kg^{-2}
    • $M$ = kg
    • $m$ = kg
    • $r$ = m
Inverse square law. r is measured between centres of the masses, not surfaces.
Gravitational field strength (radial field)
$$g = \frac{GM}{r^2}$$
  • Where:
    • $g$ = N kg^{-1}
    • $G$ = N \(m^{2}\) kg^{-2}
    • $M$ = kg
    • $r$ = m
Derived from g = F/m and F = GMm/\(r^{2}\). Gives field strength at distance r from a point or spherical mass.
Gravitational potential
$$V = -\frac{GM}{r}$$
  • Where:
    • $V$ = J kg^{-1}
    • $G$ = N \(m^{2}\) kg^{-2}
    • $M$ = kg
    • $r$ = m
Always negative. V = 0 at infinity. More negative closer to the mass.
Kepler's third law
$$T^2 = \frac{4\pi^2}{GM}r^3$$
  • Where:
    • $T$ = s
    • $G$ = N \(m^{2}\) kg^{-2}
    • $M$ = kg (central body)
    • $r$ = m
Derived by equating gravity to centripetal force. Use to find orbital period or mass of central body.
Gravitational field strength (definition)
$$g = \frac{F}{m}$$
  • Where:
    • $g$ = N kg^{-1}
    • $F$ = N
    • $m$ = kg
Must memorise. The defining equation for gravitational field strength.
Escape velocity
$$v = \sqrt{\frac{2GM}{r}}$$
  • Where:
    • $v$ = m \(s^{-1}\)
    • $G$ = N \(m^{2}\) kg^{-2}
    • $M$ = kg
    • $r$ = m
Must memorise. Derived from energy conservation: KE + PE = 0. Independent of the mass of the escaping object.
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