Gravitational Fields

Newton's law of gravitation, field strength, gravitational potential, and orbital mechanics.

Spec Points Covered
  • I can define gravitational field strengthThe gravitational force per unit mass at a point in a gravitational fieldA region of space in which a mass experiences a gravitational force.. Measured in N kg⁻¹. as force per unit mass and use $g = F/m$.
  • I can state and apply Newton's law of gravitation: $F = GMm/r^2$.
  • I can derive and use $g = GM/r^2$ for the field strength around a point or spherical mass.
  • I can define gravitational potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). per unit mass in bringing a small test mass from infinity to that point. Always negative. Measured in J kg⁻¹. and use $V = -GM/r$.
  • I can explain why gravitational potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). per unit mass in bringing a small test mass from infinity to that point. Always negative. Measured in J kg⁻¹. is always negative.
  • I can calculate gravitational potential energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its position in a gravitational fieldA region of space in which a mass experiences a gravitational force.. using $E_{p} = -GMm/r$.
  • I can derive the escape velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.The minimum speed at which an object must be launched from the surface of a body to escape its gravitational field entirely (reach infinity with zero kinetic energyThe capacity to do work. Measured in joules (J).The energy an object possesses due to its motion.). using energy considerations: v = $\sqrt{2GM/r}.$
  • I can state and apply Kepler's three laws of planetary motion.
  • I can derive and use \(T^{2}\) = ($4\pi$^2/GM)\(r^{3}\) for orbital periods.
  • I can describe the properties of a geostationary orbitAn orbit with a periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s). of exactly 24 hours, directly above the equator, so the satellite remains above the same point on Earth's surface. and explain its applications.
  • I can calculate the total energy of an orbiting satellite.
  • I can sketch and interpret gravitational fieldA region of space in which a mass experiences a gravitational force. lines and equipotential surfaces.
Notes
01 Gravitational field Gravitational field → 02 This is an inverse square law $F = \frac{GMm}{r^2}$ → 03 Derived by combining g = F/m with F = GMm/\(r^{2}\) $g = \frac{GM}{r^2}$ → 04 Gravitational potential (V) Gravitational potential (V) → 05 Gravitational potential energy $E_{p} = mV = -GMm/r$ for a mass m at distance r from mass M → 06 Kepler's first law $T^2 = \frac{4\pi^2}{GM}r^3$ → 07 Geostationary orbit Geostationary orbit → 08 For a satellite in a circular orbit at radius r → 09 Gravitational field lines always point towards the mass (gravity is attractive). They show the →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
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.