LucidSTEM
A-LEVEL 9702 · A2 · TOPIC 13
Gravitational fields
The chain of the topic: a gravitational field is force per unit mass, Newton's inverse-square law sets the force between point masses, that law fixes the field strength g = GM/r² and the potential φ = −GM/r, and the same force, set equal to m v²/r, governs every circular orbit. Around the hexagon are the four ideas; above is what it builds on, below is where it leads.
TOPIC 13: GRAVITATIONAL FIELDS
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T4 Forces: field as force per mass T5 Energy: work, potential energy T12 Circular motion: F = m v²/r for orbits 13.1
13.2
13.3
13.4
TOPIC 13
GRAVITY
FIELDS
1 · THE GRAVITATIONAL FIELD
A region where a mass feels a force.
Field strength is force per unit mass: g = F / m
It is a vector, in newtons per kilogram (N kg−¹)
Field lines point the way a mass would be pulled
g = F / m
defines the field at a point
M
radial field: lines aim inward to the mass
2 · NEWTON'S LAW OF GRAVITATION
Every two masses attract, inverse-square.
Force ∝ the two masses, and ∝ 1 / r²
Always attractive; r is the centre-to-centre distance
A uniform sphere acts as a point mass at its centre
F = G m₁ m₂ / r²
G = 6.67 × 10−¹¹ N m² kg−²
m₁
m₂
r
F
F
equal and opposite pulls (Newton's third law)
3 · FIELD STRENGTH OF A POINT MASS
Put the law into g = F / m.
Divide F = GMm/r² by the test mass m to get g
g falls off as 1 / r² with distance from the centre
Near the surface r ≈ R, so g is nearly constant
g = G M / r²
g = 9.81 N kg−¹ at Earth's surface
r
g
R
g ∝ 1/r²
4 · GRAVITATIONAL POTENTIAL
Energy per unit mass, zero at infinity.
φ is work done per unit mass to bring it from infinity
Negative because gravity does the work pulling in
Energy of a mass m in the field: E₊ = mφ
φ = −G M / r
E₊ = −G M m / r
r
φ
0
φ = −GM/r
deep well near the mass
LEADS TO
T18 Electric fields: same inverse-square, but charge T17 Oscillations: orbital period and energy T25 Astronomy: orbits, escape, Hubble's law Each reuses the inverse-square field: a 1/r² force with a 1/r potential sets orbits, escape speed and the analogy to charge.
← Builds on IGCSE: Mass & weight