Gravitational Fields · revision map · A-Level 9702, Topic 13
TOPIC 13 · GRAVITATIONAL FIELDS
CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 · ONE-PAGE REVISION MAP
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GRAVITY FIELDS13
The Gravitational Field
A region where a mass feels a force. Field strength g is the force per unit mass on a small test mass.
g = F / m
unit N kg−¹
g is a vector
g is a vector
- Field lines point the way a mass would be pulled.
- Around a point mass the field is radial, lines aiming inward.
- Near a surface the lines are nearly uniform (parallel).
Newton's Law of Gravitation
Every two point masses attract along the line joining them, an inverse-square law.
F = G m₁m₂ / r²G = 6.67 × 10−¹¹ N m² kg−² · r centre to centre
- Force ∝ each mass, and ∝ 1 / r².
- Always attractive; pulls are equal and opposite (Newton's third law).
- A uniform sphere acts as a point mass at its centre.
Field Strength & Circular Orbits
Divide F = GMm/r² by the test mass m to get the field strength.
g = G M / r²
g ∝ 1/r²;
9.81 N kg−¹ at the surface
9.81 N kg−¹ at the surface
For a circular orbit, gravity is the centripetal force:
GMm / r² = mv² / r- Sets orbital speed v and period T (T² ∝ r³).
- A geostationary orbit has T = 24 h over the equator.
Gravitational Potential
Energy per unit mass, taken as zero at infinity.
- φ is the work done per unit mass to bring it from infinity to that point.
- Negative everywhere: gravity does the work pulling inward.
- Potential energy of mass m: Ep = mφ.
BUILDS ON · Circular motion · Mass & weight
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GRAVITATIONAL FIELDS
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LEADS TO · Electric fields · Astronomy