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Theme D — Fields

D.1 Gravitational Fields — IB Physics SL Revision Notes & Topical Questions

5 min read 8 parts Lesson 2 of 21 1 quiz

📚 IB Physics SL Hub / Topical Revision
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Curriculum Equation Key Circular Motion & Gravitation LawsFast Exam Solution
a_c = v² / r | F_c = (m × v²) / r | F_g = G × (m₁ × m₂) / r² | v_orbit = √(G×M / r)
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Lesson summary

D.1 Gravitational Fields — IB PHYSICS SL notes: Apply Kepler's laws and Newton's law of gravitation, define gravitational field strength and analyse circular orbits.First law — each planet moves in an ellipse with the Sun at one focusSecond law — the line joining planet and Sun s…

  • What the symbols mean
  • Around a point or spherical mass
  • Around a sphere
  • Near a planet's surface
  • Centripetal force
  • Orbital speed

Part 1 of 6Kepler's laws

1First law
  • First law each planet moves in an ellipse with the Sun at one focus
2Second law
  • Second law the line joining planet and Sun sweeps out equal areas in equal times
  • A planet moves fastest when closest to the Sun.
3Third law
  • T2/r3 is the same for all bodies orbiting the same central mass
  • Outer planets have longer years.
LawStatementConsequence
FirstOrbits are ellipses with the Sun at a focusThe distance from the Sun varies
SecondEqual areas swept in equal timesFaster when closer
ThirdT2 ∝ r3Outer planets have longer years

Part 2 of 6Newton's law of gravitation

Newton's law of gravitation
Newton's law of gravitation
  • Newton's law of gravitation every point mass attracts every other with a force proportional to the product of the masses and inversely proportional to the square of their separation
  • F = Gm1m2/r2, always attractive.
    What the symbols mean: F = gravitational force (N) · G = 6.67 × 10−11 N m2 kg−2 · m1, m2 or M, m = masses (kg) · r = distance between their centres (m)
  • G = 6.67 × 10−11 N m2 kg−2.
Distance
  • Distance r is measured between centres
Spheres
  • Spheres a uniform sphere acts on external bodies as if all its mass were at its centre

Part 3 of 6Gravitational field strength

1Gravitational field
  • Gravitational field a region in which a mass experiences a force
2Gravitational field strength
  • Gravitational field strength the force per unit mass on a small test mass placed at the point
  • g = F/m, in N kg−1.
3Around a point or spherical mass
  • Around a point or spherical mass g = GM/r2, an inverse-square law
    What the symbols mean: g = gravitational field strength (N kg−1) · G = 6.67 × 10−11 N m2 kg−2 · M = mass of the body (kg) · r = distance from its centre (m)
4Vector
  • Vector g is directed towards the mass
  • Fields from several masses add as vectors.

Part 4 of 6Field lines

Around a sphere
  • Around a sphere the lines are radial and point inward
Near a planet's surface
  • Near a planet's surface the lines are almost parallel and equally spaced, which is a uniform field
Density
  • Density closer lines mean a stronger field

Part 5 of 6Circular orbits

Centripetal force
  • Centripetal force in a circular orbit gravity provides it, GMm/r2 = mv2/r
Orbital speed
  • Orbital speed v = √(GM/r), independent of the satellite's mass
Period
  • Period with v = 2πr/T it gives T2 = 4π2r3/GM, which is Kepler's third law

Part 6 of 6Solving an orbit problem

1
Identify the central mass M and the orbital radius r (planet radius plus altitude).
2
Set the gravitational force equal to the centripetal force.
3
Cancel the satellite's mass.
4
Solve for v or T.

Key terms

TermMeaning
Gravitational fieldA region in which a mass experiences a force.
Gravitational field strengthThe force per unit mass on a small test mass placed at the point.
Newton's law of gravitationEvery point mass attracts every other with a force proportional to the product of the masses and inversely proportional to the square of their separation.
Field lineA line whose direction at each point shows the direction of the force on a test mass.
Orbital periodThe time for one complete orbit.

Avoid these mistakes

Avoid these mistakes
Using the height above the surface as r.
Thinking orbital speed depends on the satellite's mass.
Treating gravity as sometimes repulsive.

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