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Theme D — Fields

D.1.1 Newton’s Law of Gravitation — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 3 of 39 1 quiz

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Curriculum Equation Key قوانين نيوتن للحركة - Newton Laws of Motion FormulasFast Exam Solution
F = m × a | W = m × g | F₁₂ = -F₂₁
Word Equation & Conditions: القوة المحصلة = الكتلة × التسارع | Force = Mass × Acceleration
Location & Specifications: الميكانيكا الكلاسيكية والتحصيلي وفيزياء 3 ثانوي و IGCSE Physics.
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Lesson summary

D.1.1 Newton's Law of Gravitation — IB PHYSICS SL notes: State Newton's law of gravitation and use it to calculate the attractive force between point masses and spherical bodies.Universal — every object with mass attracts every other object with massAlways attractive — the force …

  • Newton's insight
  • Everyday objects
  • What the symbols mean
  • Equal and opposite
  • Planet and person
  • Uniform sphere

Part 1 of 8Gravity as a universal attraction

Universal
  • Universal every object with mass attracts every other object with mass
Always attractive
  • Always attractive the force acts along the line joining the two centres and acts on both bodies
Newton's insight
  • Newton's insight the force keeping the Moon in orbit is the same kind of force that makes an apple fall
Everyday objects
  • Everyday objects the force is tiny, so it is noticeable only when at least one body is astronomically large

Part 2 of 8The law

The law
Newton's law of gravitation
  • Newton's law of gravitation the gravitational force between two point masses is proportional to the product of the masses and inversely proportional to the square of their separation
  • F = Gm1m2 / r2
    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)
Symbols
  • F is the magnitude of the force on each mass, in newtons.
  • m1 and m2 are the masses in kilograms.
  • r is the separation of the centres in metres.
  • G is the gravitational constant, 6.67 × 10−11 N m2 kg−2.
Point masses
  • Point masses planets and stars are treated as point masses because their separation is much larger than their radii
  • The law therefore applies to planets orbiting the Sun.

Part 3 of 8Newton's third law pair

Equal and opposite
  • Equal and opposite the two forces have the same size and opposite directions, even when the masses differ greatly
Planet and person
  • Planet and person a planet pulls on you exactly as hard as you pull on it, but the accelerations differ

Part 4 of 8Spheres and the distance r

Uniform sphere
  • Uniform sphere a spherically symmetric body attracts external objects as if all its mass were at its centre
Centre to centre
  • Centre to centre r is always measured between centres
Satellites
  • Satellites for a satellite orbiting the Earth, r is the Earth's radius plus the height above the surface, not the height alone

Part 5 of 8Inverse-square law

Statement
  • F ∝ 1/r2
  • Doubling the separation divides the force by 4.
  • Tripling it divides the force by 9.
  • Halving it multiplies the force by 4.
Mass dependence
  • F is directly proportional to each mass, so doubling one mass doubles the force
Graphs
  • F against r is a curve that falls steeply and never reaches zero
  • F against 1/r2 is a straight line through the origin with gradient Gm1m2.

Part 6 of 8Size of the force

Weakest force
  • Weakest force the small value of G makes gravity the weakest of the fundamental forces
  • Two students a metre apart attract with only about 10−7 N.
Dominance
  • Dominance gravity matters only for enormous masses, because it is never repulsive and cannot be shielded
  • The effects of all the matter in a body add up.
Cavendish
  • Cavendish his torsion-balance experiment first measured G, which also allowed the mass of the Earth to be deduced
Link to field strength
  • Link to field strength combining F = GMm/r2 with F = ma gives g = GM/r2 (D.1.2)
Electric analogy
  • Electric analogy the same form appears in Coulomb's law, but electric forces can also repel

Part 7 of 8Using the law

1
Identify the two bodies and sketch the line joining their centres.
2
Convert every distance to metres and every mass to kilograms.
3
Treat the bodies as point masses with r measured to the centres.
4
Substitute into F = Gm1m2/r2.
5
State the direction of the force, towards the other body.
Changes
  • Changes use ratios, with distances inverted and squared, instead of recalculating
Sanity check
  • Sanity check forces between everyday objects must be extremely small, while planetary values reach 1020 N and beyond

Part 8 of 8More from the specification

1Newton's Law of Universal Gravitation
  • Newton's law states that every point mass attracts every other point mass with a force directly proportional to the product of their masses and inversely proportional to the square of their separation: F = G·M·m / r²,
  • where G is the gravitational constant.
    • (6.67 × 10⁻¹¹ N·m²·kg⁻²)
2Gravitational Fields and Field Lines
  • A gravitational field is defined as a region of space where a mass experiences a gravitational force (weight);
    • spherical bodies generate radial field lines directed towards the centre of mass, with field strength g = F / m = G·M / r².
3Orbital Motion and Kepler's Third Law
  • For a planet or satellite in circular orbital motion of radius r, centripetal force is provided by gravity; substituting orbital speed v = 2π·r / T yields Kepler's third law, showing that orbital period squared is proportional to orbital radius cubed (T² = [4π² / (G·M)]·r³).
    • (m·v² / r = G·M·m / r²)
4Period
  • Time for one revolution.
5Density
  • Mass per unit volume.
6Weight
  • Gravitational force on a mass.
7Field lines
  • Lines showing the direction and strength of a magnetic field.
8Orbital period
  • Time for one orbit.
9Gravitational field
  • Region where mass experiences gravitational force.
10Radial field
  • Field directed to a center and varying with distance.

Key terms

TermMeaning
Gravitational forceAttractive force between any two masses, acting along the line joining their centres.
Inverse-square lawForce proportional to 1/r²; doubling the distance reduces the force to one quarter.
Gravitational constant, G6.67 × 10⁻¹¹ N m² kg⁻²; sets the strength of gravity.
Point massAn object whose size is negligible compared with the distances involved.
Newton's third law pairTwo equal and opposite forces acting on two different bodies.

Avoid these mistakes

1
Using the height above the surface as r instead of the distance from the centre.
2
Thinking the heavier body exerts the larger force — both feel forces of equal magnitude.
3
Forgetting to square r, or squaring G or the masses by accident.
4
Using g = 9.8 N kg^{−1} far from Earth — g itself changes with r.
5
Treating the force as zero when masses are small — it exists but is very small.

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