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
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.
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 / r2What 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
| Term | Meaning |
|---|---|
| Gravitational force | Attractive force between any two masses, acting along the line joining their centres. |
| Inverse-square law | Force proportional to 1/r²; doubling the distance reduces the force to one quarter. |
| Gravitational constant, G | 6.67 × 10⁻¹¹ N m² kg⁻²; sets the strength of gravity. |
| Point mass | An object whose size is negligible compared with the distances involved. |
| Newton's third law pair | Two 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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