Newton's law of universal gravitation
G3.1 G3.2 G4.1
By the end of this lesson you should be able to
- Describe the Law of Universal Gravitation. G3.1
- Solve problems involving the magnitude of the gravitational force between two masses using F = GMm/r^2. G3.2
- Appreciate the significant contributions of scientists such as Isaac Newton, Johannes Kepler, Émilie du Châtelet and Katherine Johnson who furthered our understanding of gravity and motion. G4.1
Key ideas
- Every mass attracts every other mass. The force is proportional to the product of the masses and inversely proportional to the square of the distance between their centres.
- The forces on the two masses are equal and opposite (Newton's third law), whatever the masses.
- Inverse square: double the distance → ¼ the force; triple → 1/9.
- For an object above a planet, r = planet radius + altitude.
Key formulas (QCAA formula book notation)
\[
F = \frac{G M m}{r^2}
\]
\[
G = 6.67 \times 10^{-11}\ \text{N m}^2\,\text{kg}^{-2}
\]
Worked example
Find the gravitational force between Earth (5.97 × 10²⁴ kg) and a 1000 kg satellite 400 km above the surface (Earth radius 6.37 × 10⁶ m).
- \(r = 6.37 \times 10^6 + 4.0 \times 10^5 = 6.77 \times 10^6\) m
- \(F = \frac{(6.67\times10^{-11})(5.97\times10^{24})(1000)}{(6.77\times10^6)^2} = 8.7 \times 10^3\) N
Common mistakes
- Using the altitude instead of the centre-to-centre distance.
- Forgetting to square r.
- Thinking the smaller mass feels a bigger force.
Do
- Read: Textbook (Oxford Physics for Queensland Units 3 & 4) section 5.1-5.2
- Do: CYL 5.1 Q1; CYL 5.2 Q3, 5, 9
Try it
Watch
- Newton's Universal Law of Gravitation Introduction · Flipping Physics
Further reading
- OpenStax College Physics (AP) 6.5 Newton's universal law of gravitation (OpenStax, CC BY 4.0)
- Full topic notes: Gravity & Motion