Newton's law of gravitation
● VERBATIM — examined word-for-wordThe gravitational force of attraction between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the separation between their centres.
F = Gm₁m₂ / r², G = 6.67 × 10⁻¹¹ N m² kg⁻²What this actually means
Three ingredients must appear for full marks: two POINT masses, proportional to the PRODUCT of the masses, and inversely proportional to the SQUARE of their separation. Miss any one and the mark goes.
Note the word product. 'Proportional to their masses' is vague and examiners have penalised it. Also say separation between their centres, not 'the distance between them', because for spheres the r in the formula runs centre to centre, not surface to surface.
G is the only quantity in this whole topic printed on the data sheet. Everything else, g = GM/r², φ = −GM/r, v = √(GM/r), you must recall. G = 6.67 × 10⁻¹¹ N m² kg⁻².
The forces on the two bodies are equal in magnitude and opposite in direction, by Newton's third law, no matter how lopsided the masses are. The Earth pulls the Moon with exactly the force the Moon pulls the Earth. A favourite MCQ asks for the ratio of the two, and the answer is 1.
In practice the smartest move is often not to substitute at all. If two situations share the same planet, divide the two equations so G and M cancel and you are left with a clean ratio. Reaching for G and M when a ratio would do is how people burn time and drop sig-fig marks.
Saying 'proportional to their masses' instead of 'to the product of their masses'.
Prove it — watch it be true
- Switch on the two-mass mode so a second body appears alongside the planet.
- Read the F readout on each body and confirm the two magnitudes are equal even when the masses are very different.
- Halve the separation using the position control and check the F readout goes up by a factor of four, the inverse-square signature.