Newton's Law of Gravitation
Newton's Law of Gravitation
- One law gives the size of the pull between any two masses in the universe.
The law
Symbols
- = gravitational force between the masses (N)
- = the gravitational constant, 6.67 × 10⁻¹¹ (N m² kg⁻²)
- = the two (point) masses (kg)
- = separation of their centres (m)
- The two-mark statement: the force is proportional to the product of the masses, and inversely proportional to the square of their separation (9702/42/O/N/25 Q2(a)).
- The law is written for point masses. A uniform sphere behaves as if all its mass sat at its centre, so planets count, provided r is measured between centres.
- The force is always attractive, and the two masses pull on each other with equal and opposite forces (Newton's third law, lesson 3.03).
Why an inverse square
Think of the field lines leaving a mass: at distance r they cross a sphere of area . Double the distance and the same lines spread over four times the area, so their concentration, and the force, falls to a quarter. The same geometry gives the inverse-square law for light intensity and for electric fields.
Worked example
Exam version: does gravity matter between molecules?
Two hydrogen molecules (mass 3.34 × 10⁻²⁷ kg each) sit 2.7 × 10⁻⁹ m apart. Find the gravitational force between them, and compare it with a molecule's weight (about 10⁻²⁶ N). (9702/42/O/N/25 Q2(d))
- .
- That is 10²⁰ times smaller than the weight: gravity between molecules is negligible, which supports the kinetic-theory assumption of no forces between them.
Answer