Universal gravitation: the inverse square law
Move away from the centre of a planet, make the planet heavier or lighter, and change your own mass. See how gravity and your weight change, and find the inverse square law.
Core concept
Every two bodies attract each other with a force F = G m₁ m₂ ÷ d²: double the mass and the force doubles, double the distance and it falls to a quarter; so g, and your weight, depend on the planet's mass and your distance from its centre
Topic: The universe
Isaac Newton realised that the force: A push or a pull. Forces can start, stop or turn things. All key words that makes an apple fall also keeps the Moon in its orbit. His law of universal gravitation says every two bodies in the universe attract each other with a force F = G m₁ m₂ ÷ d², where m₁ and m₂ are their masses, d is the distance between their centres and G is the universal gravitational constant, 6.67 × 10⁻¹¹ N m²/kg². The force is proportional to each mass: How much matter something has, measured in grams or kilograms. It is the same everywhere. All key words and inversely proportional to the square of the distance. Your weight: The pull of gravity on something, measured in newtons. It is less on the Moon. All key words is the Earth's pull on you; at the surface, one radius from the centre, g is 9.8 N/kg. In this lab you measure distance in Earth radii (R) and the planet's mass in Earth masses (M). The same gravity: The pull that makes things fall towards the Earth. All key words holds galaxies together; Hubble found that galaxies are moving apart, the evidence: What you saw or measured that shows whether an idea is right. All key words that the universe began with a Big Bang about 13.8 billion years ago.
What you will learn
- State Newton's law of universal gravitation.
- Explain the inverse square law with examples.
- Calculate how g and weight change with mass and distance.
- Explain why the same body weighs differently on different planets.
Before you start
- Know that weight = mass × g.
Materials
- A ball on a string, to show how gravity keeps the Moon in orbit
Equipment
- A bathroom scale
Procedure
- Record your weight at the Earth's surface (1 R).
- Record at 2 R, 3 R and 4 R.
- Record on a planet of 2 Earth masses and of 0.5 Earth masses, at 1 R.
- Record with a mass of 30 kg.
How this simulation is simplified
- At the Earth's surface (1 R from its centre) g = 9.8 N/kg.
- The other planets have the Earth's size, so only their mass changes.