Introduction: What is Gravity?
Why does an apple fall from a tree? Why does the Moon stay in orbit around the Earth? These seemingly unrelated events are governed by the same fundamental force: gravity. Gravity is an attractive force that acts between any two objects that have mass , no matter how far apart they are.
What makes gravity particularly remarkable is that it acts across empty space. The Earth pulls on the Moon across 384,000 km of vacuum, and the Sun pulls on the Earth across 150 million kilometres. To make sense of this, physicists use the concept of a gravitational field , an invisible influence that a mass creates in the space around it.
In this subtopic, you will study:
- Newton's law of universal gravitation
- Gravitational field strength
- Gravitational potential energy
- How gravitational fields are visualised using field lines and equipotential surfaces
Newton's law of gravitation is a classical description of gravity. It works extremely well for most everyday and astronomical calculations, though it is superseded by Einstein's General Theory of Relativity for extreme conditions (very strong fields or very high speeds).
Newton's Law of Universal Gravitation
Newton's law of universal gravitation states that every pair of masses in the universe attracts every other pair with a force that depends on their masses and the distance between them.
Newton's Law of Universal Gravitation: Every two point masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres:
Defining the symbols:
- , gravitational force between the two masses (N)
- , universal gravitational constant,
- , , the two masses (kg)
- , the distance between the centres of the two masses (m)
Two key relationships:
- Force is proportional to mass: If either mass doubles, the force doubles.
- Inverse square law: If the distance doubles, the force becomes one-quarter as large.
Think of gravity like the brightness of a light bulb. As you move further away, the light spreads over a larger area and appears dimmer , following the same inverse square relationship. Double the distance, and the brightness (like gravity) drops to one-quarter.
For spherical masses such as planets, the entire mass can be treated as if it were concentrated at the geometric centre. This is why is always the centre-to-centre distance, not the surface-to-surface distance.
A very common error is forgetting to square in the denominator. Always write out explicitly and double-check before substituting values.