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# Gravitational force

## Gravitational force as a fundamental force

The gravitational force $\vecphy{F}$ is the force of attraction between the masses of two or more bodies.

The gravitational force of a much larger mass (e.g. a planet) on a small mass (e.g. a human being) is called the weight of the smaller mass.

Like the other fundamental forces (electromagnetic, strong nuclear and weak nuclear forces), the gravitational force is a non-contact force. That means that bodies do not need to touch to have an impact on each other.

While the electric force can repel or attract, the gravitational force can only attract.

The gravitational force is the weakest of the fundamental forces. The electromagnetic force is $10^{36}$ times stronger than the gravitational force.

If the gravitational force was much stronger, the universe would quickly collapse as all mass attracts all other mass.

The unit of the gravitational force $\vecphy{F}$ (like that of other forces) is the newton $(\text{N})$.

The gravitational force causes these two masses to be attracted to each other.

## Law of universal gravitation

The magnitude of gravitational force between two point masses is given by the law of universal gravitation: $$F=\frac{GMm}{r^2}$$

A point mass is a mass concentrated at one point in space (i.e. it has no physical dimensions).

Non-point masses can be thought of to be comprised of a multitude of point masses (each of which exerts separate gravitational forces). However, they are often approximated as point masses for simplicity.

The law states that the force is directly proportional to the masses of the two bodies ($M$ and $m$) and inversely proportional to the square of the distance between the two bodies $(r)$.

The coefficient of proportionality is the universal gravitational constant $(G)$: $$G=6.674\times 10^{-11} \text{ N} \text{ m}^2 \text{ kg}^{-2}=6.674\times 10^{-11} \text{ m}^3 \text{ kg}^{-1}\text{s}^{-2}$$

Two masses exert gravitational forces on each other. The magnitude (but not the direction) of the two forces is equal even if the masses are different.

## Implications of the law of universal gravitation

The law of universal gravitation implies that the gravitational force becomes infinitely large as $r\rightarrow 0$ and infinitely small as $r\rightarrow\infty$.

This means that the gravitational force becomes stronger as they get closer to each other weaker as the distance between them increases.

The gravitational force of the sun on the earth is greater than the sun's gravitational force on Pluto. This is because Pluto is much further away from the sun.

The formula only gives the magnitude of the force (the force itself would also require information about the direction). As the force is attractive, it points towards the direction of the centre of mass of the other body.

Two masses exert gravitational forces on each other. The magnitude (but not the direction) of the two forces is equal even if the masses are different.