How are gravitational force and distance related?

Gravitational force and distance are inversely proportional; as the distance between two objects increases, the gravitational force decreases.

The relationship between gravitational force and distance is described by Newton's Law of Universal Gravitation. This law states that every particle of matter in the universe attracts every other particle 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. This is often summarised as F = G(m1m2)/r^2, where F is the force of attraction between the masses, G is the gravitational constant, m1 and m2 are the two masses, and r is the distance between the centres of the two masses.

The inverse square law is a key part of this equation. It means that if you double the distance between two objects, the gravitational force becomes a quarter of what it was. If you triple the distance, the force becomes a ninth of its original value, and so on. This rapid decrease with distance is why, for example, we are not noticeably pulled towards objects like cars or buildings, despite their mass. The gravitational force they exert is minuscule compared to the force exerted by the Earth, because we are so much closer to the Earth's centre of mass.

However, it's important to note that while the force decreases with distance, it never becomes zero. No matter how far apart two objects are, there is still a gravitational force between them, however small. This is why, for instance, the Earth is still affected by the gravity of distant stars and galaxies.

IB Physics Tutor Summary: Gravitational force weakens as the distance between two objects increases, according to Newton's Law of Universal Gravitation. This law explains that the gravitational pull is weaker when objects are farther apart because it's inversely proportional to the square of their distance. However, no matter how far apart, the gravitational force never reaches zero, meaning everything in the universe exerts some gravitational pull on everything else.