Why does Earth's gravity pull us towards its centre?

Earth's gravity pulls us towards its centre because it is the point where all of Earth's mass is concentrated.

Gravity is a force that attracts two objects towards each other. In the case of Earth, this force is exerted by its mass, which is distributed throughout its volume. However, due to the spherical shape of the Earth, the effect of this mass is as if it were all concentrated at the centre. This is a consequence of the shell theorem, a principle in classical mechanics, which states that a spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its centre.

The force of gravity is described by Newton's law of universal gravitation, which 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 means that the closer objects are to each other, the stronger the gravitational pull between them.

In the context of Earth and us, humans, the force of gravity pulls us towards the centre of the Earth because that's where the majority of Earth's mass appears to be from our perspective on the surface. This force is what keeps us grounded and prevents us from floating off into space.

It's also worth noting that while we say gravity pulls us 'down', this is really a shorthand for saying it pulls us towards the centre of the Earth. If you were to dig a hole through the Earth and jump in, you would fall 'down' towards the centre, but then as you passed the centre, you would start falling 'up' towards the surface on the other side. This is because gravity is always pulling you towards the centre of the Earth, no matter where you are on or in the planet.

In conclusion, Earth's gravity pulls us towards its centre because that is the point where all of Earth's mass effectively acts. This gravitational pull is what keeps us firmly on the ground and defines our perception of 'up' and 'down'.