# 16.16 Gravity

Before you read this, I suggest you read posts 16.12 and 16.13.

When we push or pull something we change its motion by exerting a force on it (post 16.13). Now suppose I’m holding an object. The object is not moving (in my frame of reference). But if I stop holding the object, it drops. In other words it is no longer stationary – it starts to move. Why? I haven’t pushed it or pulled it!

The reason is that it is in a gravitational field that is exerted by the planet earth. The strength of the field is given by the equation g = GM/r2. In this equation, G is a constant (called the gravitational constant) whose value is 6.674 × 10-11.m3.kg-1 s-2 (see post 16.7 if you’re unfamiliar with the way I’ve written this number and see posts 16.12 and 16.13 if you don’t understand the units m3.kg-1.s-2); M is the mass of the earth (5.972 × 1024 kg) and r is the distance of the object from the centre of the earth (for most everyday purposes, the radius of the earth which is about 6 × 103 km).

What does “gravitational field” mean? It simply means that if we place an object in the space in which the field exists, the object will experience a force of mg, in this case directed towards the centre of the earth, where m is its mass. If m is constant, the object has an acceleration equal to this force divided by the mass of the object (see post 16.13) which is mg/m = g. So g also represents the acceleration due to gravity (about 9.8 m.s-2 on the surface of the earth – it varies a bit because the earth is not a perfect sphere).

What’s so special about the earth that makes it create a gravitational field? Nothing! My mass is 70 kg so I create a gravitational field, at a distance of 1.0 m from me, of (6.674 × 10-11 × 70)/(1.0 × 1.0) = 4.7 × 10-10 m.s-2. This is such a small number that it is negligible. Why is the planet earth so much more attractive than me? Because it has a much bigger mass! What causes this gravitational effect? Newton was able to deduce how to calculate the strength of a gravitational field over 300 years ago. He realised that it was an inherent property of mass. Nobody knew why until 1915. But it didn’t matter because people realised that mass had this property and were able to calculate its effect. In 1915, Einstein published his general theory of relativity that explained gravitational fields by mass distorting space and time, so that objects thend to “roll” towards each other.