## How to measure the weight of the Earth?

What is the weight of the Earth, and how do we measure it? It is not like we can ask the Earth to step on a weighing machine right? So how does one measure the weight of the Earth?

Well to answer the first question, regarding how much the Earth weighs?

It weighs about 6E+24 kilograms or 6*10^24 kilograms orĀ 6,000,000,000,000 ,000,000,000,000.

To be more exact it actually weighs:-

5.9736E+24 kilograms or 5.9736*10^24 kilograms.

Now how does one even begin to calculate this weight?

Well the concept of calculating this weight is through gravitational attraction between objects. As read on howstuffworks.com, every object attract every other. If we were to place 2 bowling balls next to each other, and we use a very sensitive measure, we can actually measure the gravitational force between them.

This combined with Newton’s expression for gravitational force between spherical objects, i.e.

Image via Wikipedia

F = G * M1 * M2 / R, can help us determine the weight.

Here F = force between the objects,

G = is the gravitational constant which is 6.67259*10^-11 m3/s2 kg

M1 and M2 are the masses of the two objects and

R = Distance between the objects

Now we can measure the mass of the Earth, by assuming the other mass to be a 1 kg sphere. The force between them will be 9.8 kg m/s^2, which is the acceleration due to gravity. The R will be the radius of the Earth, which is 6,400,000 meters. So when we do plug-in all the values, we result with 6*10^24 kilograms.