How is the weight of the planet Earth calculated?
In: Earth Science
The way it was first done with any accuracy was with the [Cavendish experiment](https://en.wikipedia.org/wiki/Cavendish_experiment) in 1798. This used several large lead balls and measured the force of gravity between them, i.e., how much one lead ball attracted the other.
This tells us how strong gravity is for a given mass at a given distance. And we also know how strong the earth’s gravity is and how far it is to the centre of the earth. So now we can use [Newton’s law of universal gravitation](https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation) to work backwards to find the earth’s mass.
There is a lot of ways to do that but i think the simplest is is firstly measure size by observing shadows like Greeks did 2k year’s ago, then measure how strong is gravity and calculate this using this number
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The first thing to be aware of is that the weight of a planet is determined by its gravitational effect on other bodies. Due to this, we can use something called Newton’s Law of Universal Gravitation. This is a formula that tells us the force of attraction between 2 bodies is proportional to the product of their masses, divided by the square root of the distance between their respective centres of mass.
F = (G*m*M)/√r
Essentially this means that since we have r: the radius of the earth, m: the mass of an object (on the earth’s surface), F: the gravitational force and G: the gravitational constant, we can rearrange this to find the mass of the earth.
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