How much does the Earth weigh?

28 November 2010

Question

One thing I have wondered is how much does earth weigh? How many pounds does earth way, and if we don't yet know, do you think it would ever be possible to guess accurately?

KEEP UP THE GREAT WORK!!!

Ben

Answer

Chris - The stated weight - mass, we should more accurately, of the Earth is about 6 x 1024 kilograms. In other words, if you turn that into tons, it's 6 with 21 zeros after it, tons. So pretty heavy, but the big question is and this is where Dave can help me out, how do we actually know that something on the scale of the Earth that we can't physically put on a pair of scales, how do we know how much that weighs because Archimedes famously said, "If you give me a lever long enough and somewhere far enough away to stand, I could lift up the Earth" but how would we have calculated how much the earth actually weighs, Dave?

Dave - Well, the simple way of doing this is because anything with a mass affects everything around it due to gravity. If it's something roughly spherically symmetrical, you can assume that all the mass is in the centre of the planet and it behaves as if it was all the mass is right in the centre, due to some neat bits of maths. Basically, what you have to do is - if you know how much gravitational force a kilogram of anything will apply to another kilogram of anything, and you know how much force a kilogram of substance is being attracted to the Earth and you know how big the Earth is, you can work out how much mass must be in the Earth. The second part of that is really easy. Working out how much force a kilogram produces is really difficult because it's about 10-11 Newtons at a metre between 2 kilograms. It's an incredibly tiny force and it wasn't done until near the end of 19th century. Chris - Henry Cavendish, wasn't it?

Dave - Yup. Indeed and you can work it out, and then from that, you can work out how heavy the Earth is, and from that, how heavy everything else is in the universe really.

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