 We know that the Earth has a mass of 5.9 times 10 to the 24 kilograms, but how do we know that? Clearly, it's not possible to put the Earth on a scale to measure this. We can calculate it. We know that close to the surface of the planet, the force of gravity, Fg is equal to mass of an object times gravitational constant g. And we know that there's also the universal law of gravity. This is equal to gravity times mass of the big objects, in this case the Earth, times the mass of the object over the radius, in this case of the Earth, if we're standing on the surface of the planet, squared. The mass of the object actually falls out and I can solve this for the mass of the Earth. So the mass of the Earth therefore must be equal to g times radius of the Earth squared over capital G. Now, today's world, I can just look up the values on the internet, right? We know that the small g is 9.8 meters per second squared. I can look up that the radius of the Earth is 6.37 times 10 to 6 meters and the capital G, the universal gravity constant, is 6.67 times 10 to the minus 11 Newton square meters per kilogram square. But, well, how do we get these values here in the first place? Let's assume we don't know any of those. Can we measure them in some way? And the answer is yes, we can. How can we measure the small g? That's actually quite simple. There are several types of experiments that can do that. One of them is when we build a pendulum, a pendulum that swings back and forth. It turns out that the period the time it takes for a pendulum to go back and forth depends on the length of the pendulum. So how long it is and the rotation constant g. So I can just build a little pendulum and measure how long it takes to swing back and forth. And so for the small g, which will give me on the surface of the planet around 9.8 meters per second squared. How can we find the radius of the earth? Well, there was an experiment done by agents Egyptians. They put two stakes in the ground, one somewhere where the Sun was shining perpendicular on it, so where there was no shadow, and at the same time you put a stake south of that point where you get a shadow. So what you can do is you can measure the length of the shadow, figure out the angle at which the Sun is shining, and then you do a bit of trigonometry. If you know the distance here, you can calculate what is the radius of the earth. Now for the universal gravitational constant g, it's a bit more tricky because it's such a small value and gravity is actually so weak. However, there was an experiment done by Mr. Cavendish, so 100 years ago, where he used some kind of a torsion beam where he had two masses being attracted to other masses and therefore starting to slightly turn, and then you can measure how much it turns, and from that you can calculate backwards. What must be the universal constant of gravity, capital G? So let's say we now have found all these values, small g, the radius of the earth, and the universal constant of gravity, we plug it into our equation, and what we will get for the mass of the earth is 5.9 6 times 10 to the 24 kilograms. Now the same trick would also work for the mass of some other planet. Let's say you want to measure the mass of the Mars, so we would first need to figure out what's the small g on Mars. It's not going to be 9.8, it's going to be much smaller. What's the radius of the Mars? And we already know the universal constant of gravity. It could work for the Sun, it could work for the Moon, any other huge object for which we want to actually know what's this mass. Without being able to put it on a scale.