The greek mathematician Eratosthenes knew that in the city of Syene in Egypt, there was no shadow at noon. So he planted a stick in Alexandria and at Noon there was a shadow, the angle of that shadow was 7.2 degrees. Since sunlight is parallel (not exactly parallel, but the Sun is so far away that it’s almost exactly parallel), this mean that the surface of the earth is curved, otherwise at Noon there would be no shadow in Syene and Alexandria. So he paid someone to measure the distance between Syene and Alexandria, which was 500 Stadia (a measurement at the time).

So if 7.2 degrees is equal to 500 Stadia (800 km), then the 360 degrees of the earth would have a circumference of the Earth. 360 X 800km / 7.2 = 40 000 km. The real circumference of the Earth is 40 075 km at the equator and 40 007 km at the meridian. So he was pretty close for someone using ancient technology.

We can also look at other planet and see that they are indeed spherical and that we have no reason to think that our planet is different. And finally today we can go into space and look at the Earth and see that it’s a sphere.

Why is that possible, well gravity exist. The mass of the earth pull on each other. So you have a force pulling the matter toward the centre, which compact the matter into a sphere. If the mass of an object isn’t big enough the force of gravity won’t be strong enough to compress the material, basically the material is too strong and will keep it’s current form. That’s is why asteroid have irregular shape and are not round. But the more mass the object is, the stronger the gravity is and the more it can compact the material into a sphere.

Here a good video explain it. Look at 2min where he start to talk about how gravity shaped the earth.

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