In some ways they orbit around each other! But two things will always orbit around their centre of mass (the point between the two where their two masses even each other out). If the sun and the earth were the same size, this would be exactly half way between the two and they’d both orbit around that halfway point. BUT the sun is so much bigger than the earth (330000 times bigger!!) that the point where the mass of the sun and the mass of the earth even each other out is actually inside the sun!! that means that for all practical purposes, we orbit round the sun…
You can get what are called binary star systems though where you get two stars orbiting round a point between the both of them…
You can set up your model to have the earth at the centre if you like, but you’ll have a huge problem explaining the motion of the other planets.
Way back hundreds of years ago before the sun-centre model was accepted everyone thought the earth was at the centre. Problem was when astronomers tracked the motion of the planets they found that at certain points in the year some of the planets would start to change direction in the sky. They tried to explain this by introducing loops into the orbit of the planet but that never really made much sense. When copernicus came along and argued that the sun was at the centre, one of the things that conviced people (notably Galileo) was that these changes of direction could be explained by an effect called ‘apparent retrograde motion’.
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spacenut1982 commented on :
If you wanted to create a scale model of the solar system then you can get the instructions here: http://www.exploratorium.edu/ronh/solar_system/