What would the orbit pattern be if the sun and planets orbited the earth?
Bodies don't actually orbit around each other. When there are a number of bodies, such and the Sun and the planets, are in motion under the control of gravity, they all orbit around the centre of mass of all of the bodies. This centre of mass is called the barycentre.
In the case of the solar system the solar system barycentre is constantly moving and is situated just below and sometimes above the surface of the Sun. The Sun and all of the planets orbit around this barycentre.
For the Sun and other planets to orbit the Earth, Earth would need to be at the barycentre. However, there is no way it could stay at the barycentre because the Sun's gravity would immediately accelerate it away at over