The fact that the Sun is in one focus is just one of those things. I can’t find a good intuitive reason why orbits are elliptical. ε=0 means the orbit is a circle, 0<ε<1 means the orbit is elliptical, and 1≤ε means that the orbit is open (not actually orbiting). Here’s a proof:An ellipse with a focus at (0,0) can be written where F is the distance from the center of the ellipse to the focus and . Put it all together, and you’ll find that this is definitely an ellipse with a focus at the point (0,0), the location being orbited around (like the Sun for instance).