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).

When you want to outsmart the world, you turn to the facts. And the facts are in the science.