Why planets revolve around sun in elliptical orbit?
Stacey Warren - Expert brainly.com
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There is no special requirement that planetary and lunar orbits must be non-circular. There is one lunar orbit in our solar system that is about as close to circular as you can get. Think of it this way. Absolutely every stable orbit in the universe is elliptical (at least if our physics applies everywhere). It happens that some of those ellipses have both loci occupying the same point in space (defining a circle). When you consider all the possibilities in all orbits (distances between loci) it is no surprise that so few orbits are 'circular'.
because of space warp. Space warp is like a casino roulette. when you spin a roulette, the thingy inside it will keep on revolving around the center in an elliptical way. that is a physical idea of gravity.
another reason is because gravitational force is inverse square with distance. so as the distance increases, the gravity lessens. this affects the orbit of the planets one way or the other
the only possible stable orbit of bodies under central force following inverse square law is elliptical. it isn't difficult to prove
equation 8.41 will give you differential equation. A bit of work should prove that the trajectory will be an ellipse in polar coordinate.