Why is planet's orbit elliptical in shape?

Answer 1

Because that's the way gravity works. If you take Newton's formula for the force

of gravity, and you have enough geometry and calculus, you can massage the

formula around and derive Kepler's three laws of planetary motion. His first law

says that planets move in ellipses with the sun at one focus. Kepler got that from

Tycho's notebooks, where he wrote down the results of years and years of watching

and measuring the positions of the planets. Kepler showed that the ellipse was the

best fit to what Tycho actually saw happening in the sky. Then 100 years later, Newton

came along and showed, with one simple formula to describe gravity, why orbits must

be ellipses.

Answer 2

Kepler discovered that the planets move in ellipses. The shape of an ellipse is described by the eccentricity. For low eccentricity such as the planets' orbits have, the orbit is very close to being a circle but the most significant difference is that the Sun is off-centre.

After Newton's law of gravity was discovered, it was found that the Sun's gravity force would make a planet move in an elliptical orbit naturally. The force is stronger when the planet is closer to the Sun, making it move more quickly and sending it out to a more distant part of the orbit where the force is weaker and the speed is less.

So the elliptical orbits have been explained and the planets' positions can be predicted accurately.