Why do planets revolve in elliptical orbits?

[spideyinspace]

we know that planets revolve in elliptical orbits but Why should planets revolve in elliptical orbits?

 

[EL]

we know that planets revolve in elliptical orbits but Why should planets revolve in elliptical orbits?

It is a consequence of Newton's law of gravitation.
See e.g. here

 

[Jonathan Scott]

we know that planets revolve in elliptical orbits but Why should planets revolve in elliptical orbits?

In Newton's theory of gravity, the gravitational force on an object moving near a more massive object is proportional to 1/r^2 where r is the distance between the objects. When one works out mathematically the path for an object which is falling freely under the influence of such a force (but doesn't have enough energy to completely escape) the general answer is an ellipse where the large mass is at one focus.

There are of course some special cases; the obvious one is that if the orbital speed is just right for the distance, the path is a circle. Another is that if the falling mass is heading straight for the other mass, the path is a straight line downwards.

In the case of the planets, the sun is so much more massive than the planets that each planet basically moves in an ellipse around the sun, but the planets also have a very slight effect on the sun (especially Jupiter) and on each other, which distort the ellipses, and there are also other effects related to relativity which cause some further very slight distortions.