Question

why do planets revolve around the sun in an elliptical orbit and why not in a circular orbit?

Answer 1

all of these explanations support the theory of kepler's law including the elliptical orbit rather than circular orbit.

go through all these properly and you will find the link of every concepts.

• Orbits are eliptical because of Newtons Law of Gravity (bodies attract each other in proportion to their mass and inversly proportional to the square of the distance between them). All worked out by Kepler some years ago. A circular orbit is a special (and very unlikely) case of an eliptical orbit.
  Bob Kirk, Bangkok, Thailand

• Yes. Isaac Newton. Read his Principia Mathematica.
  Peter Brooke, By Kinmuck, Scotland, UK

• It's not easy to arrange a perfectly circular orbit for an inverse-square law - just a small tweak (either in the initial conditions, or from interplanetary interactions or impacts) will change the path from a circular orbit to an elliptical one. But, if you look at an ellipse from the right angle, it will appear circular. So, consider it a matter of viewpoint!
  Michael Hall, Canberra, Australia

• The shape of planetary orbits follows from the observed fact that the force of gravity between two objects depends on the square of the distance between them. If you double the distance between two objects, the attractive force between them drops to a quarter of it's original value. If you triple the distance it drops to a ninth. Isaac Newton demonstrated mathematically that this law implied that the path followed by an object in a gravity field would be a parabola, a hyperbola or an ellipse. The first two are open ended. If something entered the solar system on a parabolic or hyperbolic path, we would see it just once before it disappeared into the distance. Prior to Newton, Kepler showed by measurement that the observable planets had elliptical orbits. Ellipses are closed so the planets we see in elliptical orbits stick around. A circle is a special case of an ellipse and it is theoretically possible for an orbit to be circular. In the real world, a such an orbit is unlikely.
  Mike Burton, Twickenham, UK

• A circle is a special case of an ellipse with the major and minor axes equal. To get a perfectly circular orbit of a certain radius requires the planet to have a certain velocity, which is extremely unlikely. Any deviation from that velocity will result in an elliptical orbit (up to the limit when the planet is travelling so fast it escapes). To put it another way, for every circular orbit, there are an infinite number of possible elliptical orbits, making the perfect circle extremely (dare I say infinitely?) improbable.
  Brian Norledge, Severna Park, USA

• Under Newtonian laws of motion and gravitation, the force of attraction between the Sun and the planet is inversely proportional to x^2, where x is the distance from the sun. Using calculus this can be shown to cause the body moving near the Sun to move in hyperbolas, parabolas or, in the case in which the body has less than a certain threshold of energy, in an ellipse. A circle is merely a special case of an ellipse. However, the planets do not quite move in ellipses either. The increased kinetic energy of a planet as its distance from the Sun decreases causes it to behave as though it had a greater mass, which results in the point of the orbit furthest from the Sun precessing.
  Harry Braviner, Manchester, UK

• Considering Newton's and Kepler's laws of gravitation, expertly explained above, I would suggest that the reason for a planet's eliptical orbit is down to the gravitational attraction between the central Sun and all the other planets in the solar system. For example, the relatively small graviational force from a venus on earth, dispite being very small in comparison with the Sun's force, would distort the erath's theoretical-circular orbit into an eliptical but stable shape.
  Rhodri Morgan, Brecon, Wales, UK

• Ok, the answers offered above are all excellent. I would like to know, however, if anyone has considered the fact that elliptical orbits may be due to the fact that the central object to which the subject is orbitting around is itself moving also. Taking the moon and earth as an example, first assuming the orbit of the moon is near circular, the movement of the earth around the sun causes the earth to move towards one edge of the moons orbit and away from another. This coupled with the fact that the gravitational pull of each mass is inversely proportional to the distance causes the eliptical orbit. The moon orbits the earth, similarly the earth orbits the sun. Does the sun orbit in a galaxy? If so then my theory offered here could be used to predict the movement of the sun within a galaxy and predict the centre of the galaxy using the fact that the eliptical orbits of the planets would point in the direction of the sun's movement over time.
  Dan Kim, Marston England

• Artificial satellites get their circular orbits by means of lots of fiddling around with tiny rocket thrusters. For a planet, which is where is is due to lots of random interactions with other celestial bodies, to get a similarly circular orbit would be like tossing a coin and having it land on its side. The planet that comes nearest is Venus whose orbital eccentricity is less than 1%.
  Martin Porter, Glossop, Derbyshire