Gravity & Shapes: Ellipse, Parabola, Hyperbola?

[shounakbhatta]

Hello,

I might be wrong. Please correct me. In planetary motion or in the size of galaxies:

(a) The gravitational attraction of a body, say sun and the force from other planets, creates the elliptical shapes, right?

(b) If the gravitational force of anyone body is high than the other, the ellipse or rather the eccentricity will increase. Will it result in the shape of a parabola or hyperbola?

I mean to say that the shape of a ellipse is due to the gravitational attraction. What would happen for stronger and more stronger gravitational force? Would the shape of the orbit change?

-- Shounak

 

[A.T.]

What would happen for stronger and more stronger gravitational force? Would the shape of the orbit change?

What do you mean by "stronger and more stronger"? If it is multiplied by a factor, you still have closed elipses for bound orbits. But if you change the power of the distance in the equation or use some completely different function, then you get different shapes.

Trajectories for different laws of gravity:
http://megaswf.com/serve/1161536

 

[sophiecentaur]

Are you suggesting that it is other planets that cause our orbit round the Sun to be elliptical?
This is not the case. It is elliptical for a lone planet around an isolated star.

The reason for an elliptical orbit is that there is an inverse square force law at work; the sums give you an ellipse. A circular orbit is a very special case of ellipse and involves the planet going at the same speed all the time. In practice, all orbits vary in speed and radius over their orbit period. They go slowly when at a greater distance and 'fall' inwards, gathering speed until the star is 'abeam' of them and then start to climb away again, losing speed. Eventually, their speed has dropped enough for them to start to 'fall' inwards again.
The orbiting planet has a given amount of Kinetic plus Potential Energy, which will not change because there is no friction. When nearest to the star, its KE is maximum and its PE is minimum and when it's furthest away, its KE is minimum and its PE is maximum.
The only other relevant point to make is that the orbit stays the same and axes the ellipse remain in the same orientation for ever if there are no losses or other perturbations.