# Gravity & Shapes: Ellipse, Parabola, Hyperbola?

• shounakbhatta
In summary, the elliptical orbit is due to the gravitational attraction of the planets, and the shape can change depending on the strength of the gravitational force.
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

shounakbhatta said:
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

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.

## 1. What is gravity?

Gravity is a natural phenomenon by which all objects with mass are brought towards each other. It is the force that keeps planets in orbit around the sun, and governs the motion of objects on Earth.

## 2. What is an ellipse?

An ellipse is a geometric shape that is defined as a curve on a plane that surrounds two focal points. It is similar to a circle, but with two different radii. It is often described as a "flattened" circle.

## 3. How is a parabola related to gravity?

A parabola is a symmetrical curve that is formed when an object is thrown or launched into the air. This shape is created because of the force of gravity pulling the object towards the ground. The path of a projectile, such as a thrown ball, is a parabola due to the influence of gravity.

## 4. What is a hyperbola?

A hyperbola is a geometric shape that is defined as a curve on a plane that has two branches, each of which resembles two infinitely long straight lines that are angled away from each other. It is often described as a "stretched" circle.

## 5. How do these shapes relate to orbital motion?

Ellipses, parabolas, and hyperbolas are all conic sections, meaning they are formed by the intersection of a plane and a cone. These shapes are also related to gravity as they are the paths that objects in orbit follow around larger objects, such as planets orbiting the sun. The shape of the orbit is determined by the speed and direction of the object's motion, as well as the strength of the gravitational force between the two objects.

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