# Understanding the Physical Significance of 'a' in Kepler Orbit Equation

• Jerbearrrrrr
In summary, a Kepler orbit is an elliptical path that a celestial body follows around another body under the influence of gravity. It is named after Johannes Kepler and is described by three laws: the law of ellipses, law of equal areas, and law of harmonies. The main difference between a Kepler orbit and a circular orbit is the shape, with Kepler orbits being elliptical and circular orbits being perfectly round. The eccentricity of a Kepler orbit can be calculated by dividing the distance between the foci of the ellipse by the length of the major axis. Objects in a Kepler orbit can collide if their orbits intersect at some point due to similar orbital periods or perturbations from other objects.

#### Jerbearrrrrr

Sorry if this is in the wrong forum.

I have the equation $$r = \frac{a(1-e^2)}{1+e \cos \theta}$$,
and I'm wondering what the physical significance of the numerator is.
More specifically, what is 'a' (since e is what it usually is)?

I've seen various other representations with terms like angular momentum on the top (or rather h^2/GM).

In the context of what I'm doing, it's written this way to (presumably) uncover any implicity 'e'-dependence in the orbit.

'a' is the semi-major axis of the orbit, or the average value of 'r' for the orbit.

## 1. What is a Kepler orbit?

A Kepler orbit refers to the elliptical path that a celestial body follows around another body under the influence of gravity. It is named after the German astronomer Johannes Kepler, who first described the laws governing planetary motion.

## 2. What are the three laws of Kepler orbit?

The three laws of Kepler orbit are: 1) The law of ellipses, which states that the orbit of a planet around the sun is an ellipse with the sun at one of the two foci. 2) The law of equal areas, which states that a line connecting a planet to the sun sweeps out equal areas in equal times. 3) The law of harmonies, which states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

## 3. What is the difference between a Kepler orbit and a circular orbit?

A Kepler orbit is an elliptical path while a circular orbit is a perfectly round path. Kepler orbits are also governed by three laws that describe the motion of celestial bodies, while circular orbits are described by simpler equations.

## 4. How is the eccentricity of a Kepler orbit calculated?

The eccentricity of a Kepler orbit is calculated by dividing the distance between the foci of the ellipse by the length of the major axis. This value ranges from 0 (for a perfectly circular orbit) to 1 (for a parabolic orbit).

## 5. Can objects in a Kepler orbit collide?

Yes, objects in a Kepler orbit can collide if their orbits intersect at some point. This can happen when two objects have a similar orbital period and their orbits cross paths, or when one object's orbit is perturbed by the gravity of another object.