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

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.
  • #1
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Sorry if this is in the wrong forum.

I have the equation [tex]r = \frac{a(1-e^2)}{1+e \cos \theta} [/tex],
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.
 
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  • #2
'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.

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