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General InfoEdit

Ellipse2

WhatEdit

An ellipse is mathematically defined as the set of points that satisfies the equation

r + r' = 2a

Semi Major AxisEdit

The semi major axis a is half the length of the long, or major axis of the ellipse

Semi Minor AxisEdit

The semi minor axis b is half the length of the short, or minor axis of the ellipse

Focal PointEdit

The focal points are denoted by F_1 and F_2 and the distance to from the focal points to the point X on the ellipse is denoted as r and r^'

EccentricityEdit

The eccentricity e is defined as the distance between the two foci divided by the major axis of the ellipse. The distance from the center to either foci can be expressed as ae

For a circle, e=0

PerihelionEdit

The point on the ellipse that is closest to the principal focus is called perihelion

The distance from the principal focus at perihelion is:

d = a - ea = a(1 - e)

AphelionEdit

The point on the ellipse that is farthest from the principal focus is called aphelion

The distance from the principal focus at aphelion is:

d = a + ea = a(1 + e)

RadiusEdit

The radius can be defined as:

r = \frac {a(1-e^2)}{1 + e \textrm{cos}\theta}

Relationship Between Major and Semi Major AxisEdit

b^2 = a^2(1-e^2)

Total Energy of a Binary OrbitEdit

E = -G \frac {m_1 m_2}{2a}