Two Pegs and a String
Click here for source document. Under gravity's influence, an object moves in an orbit shaped like an ellipse. To consider an ellipse in more detail; use two pegs and a string.
This method of drawing an ellipse provides us with a formal definition, which we shall adopt in this chapter, of an ellipse, namely:
An ellipse is the locus of a point that moves such that the sum of its distances from two fixed points
called the foci is constant familiar equation to the ellipse In the theory of planetary orbits, the Sun will be at one focus. Let us suppose it to be at F and both have defensible positions), and it is equal to Q = a(1+ e). 2.3.9
A line parallel to the minor axis and passing through a focus is called a
latus rectum (plural: latera recta). The length of a semi latus rectum is commonly denoted by l (sometimes by p). Its length is obtained by putting x = ae in the equation to the ellipse, and it will be readily found that l = a(1− e2 ). 2.3.10
The length of the semi latus rectum is an important quantity in orbit theory.
It will be found, for example, that the energy of a planet is closely related to the semi major axis a of its orbit, while its angular momentum is closely related to the semi latus rectum.
The circle whose diameter is the major axis of the ellipse is ca
Take a continuous loop of string and encompass two pegs.
Let the pegs be separated by distance, 2c. 
Replace the pencil with an asteroid to continue making imaginary triangles such that two nonbase sides equal 2a. At the apex of these triangles, the asteroid draws an elliptical orbit around the Sun. Two pegs represent the two foci of the orbit. Replace one peg with Sol while other focus retains an imaginary peg. In this partially drawn orbit, note that radius, r, gradually grows to max distance, Q, orbit's aphelion, farthest distance from Sol.

An ellipse is the locus of a point that moves such that the sum of its distances from two fixed points
called the foci is constant familiar equation to the ellipse In the theory of planetary orbits, the Sun will be at one focus. Let us suppose it to be at F and both have defensible positions), and it is equal to Q = a(1+ e). 2.3.9
A line parallel to the minor axis and passing through a focus is called a
latus rectum (plural: latera recta). The length of a semi latus rectum is commonly denoted by l (sometimes by p). Its length is obtained by putting x = ae in the equation to the ellipse, and it will be readily found that l = a(1− e2 ). 2.3.10
The length of the semi latus rectum is an important quantity in orbit theory.
The circle whose diameter is the major axis of the ellipse is ca
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