We need to learn about the basics of elliptical trajectory and terminology associated with it. It is important from the point of view of applying laws of Newtonian mechanics. We shall, however, be limited to the basics only.

**Conic section**

Conic section is obtained by the intersection of a plane with a cone. Two such intersections, one for a circle and one for an ellipse are shown in the figure.

Conic sections |
---|

**Elliptical trajectory **

Here, we recount the elementary geometry of an ellipse in order to understand planetary motion. The equation of an ellipse centered at the origin of a rectangular coordinate (0,0) is :

where “a” is semi-major axis and “b” is semi-minor axis as shown in the figure.

Ellipse |
---|

Note that “

**Eccentricity**

The eccentricity of a conic section is measure of “how different it is from a circle”. Higher the eccentricity, greater is deviation. The eccentricity (e) of a conic section is defined in terms of “a” and “b” as :

where “k” is 1 for an ellipse, 0 for parabola and -1 for hyperbola. The values of eccentricity for different trajectories are as give here :

- The eccentricity of a straight line is 1, if we consider b=0 for the straight line.
- The eccentricity of an ellipse falls between 0 and 1.
- The eccentricity of a circle is 0
- The eccentricity of a parabola is 1.
- The eccentricity of a hyperbola is greater than 1.

**Focal points**

Focal points (

Focal points |
---|

The focus of an ellipse is at a distance “ae” from the center on the semi-major axis. Area of the ellipse is "πab".

**Semi latus rectum**

Semi latus rectum is equal to distance between one of the foci and ellipse as measured along a line perpendicular to the major axis. This is shown in the figure.

Semi latus rectum |
---|

For an ellipse, Semi latus rectum has the expression in terms of “a” and “b” as :

We can also express the same involving eccentricity as :