Keplers Laws (1)

Semi-major axis

The longest diameter of an ellipse, dividing it into two equal halves.

Semi-minor axis

The shortest diameter of an ellipse, perpendicular to the semi-major axis.

Eccentricity (e)

A measure of how much an ellipse deviates from being circular, calculated as e = c/a where c is the distance from the center to a focus and a is the semi-major axis.

Vertex (of an ellipse)

The point where the ellipse intersects the major axis.

Co-vertex

The point where the ellipse intersects the minor axis.

Ellipse

A set of points in a plane, the sum of whose distances from two fixed points, called foci, is constant.

Polar form of an ellipse

Expressions that represent the distance r of a point on an ellipse from a focus as a function of the angle θ: r(θ) = (1 - e²) a / (1 - e cos(θ)).

Area approximation

A method of estimating the area enclosed by an ellipse, often simplified using the area of a circle.

Foci (F₁, F₂)

The two fixed points used to define an ellipse.

For small angles in ellipse area approximation

Using the formula involving angle y, where small angle approximations apply to compute area.