the ellips
the ellips analyticly
An ellips is a curve with equation x²/a² + y²/b² = 1
In this equation a is the semi major axis, b the semi minor axis.
Drag the green points on the horizontal and the vertical axis and see how the equation and the form of the ellips change.
the ellips as a locus
You can define an ellips as the locus of a point with a constant sum of the distances to two given points. These two points are called the foci.
Given a and b the semi major axis and semi minor axis of the ellips we find:
- as foci F1 = (-c, 0) and F2 = (c, 0) wih
- as eccentricity e = It's clear that you'll get an ellips if 0 < e < 1 (or: 0 < b < a) The upper limit of b is a: the eccentricity becomes 0 and the ellips becomes a circle The lower limit of b is 0: de ellips has got no height.
the sun as focus
While the earth's orbit is an ellips with the sun in one of the two foci, it's clear that the sum of the distances to the foci is constant, but the distance to the sun is not. If you just want to draw the orbit, you can use a circle. If you want to make clear when the earth is in which point on it's orbit you can draw an ellips and exaggerate the difference between major and minor axis.
A second problem is: "Which dimensions do I use for earth and sun?"
- the radius of the earth is aproximately 6400 km,
- the radius of the sun is aproximately 696 000 km,
- the average distance between earth and sun is aproximately 150 000 000 km.