I am attempting to create a small computer simulation with planetary orbits.
Calculating the position a planet has on its orbit at a certain time works fine. However, I now want to draw their orbits as well.
The problem is, that to draw an Ellipse in most computer programs, I need to specify the center (x,y) coordinates as well as a width and a height. However, the only information I have available is the following;
- The (x,y) coordinates of one of the focal points $f$, as this is the position the planet revolves around.
- The size of the semi-mayor axis $a$ of the ellipse.
- The eccentricity $\epsilon$ of the ellipse.
(Also, it is presumed that the semi-mayor axis is parallel to the x-axis.)
How can this information be used to calculate the (x,y) position of the center of the ellipse?