Calculating semi-minor axis of an ellipse I'm coding a solar system animation and so far it's done, but the the orbits of the planets are circular. To make the simulation more realistic, I want to use elliptic orbits. So I visited Mercury (planet) and Solar System Exploration: Planets: Mercury: Facts & Figures pages, but the semi-minor axis of the Mercury (or any other planet) isn't given. Then I looked for a way to calculate it and found a formula $$\epsilon=\sqrt{\frac{a^2-b^2}{a}}=\sqrt{1-\left(\frac{b}{a}\right)^2}$$ in Ellipse - Wikipedia, the free encyclopedia page, but my math knowledge falls short in applying it to my situation. Mercury Semi-major axis 57,909,050 km Eccentricity 0.205630 Aphelion 69,816,900 km Perihelion 46,001,200 km Is there a way to calculate the semi-minor axis of Mercury's orbit with the given values?

The formula you have got can be rearranged to yield the semi-minor axis,

$b = a \sqrt{1-\epsilon^2}$, where **a** is the semi-major axis. Substituting each value in the formula gives

$b = (57,909,050) \sqrt{1-0.205630^2}$
$b = 56,671,523 \space km$