# Property of elliptical orbits

I've studied that the major axis of a planets orbit = ( radius of perihelion + radius of aphelion) . But then how can we calculate the value of the minor axis if we are provided with the values of radius of perihelion and radius of aphelion only ?

• Do you know the eccentricity of the planetary orbits? – user15317 May 24 '17 at 9:25
• Look at the ratio of perihelion and aphelion radius. If they are equal, you have a circular orbit, if they are very different, a highly elliptical one -- for the same major axis size. Basic trigonometry should get you the rest of the way. – Alex May 24 '17 at 10:17

If $r_p$ is the perihelion distance (the closest distance of the planet in its elliptical orbit from the Sun), and if $r_a$ is the aphelion distance (the farthest distance from the Sun), the major axis is
$$2a = r_a+r_p$$ where $a$ is the semi-major axis (half of the major axis). The eccentricity of the orbit can be calculated from the perihelion and aphelion distances using $$e = \frac{r_a-r_p}{r_a+r_p}$$ Once the eccentricity is known, the semi-minor axis can be calculated from $$b = a\sqrt{1-e^2}$$ The minor axis, of course, is twice the semi-minor axis, or $2b$.