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 ?
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$\begingroup$ Do you know the eccentricity of the planetary orbits? $\endgroup$ – user15317 May 24 '17 at 9:25
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$\begingroup$ 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. $\endgroup$ – Alex May 24 '17 at 10:17
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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 $2b$.
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2$\begingroup$ Just to a source for these equations, check out this section of the Wiki page on ellipses. $\endgroup$ – zephyr May 24 '17 at 13:47
