# How far is Jupiter from the Earth and the Sun?

Mar 15, 2016

From both the Sun and the inner planet Earth, the average distance of Jupiter is the semi-minor axis of its orbit b = 77.75 Million km

#### Explanation:

I have used semi-major axis of Jupiter's orbit a = 5.20260 AU, Its orbit eccentricity e = 0.046498, b = a $\sqrt{1 - {e}^{2}}$ and 1 AU = b for the Earth = 149597870 km.

Despite that different planets have different aphelion and perihelion , it is easy to prove that the average distance of an outer planet from an inner planet is nearly same as the the average distance of the outer planet from the Sun.

This approximation is under the assumption that the angle 1.3 deg between the orbital planes is small. If this is included, the answer given is correct to 2-sd only as 78 million km

For any planet, the average distance from the Sun is the semi-minor axis b of its orbit. This is important for highly eccentric orbits.

Of course, the difference between a and b does not make any apparent difference, when the approximations are restricted to lesser number of significant digits (sd) .

If the data for Jupiter are revised, the answer has to be revised accordingly.

I have given 5-sd approximation. If more sd are known in the approximations for Jupiter's a and e, a few more sd can be added.
Source for Jupiter data: wiki Jupiter.