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One thing is certain: Mars can be further from Jupiter than Earth can ever be (when they're on opposite sides of the solar system), but Mars can also be closer from Jupiter than Earth can ever be.

And does this carry any physical implications?

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InquilineKea, you're an asset to this site, but time and again I have pleaded for you to increase the eligibility of your questions on numerous levels: one being title and body containing different questions; please clarify your complete concern within the body of the question, and keep providing the explicit question titles. Another point is substantiation. We have generous editors that help maintain consistent formatting etc., but they can't improve your question by putting words in your mouth - that's a job for you. Please correct this question or it will be closed. –  Grant Thomas Sep 5 '11 at 23:06
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up vote 3 down vote accepted

If Rj is the semi-major axis of Jupiter (5.2 AU) and Rx the semi-major axis of one of the inner planets then the minimum separation is Rj - Rx and maximum separation Rj + Rx so the maxima and minima are indeed larger for Mars, where Rx = 1.52 AU, than for Earth, where Rx = 1 AU. But the average of both is (Rj+Rx) + (Rj-Rx)/2 = Rj (although strictly true over a large number of orbits, so ellipticity, precession, etc. are averaged out).

It's easiest to see for Mercury, which orbits so rapidly that Jupiter is effectively stationary - at closest approach they are 5.20 - 0.39 AU apart, 44 days later (when Jupiter has moved only 1% of its 4332-day orbit) then Mercury is on the other side of the Sun and they are 5.20 + 0.39 AU apart.

No physical implications.

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An alternative is to think of it from the rest frame of Jupiter. If both orbits are assumed to be circular then the Sun will appear stationary, while the other planet will describe a circular orbit around the Sun. The average distance between Jupiter and the other planet is then just the distance from Jupiter to the planet's barycentre - which, as the Sun is so much more massive, is effectively the same as the semi-major axis of Jupiter. In reality the orbits are somewhat eccentric, but the time-averaged effect will be the same. –  strmqm Aug 5 '11 at 7:09
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