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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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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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