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7
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There are a number of things you'd have to factor in if you want an exact answer. Like the person above said, it depends on where they are in their orbits. There are also more orbital factors like their inclinations and the longitudes of the ascending nodes that will also effect the distance. You can calculate that if you'd like, but for all practical purposes, the person above me is close enough.
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The distance varies. Over the past 100 years, the range has been 2,795,274,081 miles, plus/minus 494,731,035 miles (center-to-center). Right now (Oct 26th, 00:00 UTC), the distance is 2,628,234,317 miles, which is 167,039,764 miles closer than average.
The difference between the sizes of the orbits of these planets is an average of 2,314,543,355 miles.
The difference between the sizes of the orbits of these planets is an average of 2,314,543,355 miles.
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That depends on where they are in their orbits. If they're on the same side of the sun and Neptune is at opposition to Jupiter (that is, they're in a straight line from the sun), then about 25 astronomical units (1 au = about 93 million miles). If they're on opposite sides of the sun, then about 35 au.