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Unfortunately, you can't give an exact answer, because it depends on where the planets are in their orbits. For example, they could be on opposite sides of the Sun or on the same side.

When on the same side, Jupiter could be near aphelion Neptune at perihelion, minimizing the shortest distance to 245 - 45 = 200 light minutes. Conversely, with Neptune and Jupiter both at aphelion on opposite sides of the sun the distance is maximized to 247 + 45 = 292 light minutes apart.

The best estimate for their average separation is given by the hypotenuse of a right triangle of their average solar distances, roughly (246^2 - 43^2)^(1/2) = 250 light minutes.

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