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Neptune, the 8th planet from the Sun, orbits at an average distance of about 30AU. Each Astronomical Unit is the distance from the Sun to the Earth, about 93,000,000 miles. This works out to be 500 light-seconds, or 8.3 light-minutes, from the Sun to the Earth.

Neptune is 30 times more distant, so when the Earth and Neptune are on the same side of the solar system, we are about 29 AU from Neptune, while if we are on opposite sides, it is 31 AU.

So light takes between 14,500 seconds to 15,500 seconds to get from Earth to Neptune. Since the speed of light is (we believe!) an absolute limit, nothing material could get there in less time.

How long would it take HUMANS to travel from Earth to Neptune? Right now, there is no possible way to send a person there. Even a robot probe like the New Horizons mission to Pluto, would take a dozen years or more to arrive there. As technology progresses, we will eventually be able to travel there, but I would not expect the first human to arrive in cis-Neptunian space until the year 2150 at the earliest. And that's only if we figure out some excellent reason for going there at all.

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15y ago

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