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After seeing this answer (https://space.stackexchange.com/a/60438/44505) saying that starship could get to Neptune, I wondered how long it would take to get to Neptune. Bonus question: Would it be possible to send humans onboard and have them return in a reasonable amount of time?

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  • $\begingroup$ Returning the humans from Neptune to Earth would be impossible. You would need a gigantic rocket so large that a Starship would look tiny in comparison. $\endgroup$
    – Uwe
    Sep 23, 2022 at 9:22

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The linked answer assumes an optimal Hohmann transfer. That's just an elliptic orbit touching the Earth's orbit and Neptune's orbit, so a semi major axis $a = \frac{a_{Earth} + a_{Neptune}}{2}$

Orbital period is given by:

$$T = 2 \pi \sqrt{\frac{a^3}{\mu}}$$

And substituting in $a$ that's a 61.3 years roundtrip. (Half, 30 years, for just the outbound leg).

Of course, a spacecraft travelling along this orbit spends a lot of time hanging out in the outer solar system. Ramping the speed to solar system escape velocity doesn't cost all that much more, a mere 0.5 km/s extra delta-v from low Earth orbit. That reduces the one-way travel time to 13 years.
But then you are zooming past Neptune at solar system escape velocity, with no hope of returning to Earth.

An interesting consideration is how much we can ramp up the departure speed, and still have what's called a "free return trajectory": Neptune bending our orbit back around so we can get home. This is possible with an aphelion up to 3.1 time the orbital radius of Neptune.
Outgoing leg of 14.6 years, orbit gets bent around for free by Neptune's gravity, and then another 14.6 years to get home for a total of 29.2 years.

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    $\begingroup$ Better bring some canned goods. $\endgroup$
    – GdD
    Sep 23, 2022 at 13:26

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