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Sci-fi writer needs to get from Lunar Orbit to Enceladus Orbit in least amount of time with a travel acceleration of 1.5G no more than 3G for navigation changes.

What resources are available that I can use to work it out or learn how?

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    $\begingroup$ The distance between Earth and Saturn is not constant, minimum is 7.991 AU, maximum 11.086 AU. $\endgroup$
    – Uwe
    Commented Aug 17, 2023 at 16:55
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    $\begingroup$ Is this a spacecraft that can accelerate at 1.5 gees continuously for the entire trip? $\endgroup$
    – notovny
    Commented Aug 17, 2023 at 17:08
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    $\begingroup$ Since this is a purely fictional scenario, suggest you ask on the worldbuilding stack site instead. It's also too broad of a topic for this site to teach you how to do it. $\endgroup$ Commented Aug 17, 2023 at 17:09
  • $\begingroup$ With current technology, rocket engine burn times are measured in minutes. Continuous acceleration consumes a vast amount of fuel. But at 1.5 $g$ you can get to Saturn in around 9 days. FWIW, here's a 30 year plot of the Earth-Saturn distance, calculated using JPL data, with a 7 day timestep. i.sstatic.net/LGmFb.png $\endgroup$
    – PM 2Ring
    Commented Aug 17, 2023 at 18:25
  • $\begingroup$ @OrganicMarble I've adjusted the wording slightly to change from "teach me" to a reference-request and added an answer to get things started. $\endgroup$
    – uhoh
    Commented Aug 17, 2023 at 21:01

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Welcome to Stack Exchange!

It's generally important to add some evidence of prior research to questions, so I'll post this too-long-to-be-a-comment comment as an answer to get you started at least.

Since your propulsion system can burn continuously throughout the mission, the trajectory is non-Keplerian. Usually interplanetary missions have a big "long" burn (minutes to hours) to break out of Earth orbit and get into a heliocentric orbit, then often but not always use gravitational assists (flybys) of other planets to gain speed and change direction one or many times. More flybys means (roughly) longer time but more spacecraft mass for a given launch system.

At all times (except during the flyby's) the spacecraft are traveling in heliocentric orbits - ellipses except for a few hyperbolas (e.g. New Horizons, the Voyagers) that will keep on going further and further until they hit something.

A second kind of mission uses electric propulsion which can burn for months or conceivably years. These spiral-lilke trajectories are non-Keplerian - they are not elliptical or hyperbolic.

A third kind is the solar sail, which can pick up huge velocities by starting very close to the Sun. These spiral-like trajectories can also escape to infinity, but once far from the Sun they can't stop and smell the roses anywhere. They are extremely tiny mass spacecraft that can only keep going.

A fourth kind of mission which is relegated to the future (nuclear propulsion) and has quite a nice home in SciFi is the "torch ship". This is some kind of propulsion system that has a non-standard power source like nuclear fission or fusion or antimatter. See for example Wikipedia's Space travel in science fiction; Means of travel.

This is your kind of mission. Your propulsion system can run for years at a time without running out of juice.

...least amount of time with a travel acceleration of 1.5G no more than 3G for navigation changes...

This is often colloquially referred to as a "torch ship". See:

and maybe

Now on to the problem

This is not an easy problem to solve, you need some creativity and a simulator (a computer program or game).

But since the idea of torch ships has been around a long time and simulators are aplenty these days (Kerbal, Universe Sandbox,

I also think it's very likely that Scott Manley has one or two videos that address interplanetary trajectory simulation using these programs and possibly the torch ship problem as well!

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