Thought experiment: Suppose we build a spacecraft with a low thrust electric propulsion and have a flight plan that involves constant acceleration on the first half of the journey, breaking on the second. Sounds ridiculous? Let's plug some numbers into the formula given here:
acceleration $a = 0.001 m/s^2$
Distance Earth-Jupiter $x=9.3 * 10^6 km$ Travel time $t=705d$
Start weight would be 80% fuel This assumes the exhaust velocity in the wikipedia article on the Vasimir, $v_e = 40km/s$
I think two years and 80% fuel ist not too terrible.
I'm not 100% sure such a craft could manage orbital insertion anywhere, I think leaving earth moon should be doable. The only beauty I see about such a craft would be that it could be built ultra light (in orbit) as it would never have to endure the stress of earth's gravity or a liftoff. but this is outside of the scope of my question.
My estimate does not take into account that such a craft would spend quite some time and fuel not simply flying from a to b but working against gravity wells: Earth, possibly earth-moon, sun. The proper way would be to simulate a flight plan. What is a non proper way that gives a reasonable estimate with a handful of iterations?
The scenario for the answer should be: starting from LEO and arriving at Jupiter in a heliocentric orbit using a low, constant acceleration.
This question tackles a similar scenario but with a fictional high-g drive where the considerations I'm interested in are not relevant.