Ygthkb

Jupiter's moons in their closest point to Mars (when Jupiter is closest to the sun) are like 7 times the distance between Earth and Mars, and in a return journey they will farther away. Is there any chance to reach them in the following decades? I would like to know how far the technology for going there is in a one shot journey, once humans are able to go to Mars, how much will they have to improve (in other topic someone mentioned that something that consumes fuel is the proximity to the sun pulling and decelerating the spaceship, besides from Mars escaping the planet will consume less fuel) to reach Jupiter from Mars, and also, how about if it's possible to set a permanent base in Ceres, Pallas or Vesta, for at least a partial resupply, could that help or be feasible at all?

Let's go back our old friend the Pork chop plotter. Earth to Jupiter using minimum fuel takes around 2 years and you get one opportunity per year, more or less, to get there. You can shorten the journey to perhaps 20 months with minimal extra fuel. The delta-V required at Earth (over and above escape velocity) is about 9.3 km/s (you can in theory aerobrake at Jupiter, although the velocities involved, and the radiation environment might make this a bit exciting).

Mars to Jupiter with minimal fuel takes longer. Intuitively I think this is because Mars' orbital velocity around the Sun is lower. Journey times are around 30 months, but the delta-V needed (again over and above Mars escape) is only about 6 km/s.

A fully-fueled SpaceX Starship is expected to have about 9 km/s delta-V capability (with a very small payload) so it could reach Jupiter if refuelled in high elliptical Earth orbit, or possibly directly from the surface of Mars. Refueling in Low Mars orbit would certainly be enough.

Bases on asteroids seem unlikely to help much. Matching orbit with them is too hard and you probably still have to get the fuel there. If you could make fuel on Ceres that would be quite appealing in terms of delta-V and payload mass, although the mission would get still slower.

TLDR: If you can make fuel on Mars, or on Ceres, it will help you move more payload to Jupiter without needing to launch insane amounts of fuel from Earth, but such missions are generally longer in duration than direct missions.

I whomped up a spreadsheet to compare scenarios like this: Hohmann.xls.

Typing Earth into departure planet cell and Mars into destination planet I get

Launch windows open each 2.14 years (synodic period)

Trip time .71 years

Delta V Low Earth Orbit to Low Mars Orbit: 5.7 km/s

Typing Mars into departure planet and Jupiter into destination:

Launch window: Each 2.23 years
Trip time 3.1 years

Delta V Low Mars Orbit to Jupiter Capture orbit: 4.4 km/s

Jupiter capture orbit has periapsis 300 km above Jupiter's cloud tops and apoapsis about 4.8 million kilometers.

Matching orbit with a moon would take more. Altitude of Jupiter's larger moons can be found in cells J27 to J30. For example setting Jupiter's destination orbit at Europa's altitude boosts delta V to more than 10 km/s. This doesn't take into account Europa's gravity.

Due to Jupiter's strong magnetic field Jupiter's moons suffer from a very harsh radiation environment.

Caveat: My spreadsheet assumes circular, coplanar orbits. So accuracy is only ballpark.

TL;DR Going from Mars to Jupiter's moons is a lot harder than going from Earth to Mars.