The answer to ”how long does it take to get to Jupiter” has changed in the last few years. The Galileo spacecraft used Hohmann transfer orbits to arrive in orbit. It was launched in October, 1989 and arrived in orbit in December of 1995. That was a 6 year flight. The New Horizons spacecraft was built using a different type of engine than the Galileo and could take a more direct route. It was launched on January 19, 2006 and flew past Jupiter just 13 months later on its way to Pluto. As you can see, propulsion technology made a giant leap in just a few years.
One question that comes to mind is what is a Hohmann transfer orbit. The short answer is that it is a way to use a planet’s gravity to propel a spacecraft toward another planet. Sort of a slingshot affect. The long answer is that a Hohmann transfer orbit is an elliptical orbit used to transfer between two coplaner, circular orbits. It typically requires two engine impulses to move a spacecraft on and off a single transfer orbit. The maneuver is named after Walter Hohmann who published the first description of the maneuver in 1925. As it applies directly to the problem of a spaceflight, a Hohmann transfer would look like this: The spacecraft would have a certain velocity from its initial orbit around Earth. At the end of the initial orbit around the Sun the craft will need another velocity to enter the second orbit, requiring an engine impulse. For Jupiter, the velocity would have to be less than the velocity needed to continue in the initial orbit, so the craft will have to decelerate. That is not the end of it because the spacecraft is still going to fast to be captured by Jupiter gravity. So, it has to move into another orbit of Earth, so another Hohmann transfer is necessary. This is still not the end, another transfer has to be made to make sure the spacecraft can settle in around Jupiter. Calculating fuel and burst durations are the simple parts. Timing the launch of the craft so that it exits the transfer orbit at the same time as the target planet is arriving in that part of its orbit is the trick.
How long does it take to get to Jupiter has changed dramatically since the 1980s. Scientists are working on ways to get to any part of our Solar System in less than a year. No one is sure where that search will lead, but it is sure to be exciting when the final discovery is made.