How to fly to Jupiter on a low budget using only gravity and inertial motion.  The Galileo spacecraft was launched from the space shuttle in the Fall of 1989.  Gravity pulls the spacecraft towards the Sun, but Galileo is aimed to intercept Venus in early 1990.  The gravity of Venus acts like a slingshot boosting its speed and ability to avoid being pulled in more by the Sun's gravity.  Galileo now has enough inertial motion and speed to return to Earth by December 1990.  As in the case of Venus, Galileo is programmed to just miss the Earth.  The Earth's gravity increases the speed of Galileo and furthers its ability to escape some of  the Sun's gravitational attraction.  It orbits the Sun in such a way that it passes the asteroid Gaspra in the Fall of 1991 and then returns to the Earth again late 1992.  Again it just misses the Earth and gets its final slingshot boost to head towards Jupiter.  It passes the asteroid Ida in August 1993 and eventually reaches Jupiter in late 1995.  A probe was released into Jupiter's atmosphere and the spacecraft orbited Jupiter taking many close up pictures of Jupiter and its moons.

Note that this incredible navigational feat is not possible without the radical shift in cosmology that took place in the 17th century.  Scientists had to believe that planets were physical places just like the Earth, the universal force of gravity had to be deduced by Newton from Kepler's third law, and the counter-intuitive notion of inertial motion had to be discovered.