Nasa's Voyager spacecraft have enthralled everyone with their exploits at the edge of the Solar System, but their launch in 1977 was only possible because of some clever maths and the persistence of a PhD student who worked out how to slingshot probes into deep space.
On the 3 October, 1942, the nose cone of an early V2 test rocket soared high above the north German coast before falling back to a crash-landing in the Baltic Sea. For the first time in history, an object built by humans had crossed the invisible Karman line, which marks the edge of space. Astonishingly, within 70 years - just one human lifespan - we'd hurled another spacecraft right to the edge of the Solar System. Today, 35 years after leaving Earth, Voyager 1 is 18.4 billion km (11.4 billion miles) from Earth and about to cross over the boundary marking the extent of the Sun's influence, where the solar wind meets interstellar space. Sometime in the next five years, it will likely break through this so called "bowshock" and head out into the galaxy beyond. Its twin, Voyager 2, having flown past all the outer giant planets, should pass over into interstellar not long after.
Going back in time, in 1957, as Sputnik 1 became the first engineered object to orbit our home planet, mission planners started to look towards other worlds to propel their probes. At that time, Nasa couldn't guarantee a spacecraft for more than a few months of operational life, and so the outer planets were considered out of reach. That was until a 25-year-old mathematics graduate called Michael Minovitch came along in 1961. Excited by UCLA's new IBM 7090 computer, the fastest on Earth at the time, Minovitch decided to take on the hardest problem in celestial mechanics: the "three body problem". Astronomers had been pondering the three-body problem for at least 300 years, ever since they'd started plotting the path that comets took as they fell through the inner Solar System towards the Sun. Undeterred by the fact that some of the finest minds in history, including Isaac Newton hadn't solved the three-body problem, Minovitch became focused on cracking it. He intended to use the IBM 7090 computer to home in on a solution using a method of iteration.
Using a solution to the three-body problem, a single mission, launching from Earth in 1977, could sling a spacecraft past all four planets within 12 years. Such an opportunity would not present itself again for another 176 years. With further lobbying from Minovitch and high level intervention from Maxwell Hunter, who advised the president on US space policy, Nasa eventually embraced Minovitch's slingshot propulsion and Flandro's idea for a "grand tour" of the planets.