In late 1973, sponsored by The Sunday Times, Simon began travelling around the world on a 500 cc Triumph Tiger 100 motorcycle. For four years he travelled over 64,000 miles (103,000 km) through 45 countries. Most accounts from his trip are detailed in his book, Jupiter's Travels, while some of the book's gaps are filled in its second part, the book Riding High.

In 2001, Simon started a new motorcycle journey, this time on a modified BMW R80GS, that roughly followed the same route as his 1973 trip. He was around 70 years old at that time and completed the journey in three years. His new book, Dreaming of Jupiter, detailing this journey, was released in March 2007