This classic "square" (actually trapezoidal – there's reason to be mathematically correct) was once the scene of medieval executions.

But as afternoon transforms into night, the piazza reverts to what it has always been: a meeting place for the people of Padua.

At the three-quarter mark of a long day, in the shade of the extraordinary Palazzo della Ragione, perhaps Italy's most impressive town hall, this is the perfect place for a sundowner. It feels as if time and space are standing still.

Yet we're here in Padua to honour Galileo Galilei, the one man, above even Copernicus, who proved Earth revolves around the sun, rather than vice versa. Not only is the Earth revolving, but so are we.

So I sit down before I get dizzy, and then applaud as Galileo's sun sets safely.

Most of us flock to Italy to eat great food, see great cities, sample great shops or pay homage to the great masters of the Renaissance. If we stick to the last category, we usually have a wish list of painters and sculptors whose work we need to witness. Leonardo, Michelangelo, Raphael, Botticelli, Lippi, Fra Angelico et al.

But the one towering genius of the Italian Renaissance who is usually forgotten in this annual migration is Galileo.

Why? Because he was a mathematician, scientist, philosopher, astronomer and polymath who never left behind a single fresco or painting.

And yet Galileo must have drunk an al fresco aperitif in this very same colonnaded piazza where I'm watching the sunset now.

About 400 years ago, Galileo was professor of mathematics at the University of Padua for 18 of the most important years of his life, from 1592-1610.

While in Padua, he discovered many of the scientific principles that, famously, would eventually see him found guilty of heresy by Pope Urban VIII and confined to home imprisonment for the rest of his life.

Just an hour before tucking into my aperitif (three parts prosecco, one part soda and two parts Aperol) I had visited the city's Palazzo Bo, where Galileo delivered his ground-breaking lectures. "Galileo's chair" is one of the palazzo's greatest treasures.

Even more famous is the university's beautifully egg-shaped and multi-storied Anatomy Theatre. Built in 1594, the oldest permanent anatomy theatre in the world was where Galileo – a former student of medicine – watched dissections of the human body.

Galileo's name is often spotted when you're walking around Padua, from the physics department which bears his name to the ancient observation tower that is now the focal point of Padua's astronomy department.

The later is a delightful construction that deserves the backstory many locals give it – the tower where Galileo observed the heavens each night through his newly discovered telescope, when the stars were unpolluted by the electric lighting of a modern city.

Sadly, that's a fallacy. Galileo did discover immense secrets of the universe during his time in Padua. So if his observation tower can no longer be seen, what about the house where Galileo fathered his three children?

That too has long gone. Yet his personal life is a fascinating glimpse into the perpetual tug-of-war between faith and science.

Galileo was such a committed Catholic he almost became a monk. Nevertheless, he never married Marina Gamba, his life-long partner and mother of his children, because he felt she wasn't of sufficient class to satisfy his aristocratic family. He sent both his daughters (Virginia and Livia) to a nunnery, feeling their illegitimacy (hardly their fault!) made them unmarriageable, while his son, Vincenzo, was adopted and inherited his fortune.

So what is there for the 21st-century tourist to see of the Padua Galileo would have known?

Most of the city. In the 16th century, Padua was already one of the great university cities of the world, founded in 1222. It remains a relaxed university town today – a city of students and cycles: Cambridge with chic.

Galileo would have gone to see the vast 13th-century Basilica of St Anthony, Padua's home-grown saint. And its 16th-century botanic gardens. Plus the second-century Roman Arena, the best preserved in Italy.

But perhaps most of all, Galileo would have gone to see Giotto di Bondone's great masterpiece, painted in just two years (1304-05) at the Scrovegni Chapel – the precursor of Michelangelo's Sistine Chapel paintings.

Nothing prepares you for the vibrancy of Giotto's paintings, or the drama in his wall paintings (look at the one showing the slaughter of the innocents and the exquisitely painted tears on the faces of the mothers whose first-born sons have been slaughtered by Herod in his hunt for the baby Jesus).

Marvel at Giotto's version of the Last Judgment, particularly his depiction of hell as described by Dante in his Inferno.

But dwell longest on Giotto's vividly blue, star-crossed night sky. How Galileo must have studied that painted interpretation.

What does it say? Look up, young man. Look up!

TRIP NOTES

MORE INFORMATION

welcomepadova.it

GETTING THERE

Qantas with Emirates operates daily flights from Sydney and Melbourne to Venice via Dubai. See emirates.com/au or qantas.com

TOURING THERE

Venice is included on a 12-day Ultimate Italy trip by Luxury Gold by Insight Vacations from $7325 per person. Phone 1800 001 771 or see insightvacations.com. Padua is an easy 40-minute train ride from Venice, tickets about $14 each way.

STAYING THERE

NH Mantega, Padua is a chic, modernistic hotel within easy walking distance of Padua train station and all the city's main attractions. See nh-hotels.com

Steve Meacham travelled as a guest of Insight Vacations.