He praised the Poles' spirit and name-checked their heroes, including Copernicus.

"Think of that," he added in an off-script improv on the man who proved the world was not the centre of the universe.

What he meant, as with many of Trump's unscripted comments, is hard to parse.

But he may have been contemplating his own, and his country's, place in the universe, on the eve of the G20 gathering of the world's most powerful leaders.

The leader of the free world, perhaps more than ever, is not that. Trump went to Hamburg as a nationalist at a meeting of internationalists, a non-believer in the temple of globalism.

Germany has put together a broad, packed agenda of issues intended to foster global solidarity and action on climate change, trade, migration and security.

"America First" Trump, with his transactional style and populist instincts, is not in his element.

But, as with Copernicus, he may be revealing a greater truth rather than changing the order of things.

Independent of its Twittering president, the US is often no longer the first port of call for economic and political leadership. The centre of political gravity has moved.

In Warsaw, Trump cast himself in a new role: defender of Western civilisation.

"The fundamental question of our time is whether the West has the will to survive," Trump said. "Do we have the confidence in our values to defend them at any cost?

"The West will never, ever be broken. Our values will prevail. Our people will thrive. And our civilisation will triumph."

As the US retreats westwards, G20 observers are looking elsewhere for champions of a truly international liberal order.

German Chancellor Angela Merkel has experience, gravitas and international respect. She also has an advantage: as host, she set the priorities of the G20 meeting.

In a speech to the German parliament on Thursday, she didn't gloss over the US problem.

"The differences are obvious and it would be dishonest to try to cover that up," she said. With most of the rest of the G20, she is dismayed at Trump's withdrawal from the Paris climate agreement.

She took a second swing at Trump: "Those who think that the problems of this world can be solved with isolationism or protectionism are terribly wrong."

She has allies. Her words were close to those of Chinese President Xi Jinping, who cast himself as a free-trade evangelist at Davos in January: "Pursuing protectionism is like locking oneself in a dark room," he said. "Wind and rain may be kept outside, but so is light and air."

Ye Yu, of the Shanghai Institutes for International Studies, says China "would like to see G20 countries work together to contain anti-globalisation sentiment".

They don't want to formalise an anti-US alliance, but rather "pull the United States back toward seeking an enlightened self-interest, rather than pursuing an 'America First' stance at the cost of all other countries", Ye Yu wrote this week.

It's one theory. Another is that China is seeking to move into the vacuum left by the US. Many have noted a growing influence of, and respect for, China in Europe. President Xi has just opened a new panda garden at Berlin Zoo.

Prime Minister Malcolm Turnbull has championed free trade and open markets, and got on the front foot over the need for China to do more to rein in North Korea on Thursday, the day before the summit began.

But Turnbull, like so many world leaders, chose his words carefully when asked about Trump's America First rhetoric, and declined to criticise the US leader's anti-free trade agenda.

The British government is also staunchly pro free trade, even more so with an impending Brexit. Prime Minister Theresa May will also take up climate change in her one-on-one with Trump in the G20 wings.

French leader Emmanuel Macron said he hoped "the others can be brought back to their senses" on the Paris accords. He is likely to be a strong voice for liberal progressivism, at the G20 and beyond.

Andrew Hammond, an associate at the London School of Economics IDEAS centre, points out that the G20 isn't necessarily a unifying entity – Russia and Turkey, for example, have radically different political viewpoints. And Merkel has designed the forum to draw out those differences, not paper over them.

"There will be some tough conversations," Hammond says.

There is a school of thought that Trump is not a political black swan. Donald Rumsfeld, as US defence secretary in 2003, divided Europe into "old" and "new" countries, with "the centre of gravity moving to the east". Then, Hungary, Poland and the Czech Republic were allies in the United States' policy on Iraq, while France and Germany were opposed. Now, Trump draws rapturous applause in Warsaw but angry demonstrations in Hamburg. He finds a familiar scepticism about internationalism in Europe's east.

But the problem with Trump is not so much his policies as his approach, Hammond says.

"Trump seems to have a transactional kind of style, thinking about everything in the short term: what's a win, what's a loss, what's the cost/benefit analysis," he says. "Other US leaders have said, 'What's the US strategic interest over a multi-year, multi-decade horizon?' There is a concern that [Trump's] transactional approach doesn't lend itself to long-term strategic thinking."

Hammond says Australia could play an important role at the G20, because it is not 100 per cent aligned with either Europe or Trump.

"[Turnbull] is a key swing player I think in the big debates."

Ahead of the summit, Turnbull told Fairfax Media he would focus his efforts on counterterrorism, getting global agreement on cracking digital encryption in such apps as WhatsApp, Signal and Telegram that allow terrorists to operate in so-called "ungoverned spaces", and bringing down trade barriers.

On trade, on the need to crack secure cyber communications and even on climate change, Turnbull's aims at the G20 line up much more with those of the Europeans than those of the United States, which looks increasingly isolated.

But as is so often the case at such summits, the provocative actions of a rogue state look set to bring back together allies – in this case, in the West – who have recently grown distant.

Soon after his first bilateral meeting with Merkel, Turnbull made clear North Korea would dominate proceedings and that Australia would be in lock step with United States and its other allies over the issue.

"The reckless and provocative actions, the latest escalation by the North Korean regime, has been condemned by all of the nations gathering here today in Hamburg, and we will see a strong commitment to condemn and strengthen ... the sanctions [that] have already been applied to the North Korean regime," he said.

Crucially, though not surprisingly, Turnbull declined to criticise – over and again – any aspect of Trump's agenda after his meeting with Merkel on Thursday.

Like many world leaders – at least at this stage – the judgment seems to be that keeping the bear happy, rather than poking it, is still the best approach.

Interestingly, Turnbull also added further nuance to his call for China to do more to rein in the hermit kingdom.

"The actions by the North Korean regime are illegal, they are dangerous, they're a provocation and they've been escalating them," he said. "The nation with the greatest leverage over North Korea is China."

"We recognise that North Korea is not a compliant, client state of China – like East Germany was to the old Soviet Union – so the relationship between China and North Korea is not without its difficulties. But the fact is China has the greatest leverage and, of course, we urge China to bring more pressure, more economic pressure in particular, to bear on North Korea to bring that regime to its senses."

Turnbull's point about North Korea not being a "client state" is a new wrinkle in his language, designed to allow China a little more wriggle room and critical distance from North Korea – and therefore, maybe, allow for stronger action, such as China actually enforcing sanctions, rather than just talking about them.

The Prime Minister is likely to have a low-key "pull-aside" with Trump on Friday, in which he will make his views clear on countering terrorism, and on how to tackle North Korea.

More formal meetings with South Korea's new president, Moon Jae-In, Indonesian President Joko Widodo and Vietnamese Prime Minister Nguyen Xuan Phuc, who is attending the G20 summit as a guest, will probably focus on North Korea's actions.

Turnbull's job is to play the role of Asia-Pacific multilateralist, and he appears to relish it. In a few short days, it will be clear whether he – and fellow travellers such as Merkel, May and Macron – have been able to achieve anything concrete on the Korean peninsula.

Despite all the goodwill, the prospects for a genuine breakthrough appear grim.

But is the G20 the right venue to assemble a new world order?

Previously a gathering of finance ministers, the G20 was upgraded to heads of state at the initiative of then US president George Bush in November 2008, in response to the global financial crisis.

At the time it was hailed as a kind of "steering committee" for the world – more inclusive than the G7/8, more responsive than the UN.

But in 2014, a European Central Bank study concluded that G20 summits "have not had a strong, consistent and durable effect" on the world's financial markets.

"The information and decision content of G20 summits is of limited relevance for market participants," it concluded. In layman's terms, it was all talk, no action, as far as economists were concerned.

The G20 has a habit of making grand declarations but achieving little, says Heribert Dieter, of the German Institute for International and Security Affairs in Berlin.

Writing for the Council on Foreign Relations thinktank, he said the G20 had still not delivered a coherent strategy on regulating financial markets.

"The preferences of G20 countries are divergent; therefore, the group has been unable to accomplish its core mission," Dieter said. It had also failed on free trade.

"A spirit of protectionism characterised the trade policy of some G20 countries, and the advent of the Trump administration has made the departure from an open multilateral trading system more visible than before."

Yasushi Kudo, of Japanese thinktank The Genron NPO, agrees.

"President Trump's avowed 'America First' policy and his preference for bilateral deals will continue to undermine the raison d'etre of the G20," he wrote.

"Overt and covert moves by superpowers to bolster their influence by making use of the fragile international environment are likely to erode the foundation of the established frameworks that have hitherto sustained the world order."

This year's G20 will provide a general sense of co-operation for the common good, he said, but beyond that "the G20 will be another political show that uses ambiguous rhetoric to conceal instability and potential confrontations".