As a general rule, alliances between nations as close as Australia and the United States are bigger than the leaders. But with Donald Trump as leader, the general rules have been discarded. While Trump remains president, Australia should be very wary of seeking closer ties, but rather should be willing to let the bigger partner know that we might be small, but we are vital.

On Monday morning, the NFL Super Bowl between the New England Patriots and the Atlanta Falcons will be played, and despite no Australian participating in the event, barely any Australians even playing the sport, and only a few more who understand it, it will be broadcast live on free-to-air TV over six hours. In a couple of weeks, American cable network HBO will begin broadcasting the TV series Big Little Lies based on the novel by the Australian author Liane Moriarty and starring Nicole Kidman.

The US and Australia are, it is fair to say, very much culturally intertwined.

That will not change no matter how many times Trump abuses our prime minister. The news this week that Trump yelled at Malcolm Turnbull over the phone about how bad a deal the plan was for the US to take 1,250 refugees from Manus Island and Nauru rings so true that there is little worth in either government running with the “courteous discussion” line.

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Trump showing anyone a lack of respect – let alone the leader of one of the US’s closest allies – is not only not surprising, it is expected.

And while it won’t end any alliance between the two nations, it should be a sign that things must change.

The relationship is of course more than just cultural, but it has greatly shifted over the years.

No longer, as was the case during the cold war, does Australia catch a cold every time the US sneezes. Since the 1990s, as we increased our exports to China, we have been able to go along somewhat different economic paths.

That isn’t to say the US is not important to our economy – it is our third biggest trading partner. But it is a distant third – the amount of trade with the US is roughly worth about 30% of our trade with China.

And imports account for most of that trade. Our trade deficit with the US is larger than with any other nation. In 2016, we imported about $17bn more in merchandise from the US than we exported to them.

By contrast, our merchandise exports to China were $21bn more than what we imported:

The US does remain the biggest source of foreign investment for Australia, but our economic fortunes are now very much more connected to China than America.

The relationship is of course bound by more than economics. Since WWII, as is often noted, we have fought alongside the US in every major war – Korea, Vietnam, the Gulf, Afghanistan, Iraq and now against Islamic State.

But it is a relationship where Australia often gets ignored or forgotten.

You don’t need to be prime ministers Trunbull, or John Hunt to know that Americans can often be less knowledgeable of us than we are of them.

Similarly, despite that willingness to be side by side in battle, our sacrifice is not always appreciated in a fitting manner.

Robert MacNamara, the secretary of defence from 1961 to 1968, for example, remarked in the documentary The Fog of War that the US should have realised its cause in Vietnam was wrong because “none of our allies supported us; not Japan, not Germany, not Britain or France”.

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None?

That’s a pretty sharp slap to the face of the nearly 60,000 Australian men and women who served in the Vietnam War, let alone the 521 who died.

But the military alliance with the US is not all one way.

Since 1956, Australia has been part of the “five eyes” intelligence-sharing alliance. Our position on the globe is also vital for US defence interests, giving it the ability to monitor signals and control drones in Afghanistan, and keep in touch with US satellites for its early warning missile defence system.

You wonder if at any point in his conversation with Trump whether Turnbull felt like suggesting that the US president google “Pine Gap”?

He could also have suggested that Trump ask his defence chiefs where Darwin is located on a map so he could find out where a thousand or so US marines are stationed, or maybe he could also ask just why F-22 Raptors will be flying out of RAAF Base Tindal?

We are small, but vital to US interests.

The importance of leaders across alliances is rather overstated and good for PR purposes. It allows the leaders to leak to journalists news of how the prime minister got on so well with the president that special favours were being done for us.

Mostly it’s hogwash – as the latest spin early this week turned out to be.

But leaders do matter – especially when one is as reckless as Trump.

Trump is unlikely to do us much direct damage. He could try to pull out of our free-trade agreement, but that would more likely hurt the US economy than ours. Most of the damage he could do economically would come via ricochets, should he send the US into a trade war with China.

Such a war might slow the world economy and thus weaken the demand for our exports, but were it to allow China to take a more central role in the world economy Australia could possibly benefit .

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The reality is there is little to be gained at the moment from Turnbull seeking to engage closely with Trump.

The orange megalomaniac in the White House never sees deals as a chance for a win-win, nor even as merely a zero-sum game. As Gore Vidal would say, for Trump it is not enough to succeed, others must fail – and if that is not possible, as Turnbull found out this week, others must be humiliated.

Given our long cultural, economic and defence ties, suggestions that we shift towards a greater alliance with China are fanciful. We may sell a lot of stuff to China, but we would be extremely foolish to think China is as invested in protecting our security interests as has been the US.

But clearly while Trump is in power the relationship must change – especially the assumption that we’ll always be side by side in any battle.

While support for fighting Isis is unlikely to change soon, any Australian leader sending us to any new wars, such as against Iran or involving China – as has been predicted by Trump’s chief strategist, Steve Bannon – would face a massive political backlash.

Frighteningly, one report early this week suggested Trump’s accepting the refugee deal was based on the assumption we would reciprocate with support for such things as greater military support in Iraq and Syria, and for “freedom-of-navigation exercises in the South China Sea”.

The reality is, there is very little Trump could threaten us with. We might be small, our names might be forgotten, but we are one of the best friends the US has ever had, and it needs us. Trump might not realise it, but our government certainly should.