As the US' closest ally, Britain is affected more than any other country by the decisions Barack Obama will take. So, as Obama's inauguration in Washington DC heralds the start of the US president's second term in the White House, here's a run-through of the most important challenges coming up in the next four years.
1 – A less pushy America
Obama tailored his approach to foreign affairs against the bold interventionist 'I'm right, and I'm going to prove it with shock and awe' technique of the George Bush years. The Democrat president's quieter approach to foreign affairs will continue to have a direct impact on Britain because of the UK's closeness to the States. This is part good and part bad, Xenia Dormandy, a senior fellow at the Chatham House thinktank, believes. "People still have strong memories from the Bush years of what they saw as an aggressive, unilateral approach," she says. "The quieter Obama approach reflects positively on the US and on the UK."
The downside is that when the world needs the US to be its policeman, it will respond by abdicating its responsibility. Britain is tied to a fading superpower. What does that make us? Global views of the UK's place on the world may be downgraded as a result of Obama's aloof view.
2 – The deficit reduction battle
'When America sneezes, Europe catches a cold.' Or something like that, anyway. The point is European economies depend on the health of the US. An America that can't deal with its own internal domestic economy is an America that isn't helping support Europe coming out of its economic doldrums.
With the debt ceiling crisis still far from being fully resolved, what happens to the US' deficit reduction approach matters nearly as much as what happens in the Eurozone crisis on the other side of the Atlantic.
"Where America ends up in that debate, and how their economy performs, will either strengthen Osborne's hand or Labour's hand," Will Straw, associate director at the centre-left IPPR thinktank says. Obama's approach is much closer to Alistair Darling's, he argues. Whereas George Osborne wants a four-to-one ratio of spending cuts to tax rises, Obama would rather have these two roughly equal.
Come the next general election, it will be much easier to make an assessment of which approach has worked better. If Obama's policies start to lead to recovery, the US case study will be example number one in shadow chancellor Ed Balls' playbook.
3 – Climate change
Whichever candidate won the 2012 presidential election, the outlook for climate change activists wasn't going to be great. But with the UN negotiating process coming to a climax in 2015, environmentalists hoping to prevent a rise in the planet's temperature of more than 2C will be relieved Obama, not Mitt Romney, is the man in the White House. He doesn't stand a chance of getting any legislation through Congress, so will have to focus on executive orders and the like. But there is potential for him to bring forward meaningful measures. We shouldn't expect a pricing mechanism, like a carbon tax, or a quantity mechanism like the EU's emissions trading scheme. Instead emissions standards could be set across the board. "If Obama does show willing, that will empower those people advocating climate change in the UK," believes.
4 – The US and China
"America's policy towards China has long been one of hedging and engagement," Dormady says. "Obama leans towards engagement." This matters because the gradual shift in global power from west to east directly affects Britain's interests. There will be the usual spats here and there, especially on economic issues, but overall Obama will be focusing on getting on with the Chinese. It would have been very different if Romney was being inaugurated today, Dormandy thinks. At least, it would have been in the short-term. "This is the area where initially Romney and Obama would have had a different stance. In the end Romney would have ended up looking like Obama."
5 – Military interventions
Perhaps the biggest impact of the hands-off approach lies in the sphere of defence. Obama would rather spend America's money on development and diplomacy, not bullets and bombs. He doesn't like risking American lives, either: his preference is for special forces, for drones, for cybersecurity initiatives. "He more than any other president has got drones which work," says MP Brian Donohoe, honorary secretary of the British-American parliamentary group. Even getting the US president to engage in interventionist initiatives seems difficult. "So far Obama's been rather hands-off," Straw notes. "It required concerted action from Cameron and [former French president Nicolas] Sarkozy to bring him into Libya." With European nations now moving to confront the growing threat of terrorism across Africa's Sahel region, it's not yet clear how distant Obama will prove. Straw adds: "There's a question over what role America is to play."
6 – Middle East diplomacy
The UK government's approach to the biggest headache facing the Middle East in the next four years – Iran's imminent acquisition of a nuclear weapons capability – is virtually identical to Barack Obama's. Both London and Washington want to see engagement with Tehran, but are only prepared to go so far before they move to introduce sanctions. Obama's problem is he is "heavily boxed in by the Hill," according to Paul Ingram, executive director of the British American Security Information Council (Basic). Anti-Iranian sentiment in both the Senate and the House of Representatives should be seen in the context of the Israel question. What happens if Israel launches a unilateral military strike against Iran? Then Obama, with his hands tied by the US' strong Israeli lobby, will be standing up to defend Israel's actions – and the UK government will be in a very awkward position indeed. This would put pressure on the coalition, too, as the grassroots of the Conservative and Liberal Democrat parties are likely to have very different gut reactions. Obama will have to do all he can to pressure Israel towards moderation, but it may not be enough.
7 – Britain's nuclear deterrent
With the final decision to replace Trident looming in 2016, both the 2015 general election and the 2014 Scottish independence referendum campaigns are set to be dominated by the nuclear deterrent question. There's a strong chance the debate will be shaped by what happens between the world's two biggest players, Obama's US and Vladimir Putin's Russia. Obama had indicated to former Russian president Dmitry Medvedev in a now infamous off-mic comment that he would have more room to negotiate after his, Obama's, re-election. Well, here we are, and so Russian diplomats are awaiting negotiations between the old Cold War adversaries to recommence in earnest. What will Obama's approach be? Given his 2009 Prague speech setting out a vision towards a nuclear-weapons-free world, there's half a chance he will be looking to make significant reductions.
"The British elite are absolutely focused and obsessed almost with staying on the right side of Washington, so if the Obama administration indicates it actively wants Britain to retain a nuclear deterrent even at the cost of its conventional defence capabilities, that will have an impact," Ingram says. He thinks there are two reasons why Obama could plausibly suggest that Britain should downgrade its nuclear capabilities: either because of his "personal quest" to reduce nuclear weapons, or because the US values Britain's conventional military capabilities more. Such a call would have a huge effect on the UK's internal debate about its future as a nuclear power. Either way, Obama's second term in office will really matter to Britain in the years to come.
8 – Extradition
Perhaps this one is going on the list more out of desire than reality, because the simple fact is Obama isn't likely to budge very far on Britain's extradition arrangements with the US. It remains much harder for the UK to get an American citizen wanted for crimes committed internationally than it is the other way round, but UK calls for a renegotiated treaty are likely to fall on deaf ears. This should be sorted out so that an "equal partnership" exists, Donohoe believes.
"In the second term a president has got much more flexibility than in the first term, they can use that influence to a greater extent," he says optimistically.
"The difficulty in a second term is when you get to the third year, your influence and your powers start to be ameliorated as a consequence of everyone looking to be who the next president. For the next two years, you're more powerful than ever in terms of being able to drive through policy that makes a difference."
He points out this extra political capital could make more of a difference on an issue like gun control. On extradition, it's more a case of crossing fingers and hoping than anything else.
9 – The in-or-out European referendum question
Britain's ongoing relationship with the EU is going to be another matter hotly debated in UK politics during Obama's second term. As officials within his administration have already been making clear, the US view is firmly in the 'keep as you are' camp. Arguments about the UK acting as a bridge between Europe and the US are about more than just history and sentiment, Donohoe believes: the common language shared by the States and the UK helps Britain economically, he believes. The biggest car manufacturer in the world is Toyota, Donohoe points out. "They're only here because we speak English," he says. The value Britain places on its status as the US' closest ally will be sorely tested as the EU debate plays out. Is it really worth making the change, when Washington will become alienated as a result?
10 – Party politics
There's one final reason why Obama's second term matters, and it hasn't got anything to do with the US. Come May 2015, British voters will go to the polls with an American president entering his lame-duck period of declining influence. Had Romney been installed in the White House, he would have been starting to think about re-election by then. As it is, Obama's would-be successors will be starting their primary campaigns. By early 2015 the successes and failures of his eight years in power will be becoming clearer than ever. British voters pay attention to American domestic politics more than they do to any other foreign country. The performance of the US' 44th president across the board will have an impact on the conservatism vs intervention tensions at the heart of UK politics: the verdict on Obama's second term will play an important, if immeasurable, role in shaping attitudes as Britain's next general election approaches.