An astonishing 25,000 browsers rushed to give him their answers - ranging from "We won't" to "Somehow we will", and proposing solutions from banning nuclear weapons and tackling global warming to escaping into space. The Cambridge professor, who has been said to sell physics better than Madonna can sell sex, seems to agree with many of them.
In a few weeks, Britain's longest-surviving sufferer from motor neurone disease will meet the almost equally high-profile Sir Richard Branson to discuss how his giant brain and broken body, complete with wheelchair and voice synthesiser, are to be accommodated on the first space flight of the tycoon's Virgin Galactic service next year. It is to be a dramatic demonstration of Professor Hawking's controversial conviction that humanity will have to "spread out into space for the survival of the species".
Last week, ahead of his putative trip into orbit, he joined his old schoolfriend and colleague, the Astronomer Royal, Sir Martin Rees, to sound one of the starkest alarms yet of the dangers of nuclear proliferation and climate change. At the Royal Society, of which Sir Martin is president, they formally moved the hands of the Bulletin of the Atomic Scientists' clock to five minutes to midnight - midnight being the figurative end of civilisation.
Over the past 60 years - since it was instituted in the wake of the bombings of Hiroshima and Nagasaki - the clock has been changed 18 times in response to the nuclear threat (it was closest to midnight, two minutes, in 1953 after Russia and the US tested weapons; furthest, at 17 minutes, after the signing of the 1991 nuclear arms treaty). But this movement, closer to the hour of doom by two minutes, takes into account climate change, for the first time.
In a necessarily terse statement - he has to pre-prepare each one by laboriously selecting words from a computer screen, building up a passage, and then sending it to his voice synthesiser - Professor Hawking starkly spelt out the twin threats.
"As scientists, we understand the dangers of nuclear weapons and their devastating effects, and we are learning how human activities and technologies are affecting climate systems in ways that may forever change life on Earth," he said. "As citizens of the world, we have a duty to share that knowledge, and to alert the public to the unnecessary risks that we live with every day. We foresee great peril if governments and societies do not take action now to render nuclear weapons obsolete and to prevent further climate change."
It was an important moment in the growing campaign for urgent action to control the heating of the planet - like Sir Richard Branson's conversion to the cause, reported in The Independent on Sunday last September, and Sir David Attenborough's belated decision to throw his weight behind it last May.
It was not the first time Professor Hawking has voiced his concern; he has a good record on climate change, stretching back a decade. But it was the most public and most dramatic, and its timing - just as political pressure for action is reaching a new peak - will greatly magnify its effect.
Stephen William Hawking has had an extraordinary life. He was born in Oxford on 8 January 1942, 300 years to the day from the death of Galileo. He was raised in a somewhat bohemian household in St Albans, the son of a researcher in tropical medicine so that, he says, "I grew up thinking that a research scientist was a natural thing to be". Holidays were spent in a Gypsy caravan.
Always a clumsy, ill-coordinated child - with a lisp and terrible handwriting - he was persecuted as a swot at his minor public school, St Albans. (He revisited it for "a very enjoyable day" last year). He came into his own when he got to University College Oxford. He gained a first in physics at the age of 20, and then moved to Cambridge to study cosmology.
But life was waiting just around the corner with a cosh. His lisp became a slur. He began moving awkwardly, staggering and stumbling. At just 21 he was diagnosed with amyotrophic lateral sclerosis (ALS) a motor neurone disease of unknown cause. Doctors gave him about two years to live.
It was doubly cruel, as he was already making a noticeable mark. Just a year after his diagnosis, he attended a lecture at the Royal Society by Sir Fred Hoyle, a bombastic figure who was then one of Britain's cult scientists. When the great man asked for questions, the 22-year-old Hawking coolly told him that his calculations were wrong.
"Would you like to tell us how you know this, young man?" asked Sir Fred, with heavy sarcasm. "Because I worked it out," said the young Hawking. And he had.
Despite the progression of his disease, he continued his work. He describes it as "a condition in which the nerves controlling muscles die off, but the sensory nerves continue as before. It is not supposed to affect intelligence, but maybe I am too far gone to notice.
"Had I chosen any other career, my ALS would have ended it. But theoretical physics is all in the mind, so I was able to carry on. I can't say that my disability has helped my work, but it has allowed me to concentrate on research without having to lecture or sit on boring committees."
He found that, contrary to scientific orthodoxy, some radiation escaped from black holes (discovering something new, he says, "is the most wonderful feeling in the world, like sex but it lasts longer"), and at 37 was appointed Lucasian Professor of Mathematics at Cambridge (Sir Isaac Newton was a predecessor).
But six years later he lost his voice after a bout of pneumonia that almost killed him. Doctors saved him with a tracheotomy, an operation that allows you to breathe through your neck, but bypasses your voice box. At first he could only communicate by raising his eyebrows when someone pointed to letters on an alphabet card. Now his computer and synthesiser allow him to articulate about 15 words a minute, about a tenth as much as in normal speech.
Does he get angry about it? "He takes the view that that is a luxury he cannot afford," says his friend and assistant Judith Crowsdale. She describes a remarkably busy, uninhibited life of constant activity, including much foreign travel.
He left his wife of more than 20 years - who had supported him through his growing disability, and brought up his children - for one of his nurses, who he married.
For more than three years, he went on to suffer a series of mysterious injuries - once getting severe heatstroke and sunburn after being left out in his garden in his wheelchair on the hottest day of the year. Police investigated, but he made no complaint. Ms Crowsdale says: "We are way beyond all that now."
His friends are mainly fellow academics, but he is close to Matt Groening - who featured him in an episode of The Simpsons - enjoys the company of Jim Carrey, Richard Dreyfuss and Kevin Costner, and gets on with Al Gore.
He has long been concerned about global warming, signing (with his thumbprint) an open letter to George Bush six years ago with other leading figures, protesting against the President's decision to turn against the Kyoto Protocol and urging him "to reduce US production of greenhouse gases".
And while other scientists have drawn back from spelling out the worst possible consequences of climate change - fearing being accused of sensationalism - he has been prepared to do so, repeatedly warning that global warming could run out of control so that "Earth might one day soon resemble the planet Venus", with temperatures of 250C and sulphuric-acid rain.
His authority comes as much from his courage and sheer persistence as from his scientific knowledge. He is not, after all, a climatologist and - despite the popular hype, which has compared him to Einstein and Copernicus - the planet's top physicists failed in a poll to rate him among the top practitioners of his profession
But he himself says: "I am just a child who has never grown up. I still keep asking these how and why questions. Occasionally, I find an answer."
A brief history of (the end of) time
Stephen Hawking's blockbuster 'A Brief History of Time: From the Big Bang to Black Holes' has sold 25 million copies. Cynics say it is the least read best-seller since the Bible. His next book will be ambitiously called 'The Grand Design', but here are ideas for the three biggest perils that he believes threaten humanity.
Chapter 1: GM virus - the plague next time
Most of the threats we face come from the progress we have made in science and technology. Often they make natural ones worse. Take the pandemics that occasionally sweep through the world killing millions. Influenza has been the worst culprit, and if the bird flu now spreading round the world mutatesit could be one of the worst plagues yet. But the release - by accident or design - of a virus, genetically modified so that people could not resist it, would be far worse.
Chapter 2: Not with a whimper, but with a bang
Nine countries have nuclear weapons, and Iran and North Korea are believed to be developing them. Terrorists seek them and there are more than enough weapons held by existing nuclear powers to destroy the planet. Some experts thinka nuclear conflict in the coming decades is inevitable.
Chapter 3: If it's not Mars, it could be Venus
Waiting until the ill-effects of global warming become obvious will be too late; action must be taken now. The warming process could run out of control, as "positive feedbacks" in the Earth's natural systems magnify it. That could lead to the planet becoming uninhabitable - turning it into a hot dead one like Venus, which has long been known to have suffered the ultimate greenhouse effect.
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