Dava Sobel raises her eyes heavenwards. “I feel like Dorothy in The Wizard of Oz,” she says. “I have been picked up in a tornado in Kansas and set down in a colourful place. That’s how much my life has changed.”

Since she published Longitude, the bestselling story of an 18th-century genius who solved one of the greatest scientific problems of the age, she has been sucked from her earthly roots and propelled skywards. Time and space, the planets and the heavens — and the mysteries thereof — are her constant subjects.

As a result this 58-year-old former science writer for The New York Times now walks around with her head in the stars, her neck at a permanent upwards tilt.

Sobel flew to London from New York last week on a pilgrimage to honour that genius of longitude, John Harrison, in Westminster Abbey. On Friday she delivered an address as Prince Philip unveiled a plaque to him. Harrison, a self-taught Yorkshireman, invented a sea clock that enabled sailors to determine their position, thus ensuring Britain’s dominance of the waves for the next century. His memorial lies in the nave, close to that of the explorer David Livingstone. Fittingly, her precise mind knows its longitude: 000 degrees 07’ 35” west. Harrison would have appreciated her accuracy.

She also visited the new home of Harrison’s clock, housed in the new Time galleries at the Royal Observatory, Greenwich, which opened last month. They are the first stage of a £15m refurbishment of the 1675 Wren building which will include a new planetarium. The “Longitude effect” has helped raise both funds and the profile of the observatory.

Tom Hanks, who appeared in the lunar epic Apollo 13, paid a visit to Greenwich, not as a Hollywood star but as a Sobel devotee. As Sobel explains: “He is a very careful researcher and intelligent actor.”

Today it is Sobel who is puffing her way up the steep hill to the observatory. We cross the prime meridian, moving from eastern to western hemispheres, and in front of Harrison’s exquisite silver timepiece, the celebrated H4, she falls into a reverie. She lowers her voice. Nearby hangs Harrison’s portrait. “His eyes follow me round the room,” she says. “But I fancy his expression towards me has softened.

“You know, the first time I came here I had gone into debt. My family had bought me the ticket.” She believed that the story of Harrison would find an audience, but nobody else did. “I remember people saying to me, ‘Do you think anyone is going to read this?’ I think I got the smallest advance in history.”

She was a struggling single mother living on Long Island, her life mirroring that of JK Rowling. But Harrison was to do for Sobel what Harry Potter did for Rowling. Eleven years after its appearance, more than 500,000 copies of Sobel’s book have been sold and it has been translated into 17 languages.

Though falling short of Rowling’s Potter millions, she has made so much money from the book that she can now jet around the world, stargazing from luxurious cruise ships.

She turned the story of a humble carpenter and watchmaker into a human drama that captivated readers.

Captain Cook took a watch based on H4 on his voyage of 1775 to the South Seas, as did Captain Bligh on the Bounty.

Her book became a play by Arnold Wesker and a film with Jeremy Irons and Michael Gambon. It was followed by Galileo’s Daughter, shortlisted for a Pulitzer prize, based on letters she unearthed between Galileo and his illegitimate child. In The Planets, a study of the solar system published last year, she revealed that her “planet fetish” began at the age of eight.

She was the right person, therefore, to guide the lay reader through the particulars of time and space. Longitude is calculated by the 24-hour revolution of the Earth, one hour being 24th of a revolution and 15 degrees of longitude. But to calculate how many degrees a ship has travelled, a sailor needs to know the time in his home port and the time on board.

Harrison developed a clock that kept perfect time at sea. He won the support of the king, George III, and gained a huge sum (£23,000) in prize money, the equivalent of more than £2.5m today, before dying at the age of 83. “He solved the problem of the age,” says Sobel. “It would be like someone today discovering a cure for cancer.”

It was quite by chance that, as a science writer, she attended a symposium on longitude at Harvard which caught her imagination. After she wrote it up for Harvard Magazine, a small American publishing house commissioned the short book that was to become an international bestseller.

She now finds herself wrestling with the story of another underdog. She is writing a play about Copernicus, the Polish Catholic who had the idea that the Earth moved round the sun. “This is huge, the moment the universe is turned inside out,” she gushes. The Sobel enthusiasm again. Watch out, she may be picked up by another tornado. In any event, as she says, “I’m a long way from Kansas.”