Having reached the age of 76, it might be expected that Valentina Tereshkova would be planning a life of quiet gentility: a bit of gardening, perhaps, or catching up on reading. Far from it. The grande dame of astronautics has no intention of retiring gracefully, she has revealed. Indeed, she has a very different idea of how her future will unfold: she wants to go to Mars, her favourite planet. More to the point, she says she is happy if the mission turns out to be a one-way trip.

"Of course, it's a dream to go to Mars," says Tereshkova, who became the first woman in space after she spent three days orbiting Earth in 1963. "I want to find out whether there was life there or not. And if there was, then why did it die out? What sort of catastrophe happened?"

Such curiosity is shared by many others, of course. What distinguishes Tereshkova – nicknamed "little seagull" by Sergei Korolyov, the father of the Soviet space programme – is the fact that she is willing to take that trip without any prospect of returning to Earth. At an age when most people are thinking of settling down to play with their grandchildren, Tereshkova is now seriously contemplating taking a manned flight to another world where she would end her life eking out an existence in a tiny colony with a few other hardened Mars dwellers who would live on supplies ferried, sporadically, from Earth.

It would be little more than a suicide trip. Nevertheless, Tereshkova is committed. "I am ready," she says.

Nor is the former cosmonaut alone in committing herself to such a mission. Thousands of people from around the world have signed up to a project called Mars One, which has announced plans to launch a private mission to land a group of four men and women on Mars in 2023 to found a permanent colony. Earlier this year the group revealed it was seeking volunteers for the mission. To date, 165,000 have signed up. Most are male, a quarter come from the US and many are students.

It is an astonishing response, given that the organisers have also made it clear there would be no prospect of any return for the winning applicants. It's one thing to launch a small space probe towards Mars, it is pointed out, but quite another to land one that would be big enough to carry crew, oxygen, food and enough fuel to blast off again, after several months' exploration, to carry its astronauts back to Earth.

The answer for cosmonauts such as Tereshkova and for groups like Mars One is straightforward: dispense with all that pesky kit that you need to bring your crewmen back and instead keep them alive on Mars for the rest of their lives. This would be done by ferrying supplies to the red planet by robot spaceships.

In fact, says Bas Lansdorp, the Dutch entrepreneur behind Mars One, their plans involve rockets carrying cargo, food and living modules to Mars several years in advance of the first manned landing. Then, after their astronauts had settled for a couple of years, a further crew of four would be sent out. As to the estimated £4bn cost of Mars One, that would be met through television rights and other media sponsorship, although Lansdorp is quick to dismiss the idea that the mission would be a low-gravity version of Big Brother. He envisages orchestrating an event that would be more like London 2012 than a reality show, he insists. "Mars One should be exciting, inspiring and beautiful, just like the Olympics."

Despite the fact that no nation has ever got near to sending humans to another planet, Mars One insists the technology exists to send humans to Mars and to keep them alive there. Water could be extracted from ice in the soil and specially adapted solar panels would be able to supply ample power, for example.

As to the men and women who would go to Mars, they would be selected for their ability to co-operate, Lansdorp has insisted. "We're not looking for individuals. We are looking for perfect teams. They must be healthy, smart enough to learn new skills and with a character and mindset that can function in a small group." A selection committee is set to start studying applications this year. The aim is to select teams of four people, each from a different continent. After seven years' training, the first manned mission would be launched in 2022 and would reach Mars the following year.

Many astronomers have voiced caution about such missions, however. Mars is a much more hostile environment than people realise, they point out. Indeed, it is deadly. Its atmosphere is thin and – unlike our own atmosphere – provides little protection against the sun's powerful ultraviolet radiation. In addition, the colonists' spacecraft, which would take six months to travel from Earth, would be perilously exposed to potentially fatal radiation storms emanating from the sun. Given that the success rate of landing robot spaceships on Mars is little more than 50%, it is no certainty that a manned craft would survive the final part of its mission. Tereshkova's Martian dream needs a fair bit of work if it is to be realised, it would seem.