Called Lunar Mission One, the archive is the brainchild of David Iron, who has worked on Skynet, the UK spy satellite network, and Galileo, the European Union's global positioning system.
He will offer people a chance to place a sample of their DNA, in the form of a strand of hair, in an archive to be buried on the Moon, alongside a digital history of as much of their lives as they want to record.
Iron and his colleagues have launched a crowdfunding campaign on Kickstarter to raise the initial 600,000 pounds of seed funding needed to set up the company to commission designs for the spacecraft, which it is hoped will blast off in 2024.
Iron is working with the Rutherford Appleton Laboratory in Harwell, UK.
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Lunar Mission One plans to land a robotic spacecraft on the Moon's south pole. It will then drill at least 20 metres into the lunar crust, extracting core samples to be analysed on the craft.
"The drill will enable the geothermal gradient, and thus lunar heatflow, to be measured for the first time," Crawford said.
After about six months, capsules containing the DNA and digital data will be injected into the borehole, which will then be sealed.