During the ceremony, the ashes of one of the world's best-known theoretical physicists, who died in March aged 76, will be buried between the graves of fellow scientists Sir Isaac Newton and Charles Darwin.
Members of the public have been given a chance to apply for a public ballot and also have the option of choosing a birth date any time up until December 31, 2038 in their online applications.
The ballot for tickets to the memorial service opened earlier this month and closes at midnight on May 15. The ceremony at Westminster Abbey will take place on June 15, for which Hawking's children are offering 1,000 free tickets to the public.
The online form for the public ballot lets people scroll from 1918 to 2038 when choosing their date of birth. It remains unclear if the choice of years is deliberate.
"But so far we have had applications from all round the world, and we do mean round there are no flat-earthers here," the foundation statement added.
Hawking famously often threw up the prospect of time travel and even tried out an experiment when he organised a party for time travellers in 2009. Balloons, canapes and champagne were laid on at the event, however no one showed up.
Crucially, the invitations were not sent until the date had passed, so only those who had figured out how to go back in time could attend.
"I sat there a long time, but no one came," Prof Hawking had told reporters in 2012.
He said he hoped copies of the invitation would last for thousands of years so that one day somebody might figure it out and eventually show up in their time machine.
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