The company had originally pegged the journey for as early as this year with the space tourists traveling in a Crew Dragon spacecraft on a Falcon Heavy rocket.
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The BFR is SpaceX's newest rocket, a super powerful launch vehicle with 31 engines and the capacity to lift 150 tons into space.
When asked if he himself is the passenger, he hinted that the mystery person is Japanese by tweeting the country's flag.
"No one has visited since the last Apollo mission in 1972". Plans for that flight were eventually delayed; it's unclear if one of the two passengers from that flight will be taking the trip on the BFR.
SpaceX has established its bona fides in the aerospace business by transporting supplies to the International Space Station and by completing the tricky maneuver of recovering rockets after launch so that they can be reused.
The company first made plans to fly two private citizens around the moon in February of 2017 using the company's Falcon Heavy rocket and Dragon capsule, but those plans have apparently been revised.