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Riley Vashtee was a member of the crew of the S.S. Pentallian under Commander Kath McDonnell.
The Pentallian was mining the sentient star Torajii. When Martha Jones arrived onboard with the Tenth Doctor in the TARDIS, he was attracted to her. While trapped in an escape pod and thinking they would both soon die in the fires of the star, Martha reciprocated Riley's sentiments.
The Doctor having rescued them, though, Martha kissed him on the lips before she departed in the TARDIS with the Doctor, leaving Riley to his life on the S.S. Pentallian.