Possivelmente "First Through Time", de Stanley Bennet Hough, escrevendo como Rex Gordon. Publicado em 1962, então isso funciona. Eu tenho apenas o esboço Goodreads , mas:
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Protagonista do astronauta masculino.
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Operadora feminina de síncrotron nos EUA.
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Apocalipse futuro.
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Um dos designs de capa mostra uma silhueta contra um mostrador de relógio.
The top secret synchrotron took accurate photos of the future - and what they showed was disaster, both for the girl who ran the machine and the world she worked for. Major Judgen, astronaut, had trained for a first flight through space. Now he was called on to put his ability into an untested flight across time. Was his girl friend's death a certainty - and did that same certainty also doom the rest of humanity? Or was there a way to snatch a double victory from the discoveries to be made on the day after the world came to an end?