I believe you have the Omega 345.0808
They made 1,000 of these Speedmasters. They were made to celebrate the 20th anniversary of being certified for NASA manned space flights.
The bracelet may also be original to the watch (at least correct for the reference) as well, there should be a number on the clasp, it would be 1447.
Did your father buy this brand new? If so, it would have been purchased new between 1985-1988.
@tyrantlizardrex - they made only one watch with a display back and a copper-colored caliber 863.
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