' to what a + noun' is not grammatical here; that is all I can say.
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windyjoltRadio astronomy is a science to__an exact birth date, December 1932, can be assigned, for__was the date receiving radio waves from space.An exact birth date can be assigned to radio astronomy.
a)what/that
b)which/this
Only which and whom can be used as a relative pronoun after a preposition -- not what.
Jim, can I ask you how it works in this structure? (This is what stymied me when I was considering the original question)-- The crop was decimated, but by what (it was eaten) I do not know.