The first part would certainly be to keep it a secret or keep it spun as another crackpot scheme so life as normal would continue. Someone in an insurance field might notice and increase in amateur astronomers becoming fatal accident prone.
The corporations and governments would start various nefarious plans as Switch and Bunnies suggest.
The only real indication regular folks would have is a renewed interest in a space program from the government and unprecedented levels of international cooperation geared at creating colonies on the moon and Mars.
The general level of misandry exhibited by our culture would increase and the sexist nature of education with preference to females would be expanded particularly in science in an effort to get both breeding stock and vital workers for the colonies. Men would be actively discriminated against except for only the most disposable positions or the most brilliant of minds with regards to getting to the new colonies.
A sudden rash of kidnappings of female children, a sudden mass exodus of high level coporate and government officers and their families, taking the most beautiful of the adult women without vital skills to run the colonies and the abducted children would let the cat out of the bag.
Judgement day.
If the cat gets let out sooner Anarchy and collapse of governments until coporations can get control and execute a modified version of the previous ‘plans.’