President Giorgio Napolitano's condolence message hailed her as a "high-level personality in the world of scientific culture."
"At the same time, she represented a strong example of civil passion, leaving a noble fingerprint in public debate and in the dialogue with citizens," Napolitano said.
The Italian news agency ANSA quoted family friend Marinella Chirico as saying Hack died in a hospital after being treated for heart problems.
The current director of the observatory, Stefano Borgani, told Sky TG24 TV that Hack was one of the first astronomers to "have the intuition" that the future of astronomical observation lay in using space satellites.
An atheist who decried Vatican influence on Italian politicians, Hack helped fight a successful battle to legalize abortion in Italy. She unsuccessfully lobbied for the right to euthanasia and also championed gay rights. Among her victories was a campaign against construction of nuclear reactors in Italy.
Hack, an optimist with a cheerful disposition, studied the heavens in the firm belief there was no after-life.
"I have no fear of death," Hack once said in a TV interview. "While we are here, death isn't" with us. "When there is death, I won't be here," she said.
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