Patheos has previously reported allegations by musician Tchiya Amet, who said Tyson drugged and raped her when they were graduate students at the University of Texas at Austin.

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Saturday night, Tyson posted a lengthy response to the allegations on Facebook. He wrote that he hadn’t recognized Allers’s and Watson’s discomfort at the time of the incidents they described. He acknowledged that he had a short relationship with Amet in the 1980s, but rejected her allegation of assault.

Tyson wrote that he would fully cooperate with the investigation into the allegations.

In a statement, the producers of “Cosmos” told The Washington Post that they are “committed to a thorough investigation of this matter and to act accordingly as soon as it is concluded. … The credo at the heart of COSMOS is to follow the evidence wherever it leads.”

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Fox Entertainment and National Geographic, which air the show, said they had just become aware of the allegations and are reviewing the reports. 21st Century Fox jointly owns the National Geographic channel with the National Geographic Society.

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In an interview with The Post, Watson described an uncomfortable night with Tyson in May 2018. She had been working as his assistant on the Santa Fe set of “Cosmos” for several months and was hoping that Tyson would ask her to continue working for him when production moved to Europe.

But when Tyson invited her to his home after a day on the set, Watson said, he removed his shirt so he was only wearing an undershirt and started to serve wine and cheese. At one point, Tyson pointed the knife at Watson, she alleged. He later spoke about how all people needed “release” and asked what hers was. When Watson tried to leave, Tyson asked her to perform a handshake he said he had learned from a Native American elder, which involved feeling a person’s pulse and staring into their eyes. She said he told her, “I want to hug you right now, but if I do I’ll just want more.”

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“It felt very manipulative and strange,” Watson said of Tyson’s behavior. The hug comment made her particularly uncomfortable. “I felt like he was expressing that he wanted to have a sexual relationship with me.”

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Two days later, Watson told a producer at Cosmos what had happened and said that she wanted to quit. The producer asked her whether she wanted to file a complaint, she said, but Watson declined. “I didn’t want to cause a fuss,” she told The Post.

The producer said he thought that was a good idea and suggested that she tell the rest of the crew that she had to leave for a family emergency, Watson said.

Watson provided The Post with a text describing the incident she sent to a friend several days later.

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Producer Drew Dowdle, for whom Watson worked for seven months in 2017, told The Post that Watson told him about her experience with Tyson a few months after quitting “Cosmos.”

Tyson did not dispute the details of Watson’s account in his statement on Facebook. But he cast the encounter in a different light, saying his comment about the hug, for example, was intended “to express restrained but genuine affection.”

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In an email to The Post, Allers confirmed the details of her experience as reported by Patheos but declined to comment further. She told Patheos that she did not report the incident, which she says occurred at a social event after a 2009 meeting of the American Astronomical Society (AAS), because she didn’t think the society had a mechanism for reporting sexual harassment.

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Kevin Marvel, executive officer of the AAS, said the society has not received any complaints involving Tyson since its code of conduct was implemented in 2008. He added that the society does not conduct investigations unless it has received a complaint.

On Facebook, Tyson apologized to Allers, writing that he didn’t know she felt his behavior was “creepy.”

“In my mind’s eye,” he wrote, “I’m a friendly and accessible guy, but going forward, I can surely be more sensitive to people’s personal space, even in the midst of my planetary enthusiasm.”

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Amet did not immediately reply to an emailed request for comment from The Post.

Both Watson and Allers said they shared their accounts in hopes that they would lend credibility to Amet’s allegation, which she wrote about on her blog in 2014 and which was first reported by Patheos last year.

“I just feel like Neil needs to answer to these accusations,” Watson said. “If we don’t talk about these things, they’re not going to change.”