A cheer went up when Armstrong and Buzz Aldrin landed on the Moon's Sea of Tranquillity and the two astronauts began walking on its surface, famously announcing that the "Eagle had landed".
"I think they were all listening to it on he radio in the hospital ... it would have been a little transistor radio back then, of course," she said.
"I was just happy to have a happy, healthy baby."
Mrs Kopke welcomed her daughter Kerin at 6pm at Levin Maternity Hospital.
"She's always been my moon baby," she said.
Mrs Kopke remembered there being a lot of excitement around the hospital, and listened to the return flight lift off from the Moon while she fed her daughter, with two nurses sitting on the end of the bed.
"One was convinced they weren't going to get off, but the other was supremely confident everything was going to be fine," she said.
"There was a big cheer when they got back on the shuttle."
Much has been made of "moon babies" in the world's media in the past week, as the humankind looked back on that achievement 50 years later.
A story appeared on New Zealand television programme Seven Sharp this week highlighting a group of New Zealand mothers from the same town who gave birth that day and had stayed in contact ever since.
Incredibly, both Jacqui and Kerin were classmates through school when they were younger at Levin Intermediate, and used to joke with each other that their birthday was a public holiday in the US.
"We always thought we were special because it was a public holiday in America. We thought we were the cool kids," Jacqui said.
"We used to say to each other that we should get the day off, too."
Jacqui Isaacs, who has lived in Brisbane, Australia, for more than 20 years, said her children took her for dinner to mark the occasion.
"I suppose it was something I was always aware of, so it is a bit special, and we're still alive 50 years later, so happy days," she said.
Interestingly, they also share their birthday with some famous New Zealanders. Sir Edmund Hillary was born on the same day in 1919, while racing car driver Chris Amon was born on that day in 1943.