The day before announcing their separation, Gwyneth Paltrow and Chris Martin flew to the island of Eleuthera in the Bahamas, PEOPLE has confirmed.
Wearing sunglasses and keeping a low profile, the pair gave no indication anything was amiss between them.
"I just thought they were on vacation," says an observer at the North Eleuthera airport. "They didn't seem happy or unhappy."
A source close to Paltrow says the stars, who are parents to daughter Apple, 9 ½, and son Moses, 7 ½, retreated to the pencil-thin island (roughly two miles wide) – whose name is the Greek word for "freedom" – to avoid the maelstrom of attention following the announcement that they are consciously uncoupling.
"They're in a somewhat isolated place, so they don't have to deal with it as much," says the source.
Paltrow and Martin aren't the first celebrity couple to share a breakup moon: In 2005, Brad Pitt and Jennifer Aniston famously vacationed together on the Caribbean island of Anguilla just one week before publicly revealing their split. Josh Lucas and Jessica Ciencin Henriquez headed to Colombia to visit her family shortly after announcing they'd divorced amicably.
Reporting by STEVE HELLING