Chris Martin and Gwyneth Paltrow step out in Santa Monica in Oct. 2012
11/07/2013 at 02:00 PM EST
and Chris Martin famously keep their relationship under wraps, but the elusive couple made a rare public appearance Tuesday in the name of art – and friendship.
Paltrow, 41, and Martin, 36 – who celebrate their 10-year wedding anniversary
next month – walked arm in arm through the Los Angeles Natural History Museum to view works by their good friend Rob Reynolds at the opening of his exhibition celebrating the 100th anniversary of the L.A. Aqueduct.
An eyewitness says the couple – parents to Apple, 9, and Moses, 7 – were "clearly enjoying each other's company" as they laughed, drank and chatted with fellow guests, including Jack Black and his wife, Tanya Haden.
Perhaps their uncharacteristic public appearance is part of Paltrow's new plan
to dismiss the opinions of people she doesn't know.
"The older I get, I realize it doesn't matter what people who don't know you think," PEOPLE's 2013 Most Beautiful Woman
told the British magazine Red
. "It doesn't matter. You're wasting your energy."