With her daughter Apple

Gwyneth Paltrow and Chris Martin

Gwyneth Paltrow and Chris Martin have added to their family. Their second child, a son named Moses Martin, was born this weekend, the actress's rep tells PEOPLE. The baby was delivered at Mount Sinai Hospital in New York City.

The Shakespeare in Love Oscar winner, 33, and her British-born Coldplay frontman husband, 29, already have a daughter, Apple, born May 14, 2004. Moses is the name of a song Martin wrote for his wife in 2003.

Following months of speculation that she was pregnant, in January Paltrow confirmed that she and Martin were expecting. After a Screen Actors Guild screening of Paltrow's movie Proof, Lou Diamond Philips, about to moderate a panel on the film, introduced Paltrow as "a pregnant woman" and then asked her, "How far along are you?"

"Far enough along to feel very cumbersome," Paltrow answered.

When a member of the audience asked her how she got her hair so shiny, Paltrow replied, according to TV's The Insider: "It must be the prenatal vitamins ... I've been taking them for a few years."

Three months after the birth of daughter Apple, the new mother appeared on The Oprah Winfrey Show and admitted she couldn't understand why people were making such a fuss over the baby's name, which, in its entirety, is Apple Blythe Alison Martin.

Paltrow said that her husband suggested the name soon after she discovered she was pregnant. "It conjured such a lovely picture for me – you know, apples are so sweet and they're wholesome and it's biblical – and I just thought it sounded so lovely and ... clean," Paltrow told Winfrey. "And I just thought, 'Perfect!'"

"We love unusual names in the family," Paltrow's mom, Blythe Danner, told PEOPLE in January.

As for being a mom, Paltrow told Winfrey that the overwhelming love she feels for her child is "a whole new dimension in emotion that I've never experienced. It's crazy."

Get out the calendar. USA TODAY maps out who is due:

April

Katie Holmes, 27, and Tom Cruise, 43: Cruise told a German news outlet last week that the birth could happen any day now. He also said the couple have chosen a name, but he wouldn't share it.

May

Angelina Jolie, 30, and Brad Pitt, 42: The couple and their family — son Maddox, 4, and daughter Zahara, 1 — checked into a resort in southwest Africa last week amid reports that's where they plan on having their baby.

Brooke Shields, 40, and Chris Henchy, 42: A sister for Rowan, 2, is expected in May. The couple already have a name for her: Grier.

Mariska Hargitay, 42, and Peter Hermann, 38: It will be a son, and first child, for the Law & Order: SVU star and her husband.

Rachel Weisz, 35, and Darren Aronofsky, 37: The Oscar-winning actress (The Constant Gardener) felt the baby kicking during her big win. She said she doesn't know whether it's a boy or a girl.

June

Gwen Stefani, 36, and Gavin Rossdale, 38: At the Grammys in February, Stefani said the couple had a nursery started in their north London home but still couldn't agree on a name for the baby.

Mira Sorvino, 38, and Chris Backus, 24: This summer's baby will be No. 2 for the couple, whose daughter, Mattea, is 18 months old.

Karen Elson, 27, and Jack White, 30: The White Stripes singer and his model wife were married last June and quickly started working on a family.