By Karen S. Schneider Michelle Tauber
May 31, 2004 12:00 PM

Apple Blythe Alison Martin

MAY 13, 2004 * 9 LBS. 11 OZ.

Gwyneth Paltrow has things to do: tending to her new baby’s belly button, figuring out a feeding schedule, crocheting that baby hat and poncho in the do-it-yourself kit she received soon after her daughter Apple was born on May 13. But four days after giving birth at an English hospital, the Oscar-winning actress was “resting,” said her husband, Coldplay frontman Chris Martin, 27, as he greeted reporters outside their home in London’s posh Belgravia neighborhood. Ever press-wary, he was mum on details except to note that his wife—whose mother, Blythe Danner, and brother Jake flew in from L.A. in time for the birth—was not at home and would be “going abroad soon,” he said, adding that “Gwyneth and baby are doing well. They are in a safe place.”

In more ways than one. Nearly two years after her father, producer-director Bruce Paltrow, died of complications from throat cancer at age 58—bringing Paltrow, as she has said, to her knees in grief—she is doing more than standing tall. Throughout her pregnancy and since the birth, the 31-year-old actress has begun smiling again—an all-out, life-is-good grin rarely seen in recent years.

“She’s extremely happy,” says a close source. “She’s in a constant state of elation.”

Which is a considerably different state than she was in during her long hours of labor. From the start, Paltrow had done her best to be what Manhattan obstetrician Marc Engelbert, whom she consulted during the first months of her pregnancy, calls a “good pregnant patient.” Though she gave up her macrobiotic diet—which forbids dairy and processed flour—in favor of grilled cheese sandwiches, she kept up her yoga, hoping, apparently, that the regimen would help during childbirth. During her stays in London, Paltrow turned to obstetrician Gowri Motha, whose holistic practice includes yoga and Ayuverdic oils, for massages. But as any mom knows, massage is no match for the pains of labor. “It was a long and hard birth,” says Martin.

Her labors were followed, however, by one very sweet gesture: naming her daughter Apple. The couple’s not saying exactly why they chose the moniker. “It’s just a very cool name,” says Martin, whose band’s agent, Marty Diamond, also has a daughter named Apple. The baby’s middle names come from her grandmothers, Danner and Alison Martin.

Up next for the family? Time off. Martin, who met Paltrow at a 2002 Coldplay concert, plans to lie low until next year, and Paltrow, whose films Sky Captain and the World of Tomorrow and Proof are due later this year, has said she might not work “for ages.” As Dr. Engelbert sees it, the actress, with some 20 films to her credit, has new priorities: “Nothing is more important to her than being a mother.”