CAPE CANAVERAL, Fla. — A closeup laser inspection by Endeavour’s astronauts yesterday showed that a 3 1/2-inch-long gouge penetrates all the way through the thermal shielding on the shuttle’s belly, and had NASA urgently calculating whether risky spacewalk repairs are needed.

A chunk of insulating foam smacked the shuttle at liftoff last week in an unbelievably unlucky ricochet off the fuel tank and carved out the gouge.

The unevenly shaped gouge — which straddles two side-by-side thermal tiles and the corner of a third — is 3 1/2 inches long and just over 2 inches wide. Yesterday’s inspection showed that the damage goes all the way through the 1-inch-thick tiles, exposing the felt material sandwiched between the tiles and the shuttle’s aluminum frame.

Mission managers expect to decide today, or tomorrow at the latest, whether to send astronauts out to patch the gouge. Engineers are trying to determine whether the marred area can withstand the searing heat of atmospheric reentry at flight’s end. Actual heating tests will be conducted on similarly damaged samples.

“We have really prepared for exactly this case, since Columbia,” said John Shannon, chairman of the mission management team. “We have spent a lot of money in the program and a lot of time and a lot of people’s efforts to be ready to handle exactly this case.”

The damaged thermal tiles are located near the right main landing gear door. In a stroke of luck, they’re right beneath the aluminum framework for the right wing, which would offer extra protection during the ride back to Earth.

This area is subjected to as much as 2,300 degrees Fahrenheit during re-entry. A hole, if large and deep enough, could lead to another Columbia-type disaster. Columbia was destroyed in 2003 when hot atmospheric gases seeped into a hole in its wing and melted the wing from the inside out. A foam strike at liftoff caused the gash.

Teacher-astronaut Barbara Morgan — who was the backup for Challenger’s Christa McAuliffe in 1986 — conducted the slow and painstaking survey, along with crewmate Tracy Caldwell. They used the 100-foot robotic arm and extension boom that flew up on Endeavour, steering the instrument to a spot just above the gouge and keeping it hovered there. Laser sensors and cameras zoomed in on the damage, white and easily visible against the black tiles, from a variety of views.