WASHINGTON — Canceling NASA’s Moon-bound Constellation program is expected to cost the U.S. space agency $2.5 billion in contract termination liability and other closeout costs over the next two years, according to sources familiar with the agency’s 2011 budget proposal.

U.S. President Barack Obama is asking Congress to give NASA $19 billion in 2011 to pursue a revamped space exploration strategy that scraps a 6-year-old plan to send astronauts to the Moon in favor of keeping the international space station in service through 2020 and paying commercial firms to transport crew and cargo to the orbital outpost.

In the days leading up to the Feb. 1 release of Obama’s budget request, NASA and White House officials told reporters that that the agency stands to receive an additional $6 billion spread over five years.

For the year just ahead, however, NASA’s budget would grow by just $276 million, or 1.47 percent more than it received for 2010.

According to documents released by the White House and sources familiar with the detailed request, NASA’s Exploration Systems Mission Directorate — the part of the agency in charge of Constellation — stands to receive $4.263 billion for 2011, about $484 million more than it received for 2010.

Of that amount, the biggest chunk — about $1.9 billion — will go toward costs related to closing down the Constellation program. NASA expects to spend an additional $600 million on Constellation closeout in 2012.

Commercial spaceflight would receive roughly $800 million in 2011 and considerably more in subsequent years.

NASA also intends to spend between $550 million and $600 million annually on early development of an exploration-class heavy-lift rocket and other unspecified propulsion technologies.