What promises to be one of the most curious fights in recent congressional history is shaping up this week on the floor of the House.

The fight is over whether to appropriate $20.7 million for the National Aeronautics and Space Administration to undertake an ambitious, unmanned voyage to the giant planet Jupiter in 1982, an opportunity that will not knock again until late in 1987 and won't be as good a shot cause of the way Jupiter will be aligned with earth.

At odds in the fight are the Senate and House Appropriations committees as well as White House science adviser Frank Press and some powerful House Democrats. Players in the fight include some of the nation's outstanding scientists, the Federal Republic of Germany and California Gov. Edmund G. (Jerry) Brown Jr.

The fight has Massachusetts Republican Sen. Edward Brook pitted against Massachusetts Democratic Rep. Edward P. Boland, whose long time friendship with House Speaker Thomas P. (Tip) O'Neill Jr. has been called into question during the fight.

Nobody on Capitol Hill is willing to predict the outcome. Said one key congressional aide, "One day I think the Jupiter flight will be approved on the House floor. The next day I talk the same people I spoke with the day before and I think it's going to lose by 120 votes."

The 1982 voyage to Jupiter was turned down in June by the House Appropriations Committee and approved in the same week by the Senate Appropriations Committee. Both groups met in conference one day last week until almost midnight before throwing in the towel. The House group insisted that the Jupiter trip not take place; the Senate side insisted it must.

The mission's future now moves to the House floor, where a vote is expected as early as Tuesday. Approval on the House floor would just about assure that the mission would go to Jupiter in 1982. Disapproval would meant it would have to be taken up on the Senate floor where there seem to be enough votes for passage. If that should happen, the project would go back to the House and Senate Appropriations committees for rework.

House appropriations subcommittee Chairman Boland is against the Jupiter mission because of its timing. His subcommittee has already approved the startup of the Large Space Telescope, which will cost $435 million by the time it reaches earth orbit in 1983.

Boland says NASA should not be allowed to begin more than one big money project this year. Though it's asking only $20.7 million to start what it formerly calls the Jupiter-Orbiter-Probe, the space agency estimates the mission would cost $285 million by the time it left in 1982.

Boland's point is that the reuusable manned space shuttle is the space agency's scared cow these days and will be consuming $300 million a year until its first into orbit in 1979. He tells colleagues the only way Congress can keep the NASA budget in check is to pull the reins on smaller programs like the Jupiter project.

Not only does Boland have the support of many of his collegues, he has the friendship of Speaker O'Neill, who can call for a floor vote on the mission any time he wants. The two friends were roommates for 10 years in Washington, Supporters of the Jupiter mission fear O'Neill will call for a vote when congressmen supporting the project are absent from the House floor.

Supporters of the Junior mission have begun to blitz the House with their views. Sen. Brooke has reminded members of the Massachusetts delegation that Bay State electronics firms stand to win some of the subcontracts. Gov. Brown made some calls to the California delegation, reminding them that the project would be run by Pasadena's Jet Propulsion Laboratory.

One report had it that science asviser Press called O'Neill to remind him that scientists at Harvard University and Massachusetts Institute of Technology would have key roles in the mission. Harvard and MIT are both in Cambridge, Mass., which lies in O'Neil's district. Boland's district is in Springfield, at the other end of the state.

Press and other White House aides are understood to have invoked foreign relations in support of the project. West Germany's Budestag has already approved the expenditure of $40 million to finance that country's involvement in the projec The White House used this line during Chancellor Helmut Schmidt's visit here last week.

The way the mission is designed, an unmanned spacecraft would fly for the first time into orbit around Jupiter and would send a 500-pound prose into the Jovian atmosphere. The spacecraft in orbit would act as radio by the probe. The orbiting craft would remain in orbit for 20 months, passing by the four large moons of Jupiter on numerous occasions.

If Congress should delay the Jupiter flight until a 1987 launch, the giant planet would be so much farther from earth that the 55-pound probe would have to be dropped for the orbiting spacecraft to reach Jupiter.

Should NASA insists on keeping the atmospheric probe with the spacecraft, the cost of the mission would double to just about $600 million in 1987 project.