The futures of the Navy aircraft carrier, a Texas aerospace company and an intercontinental ballistic missile will be shaped in a series of crucial decisions Congress will start making this week.

Today, for example, the House Appropriations Committee is scheduled to provide the first big test of President Carter's ability to make cuts in the defense budget stick. The lawmakers on the committee are to vote on whether to end the era of the giant, nuclear-powered aircraft carrier and let it sink alongside the battleship of World War II.

Carter's old Navy mentor, Adm. H. G. Rickover, is urging the Congress to reject the President's recommendation and continue building the giant carriers. Former President Ford is allied with Carter in arguing it is time for the nation to switch to smaller and cheaper non-nuclear carriers.

"It's enough to make you cynical," lamented a Navy official in decrying the politics buffeting the carrier question.

His despair stems from the changes Ford ordered during the election year 1976 and the impact they will have on the 1977 carrier debat.

In January, 1976, Ford said he would put off for one year the decision on whether to buy a fourth Nimtz-class nuclear-powered carrier. Studies of an alternative ship would be made in the meantime, his Defense Secretary promised.

In May, when Ronald Reagan was accusing Ford of being weak on defense, Ford informed Congress that he welcomed the $350 million the House had added to his fiscal 1977 defense budget for another $2 billion Nimitz carrier. The National Security Council study on what ships the national buy was still in process.

"No new information bearing on the military need for this carrier was provided to justify ignoring the ongoing National Security Council study," complained Sen. Patrick J. Leahy (D-Vt.) in unsuccessfully urging his Senate colleagues last August to deny the $350 million for the carrier until the National Security Council study was completed.

After the Nov. 2 election, Ford said he did not think another Nimitz should be built after all. Defense Secretary Donald H. Rumsfed said in the Pentagon budget statement for fiscal 1978:

"It was tempting to propose building still one more large nuclear carrier, with its minimum cost of $2.2 billion. But the broad thrust of the recently completed National Security Council study drives the dedecision down another parth - to a large total number of aircraft carriers, some of which are not quite as individually capable, and therefore are not as costly."

Carter, in reviewing the Ford defense budget, agred with Ford. He is asking congressional permission to shunt $358.4 million of the $350 million voted for a fourth Nimitz class carrier last year into spare parts for the three existing goes Saving the remaining $81.6 million would help make the $2.75 billion Pentagon budget cut Carter had proposed.

"Big carrier" champions in Congress, with steady encouragement from Rickover, are fighting on two fronts to save the fourht Nimitz.

The first is the House, and Senate Appropriations committees, which are weighting the changes, called rescissions, Carter wants to make in Ford's fiscal 1977 defense budget.

On Tuesday, the House Appropriations Committee is scheduled to vote on the carrier money and other changes. It is expected to be close. Last week the House Defense Appropriations Subcommittee tied 6 to 6 on denying the $350 million for a fourth Nimitz carrier. The Senate Appropriations Committee is expected to take up the same question this week.

The second fron is the House and Senate Armed Services committees, now considering the fiscal 1978 budget as amended by Carter. These committee traditionally have been most friends to the military.

The House Seapower Subcommittee already has voted to build another Nimitz. Its parent House Armed Services Committee is expected to follow suit. Rickover has been pressing hard for this despite Carter. Rickover is arguing that another 90,000-ton nuclear-powered Nimitz would be fare more capable than the 50,000 to 60,000-ton nonnuclear carriers Ford and Carter have recommended.

Meanwhile, another part of the Navy, the "airedales" of carrier aviation, will be involved in a other fight: to save the A-7E fighter-bomber, which flies from carriers.

Carter has recommended against buying any more A-7E, a step that could relegate the manufacturer of the plane, Vought Corp. of Dallas, to the status of a subcontractor or even put it out of business.

Here again, Ford has made Carter's job easier. The fomre President in what industry executives claim was post-election spite to make it harder for Carter to make good on his promise to cut the defense budget, reduced planned purchase of A-7s from 24 to six planes for fiscal 1978.

An executive of th LTV Corp., parent company of Vought, concedes it will be an uphill fight in Congress to save the A-7, which has brought $3.3 billion into the company since 1964 LTV will try to make te case, hopefully with Navy help, that national defense requires more A-7Es.

Another dimension to this battle is Carter's pledge to decrease the sales of American weapons abroad.

Pakistan wants to buy 110 A-7s. according to Vought, and has the $700 million for them in hand. The Pentagon has recommended the sale go forward, but the State Department has not yet made a recommendatioN.

If the Navy is allowed to buy some more A-7s, goes the company argument, the plane's production line in Dallas can be kept "warm" until the Pakistani order is approve. Otherwise, the company warns, Vought will have to start laying off 7,000 employees working on the A7.

Not only is Carter recommending canceling the A-7, but his revised fiscial 1978 budget also calls for canceling the company's only other aerospace program, the nonnuclear version of the Lance missile deployed along the NATO line. Another 1,100 Vought employees in Sterling Heights, Mich., are tied to manufacturing the Lance.

"We are going to be doing all we can to insue that the final budget contains both the A-7 and the Lance battlefield missile," vowed LTV president Paul Thaye. He said 7,000 jobs hinge on the two programs.

Defense Secretary Harold Brown, in justifying the A-7 and Lance phase-outs, has said it would be inordinately expensive to keep the Vought production line open just to build six planes. The non nuclear Lance is not worth buying, he argues, because it cannot seek out the fixed target it is supposed to hit. An airplane has do that, Brown said, so it makes more sense to rely on aircraft to destroy the target as well.

LTV's Thayer is scheduled to fly here this week to rebt those and other criticims in a series of face-to-face meetings with government officials.

"But this is not going to be any big, high-powered lobbying job," said LTV spokesman Julian W. Scheer in describing the company's rescue effort. The credit cards are going to stay in our pockets." He said the customers - the Navy for the A-7 and the Army for the Lance - will have to take the lead in making the cases for continuing to buy the weapons.

The company and the Navy are already getting help on the A-7 from the Texas congressional delegation. The delegation includes George H. Mahon (D-Tex.) chairman of the House Appropriations Committee and House Majority Leader Jim Wright (D-Tex.)

There appears to be a far better chance of Congress restoring the Carter cuts in the Nimitz. A-7 and Lance programs in this year's budget battles than reversing the tide against building any more Minuteman III intercontinental ballistic missiles.

In what was charged at the time as another bit of presidential politics, Fod announced shortly before his crucial Texas primary contest with Reagan last April that he was asking Congress for an extra $260.7 million in Fiscal 1977 money to build 60 more Minuteman III missiles.

Carter plans to switch the Minuteman III money from additional whole missiles to components for them. Brown is telling protesting lawmakers that the age of the fixed-site, land-based ICBM like Minuteman is drawing to a close because of the steadily increasing accuracy of strategic weapons.