A federal judge yesterday approved reorganization of the bankrupt Penn Central Transportation Co. into a diversified real estate, pipeline, oil and amusement park company.

With close to $4 billion of assets and a new name, yet to be selected, the new company could be established by as early as next summer. It would become immediately one of the country's largest business enterprises, even though shorn of its once-proud railroad system.

Penn Central failed in mid-1970 and was the largest bankruptcy in history. At the time, it had assest valued at more than $6.5 billion, including the country's largest railroad, with 43,000 miles of track throughout the Northeast and Midwest.

In order to preserve railroad service to the densely populated region after a half-dozen smaller lines followed the Pennsy into bankruptcy, the federal government reorganized the prime routes into a government-aided firm called Consolidated Rail Corp.

U.S. District Court Judge John P. Fullam, meanwhile, has continued the task he began nearly eight years ago - conducting oversight of an attempt to reorganize what remained of Penn Central Transportation into a viable business."

In a 106-page decision yesterday, Fullham said a plan proposed by the company's court-appointed trustees "complies with all requirements of law . . . it's feasible . . . fair and equitable."

His opinion ordered some minor amendments to the plan, which the trustees are expected to approve. After that, Penn Central's various creditors must approve tha reorganization (although the judge still could sustain the plan if creditors object).

"Like all products of human endeavor, the plan may not be perfect but, in my judgment, it provides entirely fair and workable solutions to all the complex Penn Central, Fullham asserted.

The plan provides for issuance of securities in various combinations to be given to stockholders and creditors as their share of equity ownership in the new company.

Authorized common shares in the company would be 40 million, of which 23.15 million would be issued as follows: 55 percent (12.7 million shares) to secured creditors such as large insurance companies and banks that hold mortgages; 35 percent (8.1 million shares) to unsecured creditors; and 10 percent (2.3 million shares) to Penn Central Co., the current holding company for Penn Central Transportation, which is traded on the Philadelphia Stock Exchange.

First in line for immediate return, however, is the federal government. About $350 million of notes in the new firm will be issued to the U.S., with interest deferred until Dec. 31, 1987, at which time the total principal and back interest must be paid. Moreover, some principal payments must be started before 1981.

Another $451.5 million in notes and cash will be distributed to state and local governments to pay back taxes of the bankrupt firm.Within two years, 44 percent of each claim will be paid; jurisdictions that will receive back payments include Maryland ($11.4 million), D.C. ($1.64 million) and Virginia ($1.1 million).

Two series of mortgage bonds will be distributed to secured creditors to satisfy 30 percent of their claims. The secured creditors also will receive preference stock for 30 percent of their claims.

Restructured as "Company X," Penn Central will have debts of $3.5 billion but will own major hotels in New York: Great Southwest Corp., which operates amusement parks; Buckeye Pipeline Co.; Arvida Corp., a real estate developer; and a California oil company.

An initial board of directors would include representatives of institutional investors, secured banks, the trustees of the bankrupt New Haven railroad, unsecured creditors, Penn Central Co. and two officers of the new firm.

Still to be resolved by the courts is the value of former Penn Central rail properties taken over for the Conrail system. A government agency said the value should be that of "new liquidation," or less than $1 billion - far below claims of up to $12 billion sought by creditors.

In order for stocks in the firm to reflect any of the valuation settlement, proceeds must be $1.97 billion to cover debt-type securities and unpaid interest that will be due for payoff by 1987.

A Penn Central Transportation subsidiary, Pennsylvania Co., based in Arlington, is the nucleus about which the reorganized firm would be built.