Communications Satellite Corp., the Student Loan Marketing Association, and Computer Data Systems Inc. reported sharply higher earnings yesterday, with Sallie Mae posting record profits for the third quarter of $10.4 million ($10.42 a share), more the double the earnings achieved for the third quarter of 1981.

Comsat's earnings for the third quarter were $11 million ($1.38), a 73 percent increase over last year's third-quarter profits of $6.4 million (80 cents). Compared with the company's 1982 second-quarter earnings, however, the third-quarter results represented only a modest gain of $200,000 (3 cents).

Revenues for Comsat's third quarter totaled $105 million--marking the first time its revenues have exceeded $100 million in a quarter. Revenues were up 34 percent from $84.9 million in last year's third quarter. The company attributed the growth to increased demand for its satellite services.

Earnings would have been higher had Comsat not incurred a $4 million loss in the quarter for its one-third interest in Satellite Business Systems, the new long-distance telecommunications company, which has yet to break even.

Nine-month net income was $32.2 million ($4.02), a 1 percent decrease from the same period of last year when net income totaled $32.6 million. The decrease was due to a one-time accounting change.

Revenues were $299 million, up 22 percent from $244.4 million.

D.C.-based Sallie Mae posted record third-quarter profits of $10.4 million ($10.42), a 107 percent increase from $5 million ($5.03) last year. The third-quarter 1982 figures are up 17 percent from second-quarter earnings of $8.9 million ($8.91).

Nine-month net income jumped 113 percent to $26.9 million ($26.93) from $12.6 million ($12.63) last year.

Assets on Sept. 30 were up 40 percent to $6 billion.

"Sallie Mae's strong financial performance thus far during 1982 reflects the continued demand for the corporation's secondary-market services by the financial and educational institutions, state agencies and other organizations . . . ," according to Edward A. Fox, president and chief executive.

CDSI had record first-quarter income of $389,000 (26 cents), a 94 percent increase over $200,500 (28 cents) last year. The current per-share earnings reflect a 2-for-1 stock split this summer. Revenues were $8.5 million, up 109 percent from $4.1 million last year.

Officials at the Bethesda-based computer consulting and processing firm attributed the gain to the absence of start-up costs of its lucrative General Services Administration contract.