Goodyear Tire & Rubber Co. said yesterday that earnings declined 39 percent in the final quarter last year and 35 percent overall in 1979, largely the result of slumping domestic auto sales.

Goodyear, the nation's largest tire and rubber company, earned $146.2 million ($2.02 a share) on record sales of $8.24 billion last year. But in 1978 earnings totaled $226.1 million ($3.12) on sales of $7.49 billion.

In the fourth quarter, the company earned $43.2 million (60 cents) on record sales of $2.07 billion compared with profits of $71.6 million (90 cents) on sales of $2.03 billion in the same 1978 period.

"Particularly affecting Goodyear's performance in the United States during 1979 was the automobile industry's struggle with declining sales, the rise in foreign car imports, and the concern over the supply and price of gasoline," Goodyear said.

Goodyear said foreign sales rose 18.6 percent to a record $3.33 billion, with earnings rising 21.4 percent to a record $75.5 million in 1979.

The Akron-based company said it also achieved record sales and strong earnings from Goodyear Aerospace Corp. and its industrial products and chemical operations.

General Telephone & Electonics Corp., operator of the nation's largest independent telephone system, reported a 9 percent gain in consolidated net earnings for the latest quarter and a 4 percent gain for the year.

Revenues for both the quarter and year were up 14 percent from a year earlier, the company reported yesterday.

GTE said its consolidated net earnings in the latest quarter totaled $176.16 million ($1.14 a share) on revenue of $2.78 billion. In 1978, earnings were 160.3 million ($1.06) on revenue of $2.44 billion.

For the year, GTE reported net earnings of $645.07 million ($4.20) on revenues of $9.95 billion. In 1978, the company earned $622.18 million ($4.17) on revenue of $8.73 billion.

Kroger Co., the nation's second largest grocery chain, said yesterday that it earned $105.5 million ($3.85 a share) last year on sales of $9.029 billion, up from $84.6 million ($3.11) on sales of $7.828 billion in 1978.

For the fourth quarter ended last Dec. 29, Earnings totaled $32.6 million ($1.19) compared with $30.1 million $1.11) in the similar period in 1978.

"Kroger in 1979 was able to perform better than most of the retail food industry, reflecting both the results of our $750 million modernization of facilities and our merchandising," said Kroger Chairman Lyle Everingham.

R.J. Reynolds Industries Inc., a tobacco, food and transportation company, reported a 25 percent gain in earnings last year on a 33 percent rise in sales.

Net income was $551 million ($5.23 a share) on sales of $8.93 billion compared with $442 million ($4.51) in 1978 on sales of $6.71 billion. Fully diluted for options, the earnings were equal to $5.05 a share against $4.29 a year ago.

Profits for the final quarter were $135 million ($1.16) on sales of $2.49 billion compared with $122 million ($1.25) a year earlier on sales $1.73 billion.

Chairman J. Paul Sticht said the big gain for the year was in considerable part due to the acquisition of Del Monte Corp., fruit and vegetable canner.

Citing strong earnings from its flagship newspaper, the New York Times Co. reported record profit for the fourth quarter and the year.

The company earned $36.4 million ($3.06 a share) in 1979, up from $15.6 million ($1.32) in 1978, when results were affected by a strike that closed the newspaper. Revenues rose from $490.6 million to $653.1 million.

Fourth-quarter profits rose to $11.6 million (97 cents) from $2.5 million (21 cents) in the 1978 quarter. Revenues rose from $115.3 million to $184.1 million.

W. R. Grace & Co., a diversified chemical producer, earned $5.02 a share last year, up from $3.98 in 1978, as sales climbed to $5.266 billion from $4.448 billion.

Net income rose to $222.58 million from $171.2 million.

Fourth-quarter profits were $63.86 million ($1.43 a share) on sales of $1.472 billion compared with $38.48 million (88 cents) on sales of $1.223 billion.

Northrop Corp., a major aircraft manufacturer interests in construction, technical and management support services, and electronics and communications, said yesterday it posted increased earnings last year despite a 13.5 percent decline in sales.

Earnings totaled $90.3 million ($6.35 a share) up slightly from $88.4 million ($6.42) in 1978.

Northrop said 1979 sales dropped to $1.6 billion from $1.8 billion the previous year.

For the fourth quarter, Northrop earned $20.5 million ($1.44), down 19 percent from $2.53 million ($1.78) for the three-month period in 1978. Sales fell 19 percent to $391 million.