But numerous other studies, including research from the C.D.C., have come to the conclusion that sugar-laden drinks are a major factor contributing to obesity. The C.D.C.’s website notes: “Frequently drinking sugar-sweetened beverages is associated with weight gain/obesity, Type 2 diabetes, heart disease, kidney diseases, nonalcoholic liver disease, tooth decay and cavities, and gout, a type of arthritis.”

In a local television interview in May 2013, announcing a $3.8 million pledge from Coke, which would also be used to underwrite other exercise-related health programs, Dr. Fitzgerald said Power Up for 30 would add exercise before, during and after school. Noting that Georgia had moved up slightly from its position as having the second-most out-of-shape children in the nation, Dr. Fitzgerald said, “Thirty minutes of exercise will go a long way toward better health.”

Some details of the relationship between Dr. Fitzgerald and Coke were reported in earlier news accounts. After her new post was announced, U.S. Right to Know, a nonprofit research group that focuses on transparency in the food business, sent journalists links to the broadcast along with emails between Dr. Fitzgerald and Coke officials.

Dr. Fitzgerald also said on the television show that Georgia Shape would push children to eat five servings of fruits and vegetables every day.

“We’re going to concentrate on what you should eat,” she said, making no recommendation for what children should not eat. But the major focus was on increasing exercise, long a tenet of Coke’s public relations efforts. In fact, an essay on the topic by Dr. Fitzgerald is posted on Coke’s website. The title: “Solving Childhood Obesity Requires Movement.”

Dr. Fitzgerald, 71, is an obstetrician-gynecologist and a Republican who has run for Congress twice, unsuccessfully. She has close ties to her fellow Georgia Republicans Tom Price, the secretary of health and human services, and Newt Gingrich, the former speaker of the House and an informal adviser to President Trump. She has won widespread praise in Georgia for her work to reduce infant mortality, encourage language development among babies, and nudge her state up in terms of student fitness.

A series of emails, most from 2013, obtained under the Freedom of Information Act by U.S. Right to Know, illustrated a friendly relationship between Dr. Fitzgerald and Dr. Applebaum of Coke. When Dr. Applebaum was named president of the International Life Sciences Institute, the food industry’s premier research center, Dr. Fitzgerald wrote back, “Yea team.”