The city ordinance allows authorities to randomly decide which public speech they will permit, lawyer Sarah Shalf told three members of the U.S. Court of Appeals.
Burk, chair of the National Council of Women's Organizations, was in court and said a favorable ruling could make it 'somewhat more likely' her group would protest at next year's tournament.
Burk's group had asked a federal judge to block the Augusta ordinance to allow them to protest in front of the club. That request was denied, leading to the appeal.
The court is expected to rule within the next two months, attorneys said.
Burk sued the city after a sheriff denied her request to hold an April 12 protest of Augusta National's all-male membership at the private club's front gate.
Sheriff Ronnie Strength, who has authority to regulate protests under the ordinance, cited safety concerns. The closest Burk's group could protest was nearly a half mile from the front gate.
The judges repeatedly questioned Jim Ellison, an attorney for the Augusta-Richmond County Commission, and Shalf, an American Civil Liberties Union lawyer.
Judge Rosemary Barkett asked about part of the ordinance that requires any group of five or more people who plan to assemble for a demonstration to request a permit.
'Would five people standing outside of a movie theater ... saying, 'Hey, this is a great movie' ... come under this ordinance?' she asked.
Ellison said 'some common sense approaches' would have to be used by police to decide what qualifies as a demonstration.
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