(CNN) -- — No stranger to performances, SeaWorld must put on a very different kind of show Tuesday in what could be a make or break day for the aquatic entertainment giant.
SeaWorld Orlando is asking a panel of three judges on a federal appeals court to overturn safety citations and a ban instituted by the Occupational Safety and Health Administration restricting the ability of humans to interact with killer whales during performances.
The injunction was instituted after the death of veteran trainer Dawn Brancheau in 2010, when Tilikum, the orca she had worked with for years, dragged her into the water and killed her in front of horrified viewers.
OSHA said the company violated the general duty clause of the Occupational Safety and Health Act, saying it exposed its workers to a known hazard in the workplace. SeaWorld was slapped with a $75,000 fine for three safety violations, including one "willful" citation.
After SeaWorld appealed that decision, an administrative law judge last year downgraded the "willful" complaint to "serious," reducing the fine to $12,000. Crucially, the judge sided with OSHA's findings that keeping humans out of the water with killer whales unless there were physical barriers would reduce the risk of serious injury or death.
For SeaWorld, the stakes are as big as the star performers at the heart of it all.
The theme park was known for its famous Shamu shows up until 2010, which featured amazing demonstrations of trainers catapulted by orcas in graceful arcs high in the air.
With the court-ordered restrictions, some argue that SeaWorld's very livelihood is on the line in this case.
"SeaWorld offers the public an opportunity to observe humans' interaction with killer whales," the company said in court documents. "This brings profound public educational benefit, is integral to SeaWorld's care of the whales, and responds to an elemental human desire to know, understand, and interact with the natural world."
"It is clear from SeaWorld's adoption of these measures that close contact of the kind that resulted in Dawn Brancheau's death is not essential to SeaWorld's ability to draw visitors to its parks, to practice behaviors during shows, or to care for its whales," OSHA argued in a response brief.
Captive orcas have killed four people, including three trainers.
"The [$12,000 citation] amounts to basically a very expensive speeding ticket," said Benjamin Briggs, a partner with Seyfarth Shaw LLP who specializes in labor law. "The one that's going to be harder to prove is proving this type of interaction between whales and the trainers actually makes the interactions more predictable, and by reducing that, and creating greater distances, it's going to undermine not only the level of predictability but it's going to harm their ability to care for the animals and impact their operations in a more fundamental way."
Trainers have been in "close contact with whales since the 1960s," court documents say. "During this time, OSHA could have opened an investigation at any time if it believed that close contact presented a recognized hazard."
Briggs said the argument is legitimate -- but SeaWorld faces an uphill battle because what OSHA has on its side is history.
"There's a long and well-documented track record of these types of animals behaving aggressively toward humans to the point that they've caused a number of fatalities. Not only at Seaworld but at a number of places," Briggs said. "That is what OSHA is going to say, you absolutely were on notice of this, this is absolutely a recognized hazard. This kind of track record is not one you can ignore. So it's very important, it's what OSHA's case really hinges upon."
The hearing will be held at Georgetown University. Eugene Scalia, son of Supreme Court justice Antonin Scalia and former Solicitor of the Department of Labor, will handle SeaWorld's appeal. Amy Tryon will argue on behalf of the Department of Labor.
A decision is not immediately expected.