DETROIT — Detroit is eligible to shed billions in debt in the largest public bankruptcy in U.S. history, a judge said this morning in a long-awaited decision that now shifts the case toward how the city will accomplish that task.

Judge Steven Rhodes turned down objections from unions, pension funds and retirees, which, like other creditors, could lose under any plan to solve $18 billion in long-term liabilities.

But that plan isn’t on the judge’s desk yet. The issue for Rhodes, who presided over a nine-day trial, was whether Detroit met specific conditions under federal law to stay in bankruptcy court and turn its finances around after years of mismanagement, chronic population loss and collapse of the middle class.

The city has argued that it needs bankruptcy protection for the sake of beleaguered residents suffering from poor services such as slow to nonexistent police response, darkened streetlights and erratic garbage pickup — a concern mentioned by the judge during the trial.

“This once proud and prosperous city can’t pay its debts. It’s insolvent. It’s eligible for bankruptcy,” Rhodes said in announcing his decision. “At the same time, it also has an opportunity for a fresh start.”