In mid-December, federal authorities were aware that certain drones seen hovering over New Jersey and New York skies were actually permitted aircraft. However, they chose not to share this with the public, as President Trump had hinted at earlier.

A presentation by the Transportation Security Administration revealed that four drone sightings in New Jersey were not true drone activities but were optical illusions caused by authorized aircraft.

A slide from the presentation explains that “the positioning of the aircraft created an illusion for ground observers, making them appear stationary in a formation while they were actually advancing towards the observers,” referring to several reports of sightings on the night of November 26, 2024, in Somerville, NJ.

The slides were first shared by Reason.com, and also included an explanation for the three drone sightings over the Salem Nuclear Power Plant and the adjacent Hope Creek Generating Station on Dec. 12, 2024 — a day before the Federal Aviation Administration imposed airspace restrictions over New Jersey.

The report dispels Dec. 5, 2024, sightings of drones along the Jersey coastline as “aircraft arriving

from the South on approach into JFK” that “turned toward land around Sea Girt, flying for 2 to 3 minutes toward the coast, turning back out to sea, and flying 3 to 5 minutes straight away from the coast.”

Those aircraft — a Cessna C150 and UH-60 Black Hawk – would’ve appeared to hover in the sky to anyone on the ground, according to the feds. Both aircraft were authorized to be in the area.

A second Dec. 12 account of a drone over Clifton, N.J., dispersing some sort of a gray mist was also dismissed as another plane: a Beechcraft Baron 58, which experienced turbulence, “dropped approximately 100 feet before regaining altitude.”

The rapid change “over the wing’s surfaces cause wingtip vertices,” or condensation clouds, “that may appear as gray mist.”

But the incomplete presentation failed to address some of the more notable sightings, including the swarm of 12 to 30 drones spotted Dec. 8 over the Atlantic by patrolling members of the U.S. Coast Guard.

A sailor who spoke to The Post about the incident said they were sent out to look for drones when “they found us.”

“They appeared out of nowhere” at about 9 p.m., and followed the boat for approximately 15 minutes, he said. When the vessel shifted course, so too did the drones.

“They had four propellers. Seven feet across. The flashing lights, like you’ve seen. The festive green, red, and white lights.”

Trump accused the Biden administration in January of knowingly keeping New York and New Jersey residents “in suspense.”

Added Trump: “For some reason, they don’t want to tell the people, and they should. Our military knows and our president knows. And for some reason, they want to keep people in suspense.”

In December, Biden said there was “nothing nefarious” in the sky. Members of Congress concurred following a classified briefing.