It was dusk, very close to dark, at Sequoyah State Park. I had just finished hiking with my 3 dogs and was loading them into a van. I glanced up and saw a very bright round white light moving approximately northwest. I had initially been facing north loading the dogs in side of van and had turned to right (east) and noticed the object up above and to my right going over the Fort Gibson Lake eastern area about where Wildwood or Hulbert Landing is.I hurriedly loaded the dogs in the van. I immediately knew this was the same type of unknown object I had seen on October 9, 2013, a few weeks before and at a location nearby and across the lake to the west. It was also moving at approximately the same speed and the same altitude as the previously observed object.This time, there was a small private airplane, which I could hear and see, including the blinking lights, to my north within a mile or so. I estimated this airplane at 500 feet altitude. The very bright round white light continued northwest and to the south of the airplane and passed between the airplane and me. The object was approximately 75% the size of the airplane, which was approximately the size of a single engine Cessna. The airplane was proceeding approximately eastbound and undoubtedly the pilot saw this object just to the south within hundreds of feet.I reached into my van to retrieve my binoculars in my backpack I had used for birding that day. When I looked back up from van the object had vanished, perhaps blinked out or accelerated and disappeared. There had not been enough time for the object, at the current rate of speed, to have disappeared over the horizon or a tree line. This gave me an eery feeling, especially since I had seen this exact same type of object so recently at a nearby location.However, I was able to confirm the approximate size and altitude of the October 9, 2013 sighting that I had previously been only to have estimated. I filed a sighting report for that event, which had more detail about the object.