I was sitting outside around 5:30 p.m., Sept. 13, 2014, observing clouds, sky, and lamenting the fact that we had (and seem to always have) more chemtrails today. As is my custom, I had my binoculars with me to track planes and birds in the area (NW Gainesville, Florida).I saw a high altitude airplane spewing chemicals out its rear, though the plane itself was not that visible. I picked up the binoculars to track it, holding steady as I attempted to follow the plane, which I could now see through the binocs. Something caught my eye in "front" of the plane but at a much lower altitude, near some lower level clouds. It was not near the plane at all, which was going out of sight, and was at a great distance from me and the object. I immediately focused on this object with the binoculars. It seemed to be a sphere of some sort, stationary, but rapidly rotating or spinning in a counter-clockwise way, with its southern surface reflecting the sun each time it rotated. It was not moving up or down or sideways; it was stationary. I briefly glanced away from the binoculars to see if it was visible to the naked eye. It wasn't and I quickly went back to viewing through the binoculars, but thinking I would not see it again. However, I did find it immediately and stayed on it, just watching through the binocs until my neck began to ache. This had to be around five minutes or more. All the while the object stayed in its location, spinning, reflecting the sun. It seemed to be a brownish or coppery color - a darker color than the obvious reflection of the sun. That reflection is what initially caught my eye.At this point, I decided to get more comfortable in my chair and briefly sat back, without looking through the binoculars, and then attempted to resume viewing the object. Unfortunately, the object had vanished. I could not locate it and I kept looking and looking and looking in the same area - and then moved around to a wider area, but still, no spinning object. It was gone.There had been no sound that I could hear. Object might have been at an altitude of commercial aircraft, maybe lower. I simply don't know. I do know that it could not be seen without binoculars. Object didn't seem "huge" but at that distance, I have no idea as to how large or huge it might have been.I don't think this was a man-man object or a drone. In fact, my area is not known to utilize drones and at that high of an altitude I'm not sure what a drone could be doing. Certainly I would have observed a drone leaving the area or moving about the area, and I didn't. I've also not heard of drones being round or spherical in shape - and stationary.Within about five minutes or a little more after I could no longer see the spinning object, I heard a helicopter approach from the horizon west travelling to the east. We have "life flights" in this area and I assumed that was what it was. As the 'copter approached, and it was at a somewhat low altitude, it passed in front of me but not over me. I had my binocs tracking it as it had approached and noticed that it was passing quite near - but certainly lower than - where the UFO had been. As the 'copter passed in front of my position I noticed it was not a "life flight" or a news station 'copter or a private 'copter. It was painted in a dark military green with a bit of camo color on its side. We do not have a military base in Gainesville. We do have a military base in Jacksonville. Frankly, this is the first time I've ever seen a military helicopter in this area, though of course that doesn't mean that they don't fly over. To me, it seemed a bit of a coincidence that I saw this unusual object and then five minutes later a military helicopter flew in the same area (but lower) than the object.The 'copter continued to fly east and then seemed to turn off to the north. I heard it flying about in that area - we do have an an airport in that direction, so perhaps it landed there or went on to Mayport in Jacksonville.I've never seen a spinning or rotating UFO before (though at my age, I've certainly seen other anomalies in the sky both in Gainesville and Miami), so I thought I would report my sighting.