A lot of times, it's the photographer, not the camera.

As said before, use manual mode, your camera's meter is 90% likely to expose the sky, not the aircraft.
Also, the specs on the p500 says it does 5 to 8 frames/second in continuous mode; that's fairly fast in my book (my 7D does 8/sec., and it's a fairly top-of-the-line DSLR). What class SD card do you have? That might have something to do with FPS.
43 6F 6E 67 72 61 74 73 20 6F 6E 20 64 65 63 6F 64 69 6E 67 20 6D 79 20 73 65 63 72 65 74 20 63 6F 64 65 21 0D 0A 0D 0A 48 65 72 65 20 69 73 20 79 6F 75 72 20 72 65 77 61 72 64 3A 0D 0A 0D 0A 68 74 74 70 3A 2F 2F 79 6F 75 74 75 2E 62 65 2F 64 51 77 34 77