The P500 seems to have a nice large zoom lens for plane pics... and it also has manual controls, which is great!

You can play with the manual "M" mode and try increasing shutter speed.

In order to do this and get good shots you will have to open the Aperture as much as possible and Set the ISO at the highest value you can as long as your pictures don't become too noisy.

Remember, the more zoom you use, the less the max. aperture will be!!

Here is a good read that applies to many picture situations, including aircraft spotting

http://www.photographyjam.com/articles/29/camera-basics-shutter-speed-aperture-a...

Have a great spotting day!

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.