Try this with your telephoto lens (seriously). This is an image of the International Space Station when it was almost directly overhead from my home.
Canon 1D Mark IV, 500 mm f/4 L IS lens with 2x TC. Tracking by hand using a wimberly head on a CF tripod (wildlife photography setup) with image stabilization on, but focus locked. I previously focused on a star. Exposure was 1/1600 second at ISO 400, f/8. Two frames obtained within 2 seconds of each other were stacked. The stacked image was enlarged 5x and Richardson-Lucy image deconvolution applied to sharpen the image. Final levels, curves in photoshop.
You can get accurate positions of the ISS (and other satellites) from this web site for your location: http://www.heavens-above.com/
The image is by no means spectacular as amateur astronomers using big telescopes get better images, but it is the best I've seen done with a camera telephoto lens.
My skies are usually turbulent, with wind flowing over the Rocky Mountains and last night was no exception. I was also imaging through haze. So people elsewhere, especially Florida, can likely get better images with your super telephotos. It moves fast: horizon to horizon in under about 5 minutes, and best image is straight overhead, which makes it harder, but it is slower than many birds!
Now for something completely different
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!.......if it ever stops raining here that is!
