The sun, being a HUGE source of light literally shines around high flying objects, cancelling their shadow.
Take a (standard) light bulb and a pin (one of the ones with a little colored sphere on the end to hold onto).
Put the light about four feet from a bare wall and hold the pin close to the wall, so you can see the shadow of the ball clearly. Then slowly move the pin closer to the lightbulb, away from the wall. Observe as the shadow of the pin gets smaller, then diffuses because it's lost in the larger lightsource.
That's what happens to a planes shadow.