We installed an antenna next to our trailer on a mast pole. The coaxial cable we used had a gound wire in it but we didn't use it. We grounded the pole to a grounding rod in the ground and connected copper wire to it. We didn't connect the ground wire inside the cable at all. Is this a mistake?

The outer shield of the coax should indeed be grounded, for two reasons:

1. Safety! In case of a lightnig strike or a power cross that energizes the coax shield you want that voltage to find its way to earth through a low resistance ground point, and not through the electronics of your equipment inside.

2. Noise reduction! If the shield is not terminated to ground it can act as its own antenna, and cause coupling of external radio interference into the inner coax conductor, which in turn would appear as noise in the signal.

If you've seen how the cable TV company grounds the coax from the pole into your house, you'll see that they ground the shield both at the pole and at your house, for these exact reasons.