It could not have been an AWACS. They fly at high altitude, and have their radar dome above the fuselage, not below. They are completely unsuited to low altitude missions.
I know a bit about aircraft, but am not aware of any specific aircraft that fits your description. However, based on your description, it is possible to make some educated guesses.
If detection equipment of some kind needs to be mounted outside the aircraft, it is likely to need a protective dome. What you described sounds like a protective dome. Why it was black, instead of the same color as the aircraft, I do not know. Perhaps the material used could not be painted.
It is unusual for equipment needing a dome to be mounted UNDER the aircraft because it can interfere with takeoff and landing. Usually equipment of this type is mounted on the nose, tail, or above the fuselage. However, mounting UNDER the fuselage can be done if it does not extend down very far below the fuselage.
I do not know what specific equipment would need to be mounted under the fuselage (instead of in the nose or tail), but the low altitude of the aircraft provides a clue. If the equipment they mounted is looking for something that can only be detected at very short range, or if the fuselage of the aircraft would interefere with detection, then it would be mounted under the fuselage.
Regardless of what the specific equipment in the dome was, you do not need to worry about this aircraft. It has been common knowledge for some time that we have specially equipped vehicles (boats, planes, vans, etc.) looking for all kinds of bad stuff. Since you live relatively near a nuclear power plant, it only makes sense that your area would occassionally be checked as a matter of routine.
Every time I try to post a picture, the picture shows
up in the preview but when I post it I get the redX.
Can someone tell me what I am doing wrong?
Thanks!
My daughter said that was NOT the plane she saw.