We were traveling to fort myers, florida on a southwest flight and it was nighttime around anywhere between 8pm to 8:30 pm. my mother was sitting in the window seat. i was on the aisle seat and my daughter was in the middle seat. she looks over at me and mentions that she sees a light and that it was doing some very strange maneuvers. i tried to look at first but because of my angle, i couldn't see anything. i scoot over to the middle seat and look out the window. at first, it looked like a very bright elongated star, if you just looked out your window and didn't see it move, it would've been mistaken for a star. we were traveling, at least, 36,000 feet with the speed of a normal passenger jet. i don't know our exact location but we were over the gulf of mexico - it was pitch black out there. the light seemed to just hover (or it was moving with us in the same pattern). however, it would descend in a very short loop towards the water and then return to its normal path. no jet could descend and ascend in such a short time and such a tight loop. (we're used to jets as we have luke's airforce base in arizona so we know our jets). my mother said to switch seats. when i was finally in the window seat, the light just seemed stationary (however, that can't be the case, we were moving and the light was consistently in place so it too must have been moving as well). it stayed consistent in its path and it appeared above the wing of our jet. i couldn't tell how far it was from us (i'm not a pilot). i did see it make the loop and go back to its starting point. the light changed from a yellowish-white to a red light and it went away. after a while, the light returned and then it was gone again. my mom said it did some other maneuvers for her but i only saw the tight oval loop. she couldn't explain it and neither could i.