In the last 300 million years, has the moon changed its velocity from the Earth?
The Earth and the Moon should really be considered as one system; some scientists have categorized them as a double planet, since most moons we know about are far smaller than the body they orbit, and exist most likely because of orbital capture. Our Moon is an exception--current theory has it forming out of the primordial Earth in a massive impact which ejected a substantial amount of matter into orbit which coalesced into the Moon. It was much closer to the Earth then, spun quickly on its own axis relative to Earth, and orbited in a day or two instead of a month. It accelerated away from Earth after that impact, and continues to move further from us even today. However, over the eons, the gravitational interplay between Earth and Moon has resulted in the Moon's expanding orbit slowing to a great degree. So the rate of expansion is indeed slowing now; in the future it will stop, and the Moon will then begin its long journey back towards the Earth, accelerating as it does so. Eventually, it will come so close that gravitational (tidal) forces will break it apart, and the Earth will be surrounded by a Moon Ring.