burnhal, The Moon's gravitational acceleration is approximately
1.6m/s� (on the lunar surface).
An interesting property of gravitational acceleration is that it diminishes with the square of the distance; (at twice the distance it falls to one-fourth the rate). The moon being about 60 times the Earth's radius in distance from the Earth, the Earth's gravitational acceleration at that distance is about 9.81/60� = 9.81/3600 = 0.0027m/s�
The mutual gravitational attraction between the Earth and Moon causes the Moon to �fall� towards the Earth at a rate of 1.37
millimetres per second; this keeps the Moon from flying out into space as it orbits the Earth!
The maximum gravitational acceleration from the Moon felt on Earth is about 0.00004m/s� (typically about 0.000033m/s�)
Also keep in mind that while 9.81m/s is the velocity gained by an object in free fall near the Earth�s surface, beginning from a state of rest, it only falls half that far (4.9 metres) in the first second because that is its average velocity over that period of time.
Isaac Newton virtually invented gravity. Thanks to him we know a lot about
Free Fall and the Acceleration of Gravity