http://www.npr.org/2011/09/10/140361610/nasa-launches-probes-to-study-moon describes a recently launched unmanned NASA mission to the moon to map out the moon's gravitational field. What is the gravitational field? It's quite simply the acceleration due to gravity ("g" as we've been calling it in class) as a function of position around the moon!
On the surface of the earth, g is a pretty consistent 9.8 m/s^2, but it does vary depending on your position on the planet, since Earth is not a perfect sphere. And once you start to get out into space, g begins to diminish drastically, dropping off like 1/r^2, where r is the distance between you and the center of the earth!
The moon's acceleration due to gravity behaves much the same way. On the surface of the moon (at least the parts we've been to!), it's about 1/6 of our g on earth (so about 1.7 m/s^2, give or take), and also drops off like 1/r^2 (where r is the distance between you and the center of the moon) as you leave the surface.
These probes will measure these variations in the moon's g as they orbit on opposite sides of the moon! By the way, the GRACE mission (http://www.csr.utexas.edu/grace/) did the same thing on earth! Here's a map of the results, depicting the difference between the local g and the average g: http://www.csr.utexas.edu/grace/gallery/gravity/03_07_GRACE.html, where the red regions represent a higher value of g and the blue regions represent a lower value of g (measured in units of "milligals," which are named after Galileo; 1 gal = 1 cm/s^2).
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