http://nssdc.gsfc.nasa.gov/photo_gallery/photogallery-moon.html
German astronomer Johannes Kepler (1576-1630) spent years observing the motion of planets and developed a set of laws for planetary motion. Years after his death Physicist Isaac Newton (1642-1727) used these laws to help him develop his law of universal gravitation.
The law of Universal Gravitation states that: "every particle in the Universe attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them" (Serway 424). This essential means that the force of gravity increases the larger the masses are and decreases the farther away the masses are. The formula to determine the the magnitude of the gravitational force is:
Fg = G (M1M2)/R^2
G is the Universal Gravitational Constant, M1 and M2 is the mass of the two objects and R is the distance between them.
http://observe.arc.nasa.gov/nasa/gallery/
On Earth the force of gravity causes all objects to accelerate at 9.8m/s^2. For example, say you have a mass of 1kg on the surface of the earth. The force of gravity between the two objects is given by:
Fg= (6.673x10^-11)(5.9736x10^24)(1)
(6.3781x10^6)^2
Fg = 9.8 m/s^2
6.672x10^-11 is the value of the universal gravitational constant (G), 5.9736x10^24 is the mass of the Earth (M1) in kg, 1 is the mass of our object on the earth's surface (M2) in kg, and 6.3781x10^6 is the distance between the center of the Earth and the Earth's surface (R) in meters. 9.8 m/s^2 is the acceleration force between objects and the earth
http://eclipse99.ksc.nasa.gov/pages/MoonImages
On the moon this value is much less because the moon has a smaller mass and radius. If the same 1kg object is on the surface of the moon, the force of gravity on it is given by:
Fg = (6.673x10^-11)(7.349x10^22)(1)
(1.7381x10^6)^2
Fg = 1.6 m/s^2
7.349x10^22 is the mass of the moon in kg and 1.7381x10^6 is the radius of the moon in meters. On the moon objects experience roughly 1/6 the gravitational force they would on Earth.