The phenomenon associated with the gravitational force acting on any object that has mass and is situated within the earth’s gravitational field. The weight of a body (see mass) is equal to the force of gravity acting on the body. According to Newton’s second law of motion F=ma, where F is the force producing an acceleration a on a body of mass m. The weight of a body is therefore equal to the product of its mass and the acceleration due to gravity (g), which is now called the acceleration of free fall. By combining the second law of motion with Newton’s law of gravitation (F=GM1M2/d2) it follows that: g=GM/d2, where G is the gravitational constant, M is the mass of the earth, and d is the distance of the body from the centre of the earth. For a body on the earth’s surface g=9.806 65 m s−2.
A force of gravity also exists on other planets, moons, etc., but because it depends on the mass of the planet and its diameter, the strength of the force is not the same as it is on earth. If Fe is the force acting on a given mass on earth, the force Fp acting on the same mass on another planet will be given by:
where Mp and dp are the mass and diameter of the planet, respectively. Substituting values of Mp and dp for the moon shows that the force of gravity on the moon is only 1/6 of the value on earth.
https://www.nasa.gov/centers/jpl/missions/grace.html The home page of the NASA/JPL Gravity Recovery and Climate experiment to make precise measurements of the earth’s gravitational field