Fgrav is the force due to gravity G is the universal gravitation constant 6. 673 x 10-11 Nm2/kg2[4] X Research source m1 is the mass of the first object m2 is the mass of the second object d is the distance between the centers of two objects Sometimes you will see the letter r instead of the letter d. Both symbols represent the distance between the two objects.

The distance from the surface of the earth to the center is approximately 6. 38 x 106 m. [7] X Research source You can find tables and other resources online that will provide you with approximate distances of the center of the earth to objects at various elevations on the surface. [8] X Research source

For example: Determine the force of gravity on a 68 kg person on the surface of the earth. The mass of the earth is 5. 98 x 1024 kg. [10] X Research source Make sure all your variables have the proper units. m1 = 5. 98 x 1024 kg, m2 = 68 kg, G = 6. 673 x 10-11 Nm2/kg2, and d = 6. 38 x 106 m Write your equation: Fgrav = (Gm1m2)/d2 = [(6. 67 x 10-11) x 68 x (5. 98 x 1024)]/(6. 38 x 106)2 Multiply the masses of the two objects together. 68 x (5. 98 x 1024) = 4. 06 x 1026 Multiply the product of m1 and m2 by the gravitational constant G. (4. 06 x 1026) x (6. 67 x 10-11) = 2. 708 x 1016 Square the distance between the two objects. (6. 38 x 106)2 = 4. 07 x 1013 Divide the product of G x m1 x m2 by the distance squared to find the force of gravity in Newtons (N). 2. 708 x 1016/4. 07 x 1013 = 665 N The force of gravity is 665 N.

This law can be summed up with the equation F = ma, where F is the force, m is the mass of the object, and a is acceleration. Using this law, we can calculate the force of gravity of any object on the surface of the earth, using the known acceleration due to gravity.

If you want a more exact approximation of force, you can still use the above equation, Fgrav = (GMearthm)/d2 to determine force of gravity.

Let’s use the same equation from above and see how close the approximation is. Determine the force of gravity on a 68 kg person on the surface of the earth. Make sure all your variables have the proper units: m = 68 kg, g = 9. 8 m/s2. Write your equation. Fgrav = mg = 68*9. 8 = 666 N. With F = mg the force of gravity is 666 N, while using the more exact equation yields a force of 665 N. As you can see, these values are almost identical.