Newton's Law of Universal Gravitation

Question: A 7500 kg object and a 9500 kg object are separated by a distance of 5 m.

a) What amount of gravitational force exists between them?

   The equation for gravitational force between any two objects is given by F = (G m1 m2) / r^2

• F = the force of gravity (N)
• G = the universal gravitational constant = 6.67 x 10^-11 (Nm^2) / kg^2
• m1 = mass of first object
• m2 = mass of second object
• r = the distance between the centers of the two objects

   F = [(6.67 x 10^-11) (7500) (9500) ] / 5^2 = 1.9 x 10^-4 N

b) The distance between two object is increased to 10 m. What amount of force? Divide the answer into the first answer. What do you get?

   F = [(6.67 x 10^-11) (7500) (9500) ] / 10^2 = 4.7524 x 10^-5 N

    1.9 x 10^-4 N / 4.7524 x 10^-5 N = 4

c) What would the force be if you increase the distance to 15 m?
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   F = [(6.67 x 10^-11) (7500) (9500) ] / 15^2 = 2.1122 x 10^-5 N

   1.9 x 10^-4 N / 2.1122 x 10^-5 N = 9

This is an example of an inverse square, the force decreases by a factor of 4 when the distance decreases by a factor or 2....
    r = 1, 1^2 = 2
    r = 2, 2^2 = 4
    r = 3, 3^2 = 9
    r = 4, 4^2 = 16
    r = 5, 5^2 = 25
    ......


Question: Two object of equal mass M, and M2 are separated by a distance of 8 m. The gravitational force between these object is 6 N. What is the mass of  each object?

     F = (G m1 m2) / r^2 , m1 = m2 = m
     F = (G m^2) / r^2
     6 N = [(6.67 x 10^-11) m^2 ] / 8^2
     2.399 x 10^6 kg = m