Expert: Philip Stahl - 10/18/2006

Question
I dont understand the law of gravitation. can you explain? also I heard that quadrupling a distance between two objects makes gravitation stronger, is that true?  

Answer
Hello,


Newton's law of universal gravitation asserts that every body or particle in the universe attracts every other with a force (F) proportional to the product of the masses (M1, M2)  of the two bodies - and inversely proportional to the *square* of the distance (d) separating them.

We can write it:

F =  (k M1 M2)/ d^2

where k is a constant (also called the gravitational constant), M1 and M2 are the two masses - say in kilograms, and d is the distance separating them. Note that d is squared.

Let's say k = 1 (N-m^2/ kg^2),  and M1 = M2 = 1 kg.

Also let d = 1 meter

Then F = 1 N (N for newtons, the unit of force in the metric system)

Now - keep everything the same - but double the distance to 2 meters.

F =   k M1 M2/ (2)^2  =   k M1 M2/ 4

= 1/4  N

Thus, the force has gone to one fourth its original value.

Now, quadruple the original distance - so it is 4 x 1m = 4 m and do the basic math:

F = k M1 M2/ (4)^2  =  k M1 M2/ 16

= 1/ 16 Newton

Thus, we say that in quadrupling the distance the gravitational force is REDUCED to one-sixteenth its original value - NOT increased.

They key point being the farther two bodies or particles are, the weaker the gravitational attraction between them.

Footnote: the actual value of the gravitational constant is:  G = 6.67 x 10^-11 N m^2/ kg^2. I used a simpler value for 'k' to keep the math easier! It changes none of the results, however, that the force F decreases as the square of the distance.

Hopefully, this helps to illuminate this important law for you!