Law of Universal Gravitation

Every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.

Recall back to the discussion of the Ideal Gas Law where we said that work was interesting for introducing students to Direct Proportionality and Indirect Proportionality. Here we see both.

F = G \dfrac {m_1 m_2} {r^2}

Since the calculation is for a Force, we expect the units to calculate out to be

N = \dfrac {kg m} {s^2}

Not including the units of G, we have \dfrac {kg^2} {m^2}.

The units on the constant of Gravitation are \dfrac {m^3} {kg s^2}.

We will multiply these together, crossing our fingers…

\dfrac {kg^2} {m^2} * \dfrac {m^3} {kg s^2} = \dfrac {kg m} {s^2}

Exhale. The units worked out. The units of a physics calculation should always make sense, and using this sort of thinking has sometimes been called the Sanity Test.

Finally, compare the Law of Universal Gravitation to Coulomb’s Law. Can we generalize these two laws?