Newton's Law of Universal Gravitation and Gravitational Field Strength

Circular motion and gravitation come together most beautifully in the heavens, where gravity provides the centripetal force that holds planets and moons in orbit. Before exploring orbits, we need the law that governs the gravitational attraction itself. Isaac Newton proposed, in his Principia of 1687, that every particle of matter in the universe attracts every other particle. This is the law of universal gravitation, and its reach from apples to galaxies is what makes it "universal."

The law states that the gravitational force between two point masses is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. In symbols, $F = G\dfrac{m_1 m_2}{r^2}$, where $m_1$ and $m_2$ are the masses, $r$ is the separation of their cent