Newton's law of gravitation and the inverse square rule
How mass and distance set the strength of gravity, why the force falls off as one over distance squared, and how to read very small answers.
What the equation is saying
Newton's law packs three ideas into one line. The force grows in direct proportion to each mass, so doubling either body doubles the pull. It shrinks with the square of the separation, so moving twice as far apart cuts the force to a quarter. The constant G sets the overall strength of the effect, and its tiny size is why gravity is the weakest of the fundamental forces despite ruling the motion of planets.
Why the inverse square appears
The one over r squared shape is not arbitrary. Imagine the gravitational influence of a mass spreading outward evenly in every direction. The same influence has to cover the surface of an ever larger sphere as you move away, and that surface area grows with the square of the radius. Spread over a bigger area, the effect at any single point weakens as one divided by distance squared, the same geometry that dims light and sound with distance.
Reading scientific notation results
Because G is about 6.674 x 10^-11, forces between small objects come out extremely small and the tool prints them in scientific notation. A result like 1.66850e-5 N means 1.66850 times ten to the minus five, or 0.0000166850 newtons. Large astronomical pulls run the other way, so the Earth and Moon example reports 1.98040e+20 N, which is nearly two hundred billion billion newtons holding the Moon in orbit.
From force to surface gravity
The Earth surface example shows how this law connects to the familiar 9.8 m/s squared. Putting a 1 kg mass at Earth's radius gives a force of about 9.82 N, and since force equals mass times acceleration, dividing by 1 kg recovers the local acceleration due to gravity. That is why weight on Earth is almost exactly 9.8 newtons per kilogram, and why the same formula that governs orbits also sets what your bathroom scale reads.