 But resistance to change is strong, and it wasn't until the 18th century that Newton turned the tide for good. We are all familiar with his formula that force equals mass times acceleration. Newton's better understanding of gravity was the key. A good way to view gravity is to think of it as a gravitational field surrounding the object. The intrinsic strength of the field is set by the fixed mass of the object. But as you can see in this illustration, when distance from the object increases, the surface area over which the field is spread increases as well. This effectively weakens the force of gravity, felt at the more distant point. We know that the geometry for a sphere has the increase in surface area proportional to the square of the radius. So the gravitational field strength is reduced by a factor of four every time the distance increases by a factor of two. We call this the inverse square rule. We'll see this rule again when we discuss standard candles in our section on stars. It's interesting to note that the constant of proportionality, G, in Newton's universal gravitation formula, was not known to Newton. It took another hundred years before physicists and instruments sensitive enough to measure this number. But once we had it, it became possible to measure the mass of the Earth at 6 billion 600 million trillion tons. Newton broke Aristotle's 2,000-year-old dictum that there are two sets of rules for nature. One set for here on Earth and another set for the heavens. With Newton, we came to understand that there is only one set and it applies everywhere.