Gravity was not only the first of the fundamental interactions we introduced in this book, it was also the first recognized by scientists. As far back, even, as Aristotle. We described gravity as an attractive force between all particles with mass, whether they are charged or not and whether they are big or small. Gravity acts between the sun and Mars, between Earth and you, and even between the proton and electron in a hydrogen atom. How Newton’s genius realized that the correct theory of gravity should be universal, describing a force that acts between any two massive particles, no matter where and no matter how far apart they may be. It has, in other words, an infinite range.
Newton’s law of universal gravitation can be summed up as follows: 
. In words, the attractive force (F) between any two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between them. The other term (G) is simply a constant value required to bring both sides of the equation into balance.
Somewhere along the way, you may have learned that the acceleration due to gravity of any object near the surface of the earth is g = 9.8 m/s2. This well-known “gravity” that we experience every day comes simply from g = GmEarth ÷ (rEarth)2.
QUANTUM LEAP
Aristotle reasoned that a stone appears to accelerate faster than a feather when dropped due to the difference in their masses. Galileo is said to have dropped two similarly shaped objects from the leaning tower of Pisa to disprove this notion. After all, the gravitational acceleration of both is 9.8 m/s2. We now know that a feather floats down gracefully while a stone drops like a stone because of the air resistance—itself a manifestation of the electromagnetic interaction.
Gravity is in fact the weakest–by far–of the four fundamental interactions. You may not think so the next time you’re climbing a steep hill on your bike, but it is indeed the case. If this is so, then why does it turn out to be the dominant interaction in really big things like our solar system? The reason is twofold, and boils down to the range of the interaction and type of particles that interact.
Not to give away the punch line, but we’ll see in the next few sections that two other fundamental forces, the strong and weak interactions, have very short ranges of influence, and come into play only at scales comparable to the size of an atomic nucleus. At the macroscopic scale, they are completely negligible.
The electromagnetic interaction, however, has the same (infinite) range as gravity. The big difference between this and gravity is that, depending on the sign of the electric charges, the electromagnetic interaction can either attract or repel objects. It peters out at the planetary scale because macroscopic objects tend to have equal amounts of positive and negative charge in them. As a result, for moons and planets and stars the electromagnetic interaction cancels out, more or less.
As far as we know, there is no way to make gravity a repulsive force; it is always attractive. There is no gravitational repulsion to cancel out the attraction, so the attraction only accumulates the more particles there are in any system. This is why the huge masses in our solar system and beyond are influenced by gravity and gravity alone.
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