# Section 2: Nature's Strongest and Weakest Force

Figure 2: Gravitational attraction between two spheres causes a tiny change in their positions.

How weak is gravity? We can find out by comparing the gravitational force with the electromagnetic force, the other long-range force in nature, in the case of a hydrogen atom. By using Coulomb's law of electrical attraction and repulsion we can compute the magnitude of the attractive electrical force, FE, between the electron and proton and Newton's Law of universal gravitation, which we will discuss in the next section, to calculate the magnitude of the gravitational force, FG, between the two particles. We find that FG/FE 4 x 10-40. Because both forces decrease as the square of the distance between the objects, the gravitational force between the electron and proton remains almost 39 orders of magnitude weaker than the electric force at all distances. That is a number so large that we can hardly fathom it: roughly the ratio of the size of the observable universe to the size of an atomic nucleus. Relatively speaking, at short distances the strong, weak, and electromagnetic forces all have comparable strengths, 39 orders of magnitude stronger than gravity.

The contrast has practical consequences. We can easily feel the magnetic force between two refrigerator magnets, yet we don't feel the gravitational force of attraction between our hands when they are near to one another. The force is there, but too weak to notice. Physicists use sensitive instruments such as the torsion balances that we discuss below to detect the gravitational force between small objects. But the measurements require great care to ensure that residual electric and magnetic forces do not overwhelm the feeble gravitational effects.

Nevertheless, gravity is the force we experience most often. Whether lifting our arms, climbing a staircase, or throwing a ball, we routinely feel and compensate for the effects of our gravitational attraction to the Earth in our daily lives. We call the direction opposite to Earth's gravity "up." Removing the effects of Earth's gravity in a free fall off a diving board or the weightlessness of space leaves us disoriented. Gravity holds the Moon in orbit about the Earth, the Earth in orbit about the Sun, and the Sun in orbit about the center of our Milky Way galaxy. Gravity holds groups of galaxies together in clusters and, we believe, governs the largest structures in the universe.

## Gravity's role in forming stars and galaxies

Gravity also caused stars and galaxies to form in the first place. The standard model of cosmology has the universe beginning in a Big Bang roughly 14 billion years ago, followed by an expansion that continues today. At an early age, before stars existed, the universe could be described as a nearly homogeneous gas of matter and radiation. The matter consisted mostly of hydrogen atoms, helium atoms, neutrinos, and dark matter (an unknown form of matter that interacts via gravity but whose exact nature is currently a field of intense research, as we shall see in Unit 10). In regions of space where the density of matter slightly exceeded the average, the gravitational attraction between the constituents of the matter caused the gas to coalesce into large clouds. Friction inside the clouds due to collisions between the atoms and further gravitational attraction caused regions of the clouds to coalesce to densities so high as to ignite nuclear fusion, the energy source of stars.

Figure 3: Hubble Space Telescope image of a star-forming region in the Small Magellanic Cloud.

A massive star that has burnt all of its nuclear fuel can collapse under the influence of gravity into a black hole, a region of space where gravity is so strong that not even light can escape the gravitational pull. Near to a black hole, therefore, nature's weakest interaction exerts the strongest force in the universe.

How do physicists reconcile the incredible weakness of gravity relative to the electromagnetic force with the observation that gravity dominates the interactions between the largest objects in the universe? How can it take the gravitational attraction billions of years, as calculations show, to cause two hydrogen atoms starting just 10 cm apart to collide when we know that the hydrogen gas of the early universe condensed into enormous clouds and stars on a much quicker time scale? Why does Earth's gravity feel so strong while the gravitational forces between objects on the Earth are so small as to be difficult to detect? The answer, common to all of these questions, arises from the relative masses of the objects in question. Gravity is weak between objects that have small masses, but it grows in strength as the objects grow in mass. This seemingly simple answer reflects a profound difference between gravity and the other forces in nature.

## Attraction without repulsion

Gravity is an attractive force that acts between any objects at any distance regardless of their composition. The property of matter that gives rise to this attraction is essentially the mass of the object. The gravitational force between each atom in the Earth and each atom in our bodies is incredibly small. However, every one of the roughly 1050 atoms in the Earth attracts each of the approximately 1027 atoms in our bodies, leading to the appreciable force that we experience. In contrast, the other forces in nature can be both attractive and repulsive. The electric force is attractive between unlike charges and equally repulsive between like charges. Because ordinary matter, such as the Earth or our bodies, consists of equal numbers of positive and negative charges bound closely together in atoms, the net electric force between electrically neutral objects essentially vanishes.

Figure 4: Electrostatic and gravitational shielding.