The force that all objects in the universe exert on all other objects as a result of their mass.
Physicists identify four fundamental forces that account for all known physical phenomena: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. Gravity is the weakest of the four, despite its overwhelming influence in everyday life, and it has a cosmic role in controlling the structure and evolution of the universe. Gravitation is dominant on a cosmic scale because it is long range, extending to infinity. The strong and weak nuclear forces, while much stronger than gravity, are of very short range and confined to the interior of the atomic nucleus. Electromagnetism also extends to infinity, but electric charges, which are the source of electromagnetic forces, come in both positive and negative forms that by and large cancel each other out, leaving only a relatively tiny net effect. Gravity, by contrast, is always attractive, therefore always additive and reinforcing. With a sufficient amount of mass, gravity can be made arbitrarily large. It is only because of the tremendous mass of the earth that gravity becomes the dominant force in everyday life.
Sir Isaac Newton in 1684 recognized that the gravitational force between two widely separated bodies must be proportional to the mass of each and weaken as the square of the distance between them. The gravitational force of the earth on an object is called its weight, and Newton’s law states that one object twice the mass of another will weigh twice as much. It is on this basis that the mass of an object can be measured using devices such as balances and scales that actually determine weight. The law also specifies that weight will diminish with distance, so that objects at high altitudes will weigh less than they do at sea level. This loss of weight is real and easily measured with modern instruments. It must be stressed, however, that there is no corresponding loss of mass.
Because gravity extends to infinity, weight never vanishes completely and there is no such thing as true weightlessness. What is typically thought of as “weight” is actually the counterforce of the ground that supports objects and prevents them from falling due to the gravitational force. The “weightlessness” experienced by astronauts in orbit is actually free fall. In the 1580’s, Simon Stevin experimentally discovered that all objects fall in a gravitational field at exactly the same rate, a result whose importance was first recognized and widely disseminated by Galileo Galilei in 1638. Astronauts in orbit are continuously falling toward Earth, but the spacecraft enclosing them is falling in exactly the same direction at exactly the same rate. As there is no relative motion, the astronauts float in the cabin as though gravity has gone away.
Orbital motion is a combination of free fall with a large velocity at right angles to the direction of fall. Absent the gravitational force, a satellite would move away from Earth in a straight line that would eventually carry it off toward infinity. The gravitational force pulls the satellite from this straight-line motion onto a path that curves around Earth and closes onto itself repetitively. This is an orbit.
Newton’s law of gravitation explains Johannes Kepler’s three laws of orbital motion: satellites travel in ellipses with the gravitational source (the primary) at one focus of the ellipse; a line joining the primary to the satellite sweeps out equal areas in equal times as the satellite moves around the orbit; and the cube of the average distance from the primary to the satellite is proportional to the square of the orbital period.
Moving objects possess energy of motion called kinetic energy, equal to one-half of their mass multiplied by the square of their velocity. Satellites in orbit are continuously speeding up as they fall toward the primary, thereby gaining kinetic energy, and slowing down as they coast away from it, losing kinetic energy. Since the total amount of energy in a system, kinetic plus potential, can never increase or decrease, the gain or loss of kinetic energy must be balanced by a gain or loss from another source called gravitational potential energy. The gravitational potential energy of two objects mutually attracted by a gravitational force is proportional to the product of their masses divided by the distance between them.
An object in free fall decelerates as it coasts upward, eventually coming to a stop when all of its kinetic energy has been converted to potential energy. It then starts to fall downward, converting potential energy back to kinetic energy and accelerating as it does so. Because the gravitational force weakens with distance, the amount of additional kinetic energy needed to reach ever-greater heights is limited. Objects moving fast enough to have kinetic energies that exceed this limit will never stop rising and will coast away from Earth forever. The velocity associated with this energy is referred to as the local escape velocity. Escape velocity at Earth’s surface is approximately 7 miles per second (11 kilometers per second).
The total energy of a satellite determines the size of its orbit, its orbital speed, and its orbital period through Kepler’s second and third laws. Satellites in low-Earth orbit travel at slightly less than 5 miles per second (7.7 kilometers per second). The atmosphere at that altitude is extremely thin but still capable of exerting significant drag on objects traveling at such high velocities. Drag is a dissipative force which converts kinetic energy to heat and ordinarily slows objects down, but satellites under the influence of drag drop closer to the earth, converting potential energy to kinetic energy as they do so, and surprisingly end up traveling faster. When the total energy is no longer sufficient to maintain orbit, the satellite reenters the atmosphere.
In order for the satellite to reach the ground at rest, all of its orbital kinetic and potential energy must be converted into heat. Temperatures become so great that the air around the reentering satellite becomes hot enough to glow. In uncontrolled reentry, too much of the heat builds up within the satellite and the satellite vaporizes, a fate common to small meteors. Crewed spacecraft control reentry and survive by discharging the heat overboard.
The gravitational pull of the Moon is felt daily in the rising of the tides. Additionally, as Earth rotates underneath the tides, it pulls the bulge of water from west to east, working against the pull of the Moon. This produces a small tug on the Moon in the direction of its orbital motion and slightly increases the Moon’s total energy. As a consequence, the Moon’s orbit increases in size a small but measurable amount. The orbital period of the Moon increases as a result, and the month gets slightly longer. Correspondingly, the drag of the tides on the ocean floor slows down Earth, increasing the length of the day.
Although Earth and the Moon appear to be made of hard, rigid rock, each is flexible enough to bend in response to their mutual gravitational attraction. This allows tides to rise in the rock itself. Rock tides on Earth contribute to the braking effect of the ocean tides, but are very small in comparison. Earth’s gravity also raises rock tides on the Moon, which have, over billions of years, slowed the Moon’s rotation down to the point that the length of the lunar day exactly equals the orbital period: one month. As a consequence, the Moon always keeps one face toward Earth, and humankind is only privileged to see the other side of the Moon through photographs taken from lunar orbit.
This curious circumstance is called tidal locking and it is not at all rare. A majority of the natural moons in the solar system are tidally locked to their parent planet. Tidal locking is the inevitable result of the gravitational interaction of one flexible body orbiting another. When deliberately used by satellite designers to keep one end of an oblong satellite pointed toward Earth, it is referred to as gravity-gradient stabilization. (Space shuttle pilots put the shuttle into gravity-gradient stabilization during sleep periods so that noisy thruster firings to maintain attitude can be avoided.)
Although gravity was the first force to be mathematically described by physicists, it remains the least understood. Stevin’s and Galileo’s observation that all objects fall at exactly the same rate in response to the gravitational force inspired Albert Einstein in 1915 to go beyond Newton’s law of gravitation to propose the theory of general relativity. Based on Einstein’s theory of special relativity, which unites space and time into a four-dimensional universe, general relativity describes gravity as the result of localized space-time curvature in this four-dimensional universe.
General relativity predicts that clocks at high altitudes will run faster than identical clocks at low altitudes. This prediction has been verified and this phenomenon had to be included in the design of the Global Positioning System (GPS) in order to achieve required accuracy and precision. Very accurate and stable atomic clocks flown on GPS satellites consistently run faster than identical clocks on the ground.
General relativity also explains the cosmological expansion of the universe and the bizarre properties of black holes. The expansion of the universe was discovered by Edwin Hubble in 1925 through measurement of the frequency shifts of light emitted by distant galaxies. Almost all proved to be moving radially away from the Milky Way, with a speed of recession proportional to distance away: A galaxy twice as far away as another recedes from Earth twice as fast. This shocking phenomenon proved to be a direct and natural expectation of the general theory of relativity.
Apparently, the universe originated billions of years ago in a big bang that flung matter outward in all directions. Over the course of billions of years, gravity pulled the matter into clumps out of which galaxies, stars, and planets formed. Because the galaxies attract each other gravitationally, the expansion should slow as time goes by. If the universe does not contain enough matter to make the local escape velocity of the galaxies everywhere greater than the current recession velocity, then the expansion will go on forever. If the universe does contain enough matter, then the expansion will eventually slow to a halt and the universe will contract back into a single mass, possibly to explode again and expand into a brand new and different universe.
Black holes are objects whose surface gravity is so strong that in regions inside what is called the escape horizon, the local escape velocity is greater than the speed of light. As a basic tenet of special relativity is that nothing can travel faster than light, nothing that ever falls through the escape horizon can ever get out again. A second consequence is that anything that falls through the escape horizon continues to fall all the way to the center of the black hole where it and all other infalling matter are crushed to zero volume and infinite density. It appears that the laws of physics themselves cease to hold under these conditions.
Certain aspects of general relativity have not been reconciled with quantum theory, the branch of physics that explains the behavior of objects at atomic and sub-atomic levels. Physicists have succeeded in uniting the theory of electromagnetism and the theory of the weak nuclear force into one theory of electroweak interactions. They are confident that eventually the theory of electroweak interactions and the theory of the strong nuclear force will be united into a grand unified theory. The ultimate quest of theoretical physics is a single theory uniting this eventual grand unified theory with general relativity, capable of explaining all four fundamental forces, and by extension, everything in the universe.
Layzer, D. Constructing the Universe. New York: Scientific American Library, 1984. A history of astronomy’s changing view of the structure of the universe. Illuminates the basic properties of gravity and delightfully illustrates the primary role of gravity in cosmology. Misner, Charles W. Gravitation. New York: W. H. Freeman, 1973. A very popular textbook, still in print after more than a quarter of a century, explaining gravitational physics in depth. Schwinger, J. Einstein’s Legacy: The Unity of Space and Time. New York: Scientific American Library, 1986. This book requires some knowledge of algebra to be fully understood, but even without the mathematics contains a wealth of information on both special and general relativity accessible to the thoughtful and careful reader.
Forces of flight