Gravity and the gravitational field

Geophysicists utilize slight variations in gravitational force to characterize the mass of subsurface features. Particularly useful in petroleum exploration, subtle gravitational field differences can help identify solid subsurface plutonic bodies or fluid filled reservoirs.

1n 1687, English physicist Sir Isaac Newton (1642–1727) published a law of universal gravitation in his important and influential work Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). In its simplest form, Newton's law of universal gravitation states that bodies with mass attract each other with a force that varies directly as the product of their masses and inversely as the square of the distance between them. This mathematically elegant law, however, offered a remarkably reasoned and profound insight into the mechanics of the natural world because it revealed a cosmos bound together by the mutual gravitational attraction of its constituent particles. Moreover, along with Newton's laws of motion, the law of universal gravitation became the guiding model for the future development of physical law.

Newton's law of universal gravitation was derived from German mathematician and astronomer Johannes Kepler's (1571–1630) laws of planetary motion, the concept of "action-at-a-distance," and Newton's own laws of motion. Building on Italian astronomer and physicist Galileo Galilei's (1564–1642) observations of falling bodies, Newton asserted that gravity is a universal property of all matter. Although the force of gravity can become infinitesimally small at increasing distances between bodies, all bodies of mass exert gravitational force on each other. Newton extrapolated that the force of gravity (later characterized by the gravitational field) extended to infinity and, in so doing, bound the universe together.

Newton's law of gravitation, mathematically expressed as F= (G)(m₁ m₂) /r², stated that the gravitational attraction between two bodies with masses m₁ and m₂ was directly proportional to the masses of the bodies, and inversely proportional to the square of the distance (r) between the centers of the masses. Accordingly, a doubling of one mass resulted in a doubling of the gravitational attraction while a doubling of the distance between masses resulted in a reduction of the gravitational force to a fourth of its former value. Nearly a century passed, however, before English physicist Henry Cavendish (1731–1810) was to determine the missing gravitational constant (G) that allowed a reasonably accurate determination of Earth's actual gravitational force.

The force exerted by a gravitational field on a body, such as forces produced by Earth's gravitational field, is called the weight of the body. The weight of a body is equal to the product of its mass m and the acceleration due to gravity g, (w = mg). Weight should not be confused with mass, which is an intrinsic property of matter that is not altered by an change in the gravitational field (i.e., the mass of an object on Earth is the same in the lower gravity environment on the Moon ).

Newton's second law states that the net force F acting on an object is equal to the mass of the object m multiplied by its acceleration a (F = ma). Freely falling bodies experience acceleration (g) due to Earth's gravitational field. The force of this field is directed towards the center of Earth. By applying Newton's second law to freely falling bodies, with a = g and F = w, the weight of the body is given as w = mg. Because weight depends upon the gravitational field, it varies with geographical location. Because g decreases with increasing distance from the center of Earth, bodies weigh less at higher altitudes than at sea level. Because of this, weight, unlike mass, is not an inherent property of a body.

The value of "g" (9.82 m/s²) is the average measure of the strength of Earth's gravitational field (i.e., the acceleration produced on a mass regardless of the composition of the mass.) The value of "g" can vary locally depending on subsurface mass (e.g., plutonic bodies) and so the value (9.82 m/s²) is an average. Using "g" the gravitational field can then be expressed as force per kilogram exerted by Earth's gravitational field. Although Earth's gravitational field extends to infinity (i.e., as do all other objects with mass in the universe, Earth's gravitational field affects all other entities with mass), because the magnitude of the force of gravity declines as the square of the distance between objects, the force drops dramatically as objects move away from Earth.

Astronauts orbiting Earth do not experience weightlessness because of a lack of gravity. Rather, the apparent weight-lessness in a decreased Earth gravity environment results from uniform acceleration toward Earth in such a way that the spacecraft and all objects in it are constantly falling toward Earth in a manner akin to the objects inside a free-falling elevator. In order to achieve orbit, rockets must be powerful enough to achieve escape velocity, the velocity that, at a minimum, allows their vertical "fall" to match the falling away of Earth spherical surface beneath them. Earth's escape velocity measures 6.959 mi/s (11.2 km/s)—more than 25,000 mph.

Weight is usually expressed in pounds or grams. Although weight and mass are not synonymous terms, they are often used interchangeably. One concept associated with weight is Archimedes' principle that states that a body immersed in a fluid is acted upon by a force equal and opposite in direction to the weight of the displaced fluid. This principle explains the buoyancy of ships, as well as the rise of helium filled balloons.

Another important property associated with weight is specific gravity. The specific gravity of a material is the ratio of the weight of a given volume of that substance to the weight of an equal volume of water . For example, because of the salt, the specific gravity of a saltwater solution is greater than one. This high specific gravity gives saltwater its large buoyancy power because the weight of the volume displaced by an object in the ocean is larger than the weight of the volume displaced by the same object in freshwater .

The molecular weight of a substance is usually expressed in atomic mass units which is exactly 1/12 the mass of a carbon-12 atom .

Although Newton's law of gravitation offered no fundamental explanatory mechanism for gravity, it's usefulness of explanation lies in a higher level of cause and effect. An explanation of gravity continues to elude physicists. The two great theories of modern physics—relativity theory and quantum theory—explain gravity in very different ways. According to relativity theory , gravity is a consequence of the fusion of space and time. Quantum theory proposes that graviton particles (as of yet undiscovered) act as bosons (carriers) of gravitational force.

See also Aerodynamics; Astronomy; Atomic mass and weight; Aviation physiology; Big Bang theory; Crust; Earth (planet); Gravitational constant; Mohs' scale; Petroleum detection; Quantum theory and mechanics