The gravitational field is a measure of the gravitational force present in a region of space due to material objects. A quantitative description of the gravitational field is developed in the following way: take the force felt by a test body and divide it by its own mass. The test body may be moved from place to place to map out the size of the field. This equation is Newton's law of universal gravitation extended to a many-particle (or n-particle) system. Although Newton's law of gravitation is applicable in many instances, it is not applicable when relativity (special or general) must be taken into account.
The gravitational field, represented by the symbol g, is defined as the gravitational force per unit mass. For any object whose mass is constant, Newton's second law of motion states that the net external force F on a body is the product of the body's mass m and acceleration a, or F=ma. Dividing both sides of this equation by the mass m yields the equation a=F/m. This equation shows that the gravitational field g is itself a type of acceleration. Specifically, it is the acceleration of the test mass m due to gravity. Near Earth's surface the value of g is approximately 9.8 m/s2 (32 ft/s2 ).
Within the past half-century many discoveries have been made concerning our solar system's planets, planetary moons, asteroids, and other bodies. For some of these celestial bodies gravity maps have been constructed. The gravity map of a celestial body is the primary method for determining the mass distribution within that body. For example, the Magellan probe sent to the planet Venus was used not only to map its surface via radar, but to create a gravity map of the planet as well. By recording the velocity and position of the Magellan probe as it orbited Venus, information about the gravitational force exerted on Magellan due to Venus was calculated. Dividing the gravitational force F by Magellan's mass m at numerous points yielded the gravitational field just above Venus's atmosphere.
The gravitational field is useful in addressing the so-called action-at-a-distance problem. In fact, this was a criticism leveled at Newton's law of universal gravitation concerning the mechanism through which material bodies attract one another. A spring or lever through which forces are applied to various objects can be touched and held in one's hands. But the notion of all objects in the universe attracting one another through an invisible, permeating force seemed to some people during Newton's lifetime as being on the level of black magic. Isaac Newton was aware of this problem, but was unable to satisfactorily resolve it. The development of the gravitational field concept allowed people to think of the field itself as acting upon the masses present in a region of space. The gravitational field lines can be thought of as permeating a region of space so that when an object is brought into this space it is affected by, and interacts with, these lines. However, the action-at-a-distance problem was not completely remedied until the development of relativity theory in the twentieth century.
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