Inverse-square law in the context of Constant of motion

In celestial mechanics, an orbit is the curved trajectory of an object under the influence of an attracting force. Known as an orbital revolution, examples include the trajectory of a planet around a star, a natural satellite around a planet, or an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.

For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.

The gravitational constant is an empirical physical constant that gives the strength of the gravitational field induced by a mass. It is involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity. It is also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant, denoted by the capital letter G.

In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the stress–energy tensor.

In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force that varies in strength as the inverse square of the distance between them. The force may be either attractive or repulsive. The problem is to find the position or speed of the two bodies over time given their masses, positions, and velocities. Using classical mechanics, the solution can be expressed as a Kepler orbit using six orbital elements.

The Kepler problem is named after Johannes Kepler, who proposed Kepler's laws of planetary motion (which are part of classical mechanics and solved the problem for the orbits of the planets) and investigated the types of forces that would result in orbits obeying those laws (called Kepler's inverse problem).

A flash is a device used in photography that produces a brief burst of light (lasting around 1⁄200 of a second) at a color temperature of about 5500 K to help illuminate a scene. The main purpose of a flash is to illuminate a dark scene. Other uses are capturing quickly moving objects or changing the quality of light. Flash refers either to the flash of light itself or to the electronic flash unit discharging the light. Most current flash units are electronic, having evolved from single-use flashbulbs and flammable powders. Modern cameras often activate flash units automatically.

Flash units are commonly built directly into a camera. Some cameras allow separate flash units to be mounted via a standardized accessory mount bracket (a hot shoe). In professional studio equipment, flashes may be large, standalone units, or studio strobes, powered by special battery packs or connected to mains power. They are either synchronized with the camera using a flash synchronization cable or radio signal, or are light-triggered, meaning that only one flash unit needs to be synchronized with the camera, and in turn triggers the other units, called slaves.

The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative near-field behaviors dominate close to the antenna or scatterer, while electromagnetic radiation far-field behaviors predominate at greater distances.

Far-field E (electric) and B (magnetic) radiation field strengths decrease as the distance from the source increases, resulting in an inverse-square law for the power intensity of electromagnetic radiation in the transmitted signal. By contrast, the near-field's E and B strengths decrease more rapidly with distance: The radiative field decreases by the inverse-distance squared, the reactive field by an inverse-cube law, resulting in a diminished power in the parts of the electric field by an inverse fourth-power and sixth-power, respectively. The rapid drop in power contained in the near-field ensures that effects due to the near-field essentially vanish a few wavelengths away from the radiating part of the antenna, and conversely ensure that at distances a small fraction of a wavelength from the antenna, the near-field effects overwhelm the radiating far-field.

In television, film, stage, or photographic lighting, a fill light (often simply fill) may be used to reduce the contrast of a scene to match the dynamic range of the recording media and record the same amount of detail typically seen by eye in average lighting and considered normal. From that baseline of normality, using more or less fill will make shadows seem lighter or darker than normal, which will cause the viewer to react differently, by inferring both environmental and mood clues from the tone of the shadows.

Natural skylight fill is omnidirectional and diffuse, with lower rate of inverse-square fall-off than artificial sources. A common artificial lighting strategy that creates an overall appearance similar to natural fill places the fill light on the lens axis so that it will appear to cast few if any shadows from the point of view of the camera, which allows the key light that overlaps it to create the illusion of 3D in a 2D photo with the same single-source patterns typically seen with natural lighting where the sun acts as key light and the skylight as the fill. The use of centered near-axis "neutral" fill also prevents dark, unfilled voids in the lighting pattern, which can occur on faces if cheeks or brows block the fill source.