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The process of keeping track of where the ship was likely to be was called rangekeeping, because the distance to the target—the range—was a very important factor in aiming the guns accurately. As time passed, train (also called bearing), the direction to the target, also became part of rangekeeping, but tradition kept the term alive.
In geometry, the sagitta (sometimes abbreviated as sag [1]) of a circular arc is the distance from the midpoint of the arc to the midpoint of its chord. [2] It is used extensively in architecture when calculating the arc necessary to span a certain height and distance and also in optics where it is used to find the depth of a spherical mirror ...
Image distance in a spherical mirror + = () Subscripts 1 and 2 refer to initial and final optical media respectively. These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation:
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
where n is the local refractive index as a function of distance along the path C. An electromagnetic wave propagating along a path C has the phase shift over C as if it was propagating a path in a vacuum , length of which, is equal to the optical path length of C .
Arc length – Distance along a curve; Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric ...
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
For telescopic angles, the approximations of = = greatly simplify the trigonometry, enabling one to scale objects measured in milliradians through a telescope by a factor of 1000 for distance or height. An object 5 meters high, for example, will cover 1 mrad at 5000 meters, or 5 mrad at 1000 meters, or 25 mrad at 200 meters.
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