Fictitious Geography
.... In science and also in mapping we are concerned with non-fiction generally in our work. But all to often we lose sight of the fact that much of our non-fiction is built upon abstraction and arbitrarily agreed upon convention, like p-values for instance. With that in mind today I will share some words from the glossary to help us remember that right there in our "non-fiction" research is our own "fiction" that we like to call abstraction and assumption.
astre fictif A fictitious star assumed to move along the celestial equator at a uniform rate corresponding to the frequency of one of the several harmonic constituents of the tide-producing force. Each astre fictif crosses the meridian at a time corresponding to the maximum of the constituents it represents.
Besselian year The interval of time beginning when the right ascension of the fictitious mean sun, as affected by aberration and measured from the mean equinox, is 18h 40m (280°) and ending when the right ascension of the same sun is again 18h 40m. Also called a fictitious year and Besselian solar year. The beginning of a Besselian year is denoted by the notation .0.(e.g., 1950.0) The Besselian year is shorter than the tropical year by 0.148xT seconds, where T is given by (Date ‑1900)/100. The difference is usually ignored. For example, the Besselian year 1966.0 began on 1966 January 0.799d Greenwich mean sidereal time. At this instant, the date was 1966 January 0.00d at points on the meridian at 72.36°W.
Bouguer cylinder A fictitious, vertical cylinder whose upper surface passes through a point P on the Earth's surface, whose axis passes through P and is perpendicular to the terrestrial ellipsoid, and whose height is equal to the height of P above the ellipsoid. The radius is arbitrary but is usually between 40 km and 100 km. The cylinder is assumed to be filled with matter, a density of 2.67 g/cc being usual.
Coriolis force n., A fictitious force introduced by an observer in a rotating coordinate system to account for the deviation of a body from the straight-line motion it would have in a non-rotating coordinate system. A body following a straight line at constant velocity in the non-rotating system appears to follow a curved path with variable velocity in the rotating system. An observer in the rotating system ascribes a Coriolis force ‑2m(Ωx v) to the motion of a body of mass m moving with velocity v in non-rotating coordinate system; Ω is the angular rate of rotation of the observer. The quantity ‑2(Ω x v) is called the Coriolis acceleration. The force amounts to about 0.01 dynes/cm3 in mid latitudes. Also called compound centrifugal force and deflecting force.
Eötvös effect The fictitious, vertical force experienced by a body on the rotating Earth. It is the vertical component of the Coriolis force.
equator, fictitious A line, other than the equator, on the reference ellipsoid and to which angles analogous to latitude are referred.
fictitious 1. adj., In cartography, pertaining to or measured from and arbitrary line used as reference. 2. adj., In navigation, of or relating to an imaginary object that serves some useful purpose.
fictitious cartography 1. n., Cartography of places that are, in fact, fictional (i.e., maps of wholly fictional locations (e.g. Middle Earth, Arrakis) 2. n., Fictional versions of actual locations (e.g. alternate history maps).
force, fictitious A quantity introduced into an equation or description to account for the behavior of a body, but which can be dispensed with by using a different coordinate system for the equations or a different viewpoint in the description. The Coriolis force and centrifugal force are typical of such forces.
graticule, fictitious A graticule whose lines represent fictitious meridians and fictitious parallels of latitude.
Greenwich mean time The right ascension of the fictitious mean Sun. This definition was changed, in Britain, in 1925. 2. The Greenwich hour-angle of the vernal equinox of date, plus 12 hours. Also called, by the military, z-time and zulu time. This is equivalent to Universal Time 0. The definition was retained for some time but eventually abandoned. SEE ALSO Universal Time 0.
latitude, fictitious 1. The angle between the normal to a point on the ellipsoid and a reference plane other than the plane of the equator. 2. That angle, in a graticule, which corresponds to the angle specified in the preceding definition. The line in which the reference plane intersects the ellipsoid is called the fictitious equator. The angle is taken to be positive upwards from the reference plane.
longitude, fictitious 1. The dihedral angle between two planes perpendicular to a common plane of reference through the center of an ellipsoid, the one plane serving as a reference and the other containing the normal at the point whose longitude is desired. The angle is positive taken clockwise from the plane of reference. 2. The difference between the values assigned two lines representing, on a graticule, meridians on an ellipsoid; the one line is taken as reference and the other is the one representing the meridian through the point in question. 3. The arc, on a great circle denoted the fictitious equator, between two great circles passing through the poles of the fictitious equator, one of the great circles serving as a meridian of reference (fictitious prime meridian) and the other as a local meridian (fictitious meridian). A fictitious longitude may be called a grid longitude, oblique longitude or transverse longitude according as the fictitious equator is a line on a grid or is a great circle oblique or transverse to the actual equator.
Mean Observatory A fictitious observatory situated on the Greenwich Mean Astronomical Meridian. I.e., a fictitious, ideal observatory situated so that times determined by it are exactly the same as the times established by the Bureau International de l'Heure as the average of times determined at many real observatories.
meridian, fictitious The line on an ellipsoid, or the corresponding line of a graticule, in which a suitably defined plane perpendicular to the plane of the fictitious equator intersects the ellipsoid. If the chosen plane is also a reference plane, the resulting fictitious meridian is called the prime fictitious meridian.
orbit, intermediate 1. A fictitious orbit that a satellite moving in the field of a non-central force would follow if a central force were substituted for the real force at a given instant and the direction of motion were to be the same at that instant. SEE ALSO orbit, osculating. 2. Any fictitious orbit used as an intermediary and approximation in calculating an actual orbit.
parallel, fictitious A circle or line parallel to a fictitious equator and connecting all points having the same fictitious latitude. A fictitious parallel may be further specified as a transverse, oblique or grid parallel, depending on the type.
pole, fictitious One of the two points 90° from a fictitious equator. It may be called an oblique pole or a transverse pole, depending on the type of fictitious equator used.
radius (of the Earth), effective A fictitious value of the Earth's radius which, when used in a formula for the distance from a point to the geometric horizon, gives the same answer as would using the true value of the radius in a formula for the distance to the apparent horizon. If the Earth were spherical and without air, tangents drawn to the surface from a point above it would define a circle (the geometric horizon) outside of which no points on the sphere would be visible from the chosen point but all points inside it would be. If an atmosphere were added, points outside the circle would become visible because the line of sight would curve and extend to points beyond the geometric horizon and as far as a circle (the apparent horizon) of greater radius. The distance to the apparent horizon can be calculated using the same formula as is used for the distance to the geometric horizon if, in that formula, a larger value, the effective radius, is used for the radius of the Earth. The effective radius, for points of observation within the troposphere, is greater than the true radius and increases with wavelength of the radiation at which the observations are made. It is particularly useful in determining, without long calculation, whether two points a considerable distance apart will be intervisible or able to receive each others signals. For radio waves at ultra-high frequencies, the effective radius is about 4/3 the true radius.
rhumb line, fictitious A line making the same oblique angle with all fictitious meridians. It may be called a transverse rhumb-line, oblique rhumb line or grid rhumb-line, according to the type of fictitious meridian used.
Schreiber's method (of adjustment) A method of eliminating a particular unknown from a set of equations by adding to the set a fictitious observation-equation in which each coefficient is equal to the sum of all corresponding coefficients in the set multiplied by (‑1/n), where n is the total number of observed directions in that set. More generally, the normal equation of the variable is appended with negative weight. (This equation is sometimes called a Schreiber's equation.] The principle underlying the method is called Schreiber's rule. The method has lost most of its usefulness since calculating machines replaced computation by hand.
sun, dynamical mean A fictitious Sun which moves westward along the ecliptic at the average rate of the apparent (actual) Sun.
sun, fictitious mean 1. An imaginary body moving at such a constant rate along the celestial equator that its location is never more that 16m from the true Sun in hour angle and such that the rate approximates the average rate of the annual motion of the Sun. 2. The mathematical formula giving the motion of the fictitious mean sun as defined in (1.).
We should embrace the fiction in our science because understanding what we can measure and what we can not is a very important step to understanding the world around us scientifically.
In this blog we will post terms and themes of related terms and their definitions that come from the The Glossary of Mapping Sciences with commentary. In the hope that by discussing the meaning of words we come to deeper understanding and more meaningful usage.