The circle of equal altitude, also called circle of position (CoP), is defined as the locus of points on Earth on which an observer sees a celestial object...

angle of the body observed. First calculate the altitude of the celestial body H c {\displaystyle Hc} using the equation of circle of equal altitude: sin...

the Sumner line or circle of equal altitude. Thomas Hubbard Sumner was born in Boston, Massachusetts, on March 20, 1807, the son of Thomas Waldron Sumner...

and error-free calculation of navigation problems. Celestial navigation: Sight reduction, circle of equal altitude, Line Of Position, Fix... Positional...

line of position (LOP) is a small segment of the circle of equal altitude, and is represented by a straight line perpendicular to the azimuth of the celestial...

system. The midpoints of the three sides and the feet of the three altitudes all lie on a single circle, the triangle's nine-point circle. The remaining three...

history of navigation. In 1837, the American Captain Thomas Hubbard Sumner discovered the concept of celestial position lines—the circle of equal altitude—as...

approximately equal to 3.14159. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular...

triangle: one-half of the product of an altitude's length and its base's length equals the triangle's area. Thus, the longest altitude is perpendicular...

almacantara) is a circle on the celestial sphere parallel to the horizon. Two stars that lie on the same almucantar have the same altitude. The term was introduced...

Lines (or circles) of position can be derived from a variety of sources: celestial observation (a short segment of the circle of equal altitude, but generally...

who discovered the principles of celestial navigation by circle of equal altitude. These ships are crewed by a small crew of civilian mariners, supporting...

number. A circle with r = 0 {\displaystyle r=0} is a degenerate case consisting of a single point. Sector: a region bounded by two radii of equal length...

pole Circle of equal altitude Ephemeris Geodetic astronomy GNSS Satellite navigation History of longitude List of proper names of stars List of selected...

of the tropical circles is equal to the Earth's axial tilt. By definition, the positions of the Tropic of Cancer, Tropic of Capricorn, Arctic Circle and...

length of one median is equal to the circumradius. The shortest altitude (the one from the vertex with the biggest angle) is the geometric mean of the line...

that the geometric mean of the two segments equals the altitude. Expressed as a mathematical formula, if h denotes the altitude in a right triangle and...

circumpolar circle whose size is determined by the observer's latitude. Specifically, the angular measure of the radius of this circle equals the observer's...

feet of the altitudes), and the only triangle whose Steiner inellipse is a circle (specifically, the incircle). The triangle of the largest area of all...

inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle...

orbit with an altitude of 35,786 km (22,236 mi). The period of the orbit equals one sidereal day, coinciding with the rotation period of the Earth. The...

real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in...

if the midpoints of the sides and the feet of the four altitudes are eight concyclic points, on what is called the eight-point circle. More generally,...

infinitesimal circle as in Tissot's indicatrix, some visual methods project finite shapes that span a part of the map. For example, a small circle of fixed radius...

to the maximum distance of 20,000 km (12,427 mi) the antipode point smears into a large circle. This is shown in the example of two maps centered about...

combination of mass, speed and altitude, a fighter flying at low altitude but a high speed may have the same total energy as a fighter of equal mass, but...

(intersection of the altitudes) of the medial triangle coincides with the circumcenter (center of the circle through the vertices) of the original triangle...

elliptic orbit where the perigee is at the altitude of a low Earth orbit (LEO) and the apogee at the altitude of a geostationary orbit. Hohmann transfer...

sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length...

inclination of the ecliptic, and it is conventionally denoted by i. The latitude of the tropical circles is equal to i and the latitude of the polar circles is...