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In astronomy, the altitude in the horizontal coordinate system and the zenith angle are complementary angles, with the horizon perpendicular to the zenith. The astronomical meridian is also determined by the zenith, and is defined as a circle on the celestial sphere that passes through the zenith, nadir, and the celestial poles .
The process of drawing the altitude from a vertex to the foot is known as dropping the altitude at that vertex. It is a special case of orthogonal projection . Altitudes can be used in the computation of the area of a triangle : one-half of the product of an altitude's length and its base's length (symbol b ) equals the triangle's area: A = h b /2.
Azimuth is measured eastward from the north point (sometimes from the south point) of the horizon; altitude is the angle above the horizon. The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles of a spherical coordinate system: altitude and azimuth.
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
Even with these restrictions, if the polar angle (inclination) is 0° or 180°—elevation is −90° or +90°—then the azimuth angle is arbitrary; and if r is zero, both azimuth and polar angles are arbitrary. To define the coordinates as unique, the user can assert the convention that (in these cases) the arbitrary coordinates are set to zero.
The rate of decrease of temperature with elevation is known as the adiabatic lapse rate, which is approximately 9.8 °C per kilometer (or 5.4 °F [3.0 °C] per 1000 feet) of altitude. [ 12 ] The presence of water in the atmosphere complicates the process of convection.
ICAO further defines: elevation: "the vertical distance of a point or a level, on or affixed to the surface of the earth, measured from mean sea level." [2] I.e., elevation would be the altitude of the ground or a building.
where the expression between bars on the right-hand side is the magnitude of the cross product of the partial derivatives of x(s, t), and is known as the surface element. Given a vector field v on S , that is a function that assigns to each x in S a vector v ( x ), the surface integral can be defined component-wise according to the definition ...