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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.
Magnetic dip causes the compass to dip upward or downward depending on the latitude. Illustration of magnetic dip from Norman's book, The Newe Attractive Magnetic dip, dip angle, or magnetic inclination is the angle made with the horizontal by Earth's magnetic field lines.
An inclination of 63.4° is often called a critical inclination, when describing artificial satellites orbiting the Earth, because they have zero apogee drift. [3] An inclination of exactly 90° is a polar orbit, in which the spacecraft passes over the poles of the planet. An inclination greater than 90° and less than 180° is a retrograde orbit.
The value of a solar beta angle for a satellite in Earth orbit can be found using the equation = [ + ()] where is the ecliptic true solar longitude, is the right ascension of ascending node (RAAN), is the orbit's inclination, and is the obliquity of the ecliptic (approximately 23.45 degrees for Earth at present).
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. [1]They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in three dimensional linear algebra.
The angles for Earth, Uranus, and Venus are approximately 23°, 97°, and 177° respectively. In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbital plane ...
Orbits are conic sections, so the formula for the distance of a body for a given angle corresponds to the formula for that curve in polar coordinates, which is: r = p 1 + e cos θ {\displaystyle r={\frac {p}{1+e\cos \theta }}}
It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the sun’s rays and a horizontal plane. [1] [2] At solar noon, the zenith angle is at a minimum and is equal to latitude minus solar declination angle. This is the basis by which ancient mariners navigated the oceans. [3]