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Oblate spheroid eccentricity (c<a)

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... more

Prolate spheroid equation (c>a)

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... more

Spheroid Volume

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... more

Oblate spheroid equation(c<a)

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... more

Volumes of the maximum inscribed box of an elipsoid

An ellipsoid is a closed quadric surface that is a three dimensional analogue of an ellipse.a, b, c.are called the semi-principal axes.They correspond to ... more

Volume of the minimum circumscribed box of an elipsoid

An ellipsoid is a closed quadric surface that is a three dimensional analogue of an ellipse.a, b, c.are called the semi-principal axes.They correspond to ... more

Volume of an ellipsoid

An ellipsoid is a closed quadric surface that is a three dimensional analogue of an ellipse.a, b, c.are called the semi-principal axes.They correspond to ... more

Conic section (polar system and one focus on the pole and the other somewhere on the 0° ray )

conic section (or just conic) is a curve obtained as the intersection of a cone (more precisely, a right circular conical surface) with a plane. A conic ... more

Semi-Major Axis - Ellipse

In geometry, the major axis of an ellipse is the longest diameter: a line (line segment) that runs through the center and both foci, with ends at the ... more

Kepler's equation - y coordinate

In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.

It was first ... more

Nodal Precession

Nodal precession is the precession of an orbital plane around the rotation axis of an astronomical body such as Earth. This precession is due to the ... more

Semi-Minor Axis - Ellipse

In geometry, the semi-minor axis (also semiminor axis) is a line segment associated with most conic sections (that is, with ellipses and hyperbolas) that ... more

Geocentric radius of the Earth

Geodetic latitude is the angle between the normal and the equatorial plane. The distance from the Earth’s center to a point on the spheroid surface ... more

Radius from true anomaly

In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between ... more

Eccentricity e of a cylindric section

Eccentricity e of the cylindric section and semi-major axis of the cylindric section depend on the radius of the cylinder and the angle between the secant ... more

Apsis - Periapsis maximum speed

An apsis, plural apsidesis a point of greatest or least distance of a body in an elliptic orbit about a larger body. For a body orbiting the Sun the ... more

Apsis - Apoapsis minimum speed

An apsis, plural apsidesis a point of greatest or least distance of a body in an elliptic orbit about a larger body. For a body orbiting the Sun the ... more

Apsis - Periapsis minimum distance

An apsis, plural apsidesis a point of greatest or least distance of a body in an elliptic orbit about a larger body. For a body orbiting the Sun the ... more

Apsis - Apoapsis maximum distance

An apsis, plural apsidesis a point of greatest or least distance of a body in an elliptic orbit about a larger body. For a body orbiting the Sun the ... more

Ellipse Circumference (Ramanujan formula)

Ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then ... more

Near branch of a hyperbola in polar coordinates with respect to a focal point

In mathematics, a hyperbola is a type of smooth curve, lying in a plane, defined by its geometric properties or by equations for which it is the solution ... more

Heliocentric distance

In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

1- The orbit of ... more

Kepler's equation - X coordinate

In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.

It was first ... more

Apsidal precession

In celestial mechanics, apsidal precession is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical ... more

Flattening - 1st variant

Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. ... more

Orbital Period - Ellipse

In astrodynamics or celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity less than 1; this includes the special case of a circular ... more

Clairaut's theorem

Clairaut’s theorem is a general mathematical law applying to spheroids of revolution. The formula can be used to relate the gravity at any point on ... more

Mean anomaly - function of gravitational parameter

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. ... more

Free-fall time (radial trajectory of an ellipse with an eccentricity of 1 and semi-major axis R/2)

The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to ... more

Circumference of an Ellipse - Ramanujan, second approximation

An ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and ... more

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