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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

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

Radau parameter - related to Darwin / Radau equation

In astrophysics, the Darwin / Radau equation gives an approximate relation between the moment of inertia factor of a planetary body and its rotational ... 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

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

Mean Orbital Speed

The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around ... more

Eccentricity of the hyperbola

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 set. A hyperbola ... more

Glide Ratio

Gliding flight is heavier-than-air flight without the use of thrust; the term volplaning also refers to this mode of flight in animals. It is employed by ... more

Area Moment of Inertia - Filled Ellipse

The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a ... more

Circumference of an Ellipse - h component

The quantity h = (a-b)2/(a+b)2 is often used in elliptical circumference calculations e.g in Ramanujan formula for the Circumference of an Ellipse.

... more

Taylor Number

In fluid dynamics, the Taylor number (Ta) is a dimensionless quantity that characterizes the importance of centrifugal “forces” or so-called ... 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

Elliptic cylinder (Volume)

An elliptic cylinder has ellipse bases.The volume of an elliptic cylinder can be calculated by the half- axes of the ellipse base and the height of the ... more

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 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

Gearing reduction ratio

Harmonic Drive is the brand name of strain wave gear trademarked by the Harmonic Drive company, and invented in 1957 by C.W. Musser.

It is very ... more

Torsion constant (Ellipse -cross-sectional shape)

In solid mechanics, torsion is the twisting of an object due to an applied torque. The torsion constant is a geometrical property of a bar’s cross-section ... more

Kepler's Third Law - with Radial Acceleration

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

1.The orbit of a ... more

Kepler's Third Law - modern formulation

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

1.The orbit of a ... more

Magic hypercube

In mathematics, a magic hypercube is the k-dimensional generalization of magic squares, magic cubes and magic tesseracts; that is, a number of integers ... more

Semi-Minor Axis - Hyperbola

n a hyperbola, a conjugate axis or minor axis of length 2b, corresponding to the minor axis of an ellipse, can be drawn perpendicular to the transverse ... 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

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

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

Kepler's First Law

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

1.The orbit of a ... more

Characteristic Length

In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a ... more

Bending Stress

In Applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied ... more

Moment of inertia of a solid cuboid ( Axis of rotation at the height )

Moment of inertia is the mass property of a rigid body that defines the torque needed for a desired angular acceleration about an axis of rotation. Moment ... more

Kepler's Third Law

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

1.The orbit of a ... more

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