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Ellipsoidal Coordinates ("x" cartesian coordinate)

Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system that generalizes the two-dimensional elliptic coordinate system. Unlike most ... more

Mean angular motion - function of gravitational parameter

In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular ... 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

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

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

Barycenter (Two-body problem)

barycentre; from the Greek βαρύ-ς heavy + κέντρ-ον centre) is the center of mass of two or more bodies that are orbiting each other, or the point around ... more

Hyperboloid of one sheet equation

In mathematics, a hyperboloid is a quadric – a type of surface in three dimensions – . A hyperboloid of revolution of one sheet can be obtained by ... more

Law of cotangents (in term of tangents)

In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. ... more

Arbitrary-amplitude period of pendulum

A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. A so-called “simple ... more

Sortino ratio

The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes ... more

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