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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

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

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

Range of a projectile

In physics, assuming a flat Earth with a uniform gravity field, and no air resistance, a projectile launched with specific initial conditions will have a ... more

Orbital Eccentricity

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect ... more

True anomaly - circular orbit with zero inclination

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

True anomaly - elliptic orbits

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

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

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

True anomaly - circular orbit

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

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