Elliptic orbit and Specific orbital energy

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Difference between Elliptic orbit and Specific orbital energy

Elliptic orbit vs. Specific orbital energy

In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In the gravitational two-body problem, the specific orbital energy \epsilon\,\! (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy (\epsilon_p\,\!) and their total kinetic energy (\epsilon_k\,\!), divided by the reduced mass.

Apsis

An apsis (ἁψίς; plural apsides, Greek: ἁψῖδες) is an extreme point in the orbit of an object.

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Characteristic energy

In astrodynamics, the characteristic energy (C_3) is a measure of the excess specific energy over that required to just barely escape from a massive body.

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Gravitational two-body problem

←For further relevant mathematical developments see also Two-body problem, also Kepler orbit, and Kepler problem, and Equation of the center – Analytical expansions The gravitational two-body problem concerns the motion of two point particles that interact only with each other, due to gravity.

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Hyperbolic trajectory

In astrodynamics or celestial mechanics, a hyperbolic trajectory is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull.

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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 circle.

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Orbital speed

In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter or, if the object is much less massive than the largest body in the system, its speed relative to that largest body.

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Orbital state vectors

In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are cartesian vectors of position (\mathbf) and velocity (\mathbf) that together with their time (epoch) (t\) uniquely determine the trajectory of the orbiting body in space.

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Parabolic trajectory

In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1.

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Semi-major and semi-minor axes

In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter.

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Specific relative angular momentum

In celestial mechanics the specific relative angular momentum \vec plays a pivotal role in the analysis of the two-body problem.

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Standard gravitational parameter

In celestial mechanics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the body.

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Vis-viva equation

In astrodynamics, the vis-viva equation, also referred to as orbital-energy-invariance law, is one of the equations that model the motion of orbiting bodies.

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