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Related Concept Videos

Eccentricity of an Ellipse01:27

Eccentricity of an Ellipse

An ellipse is a fundamental conic section defined by the constant sum of distances from any point on its curve to two fixed points, known as the foci. This geometric property can be physically demonstrated using a pencil, string, and two pins. By anchoring the string at both ends and maintaining it taut with a pencil, one can trace the outline of an ellipse.The shape and extent of the ellipse are determined by its eccentricity, e, defined as the ratio of the distance between the center and a...
Ellipses01:30

Ellipses

An ellipse is formed when a right circular cone is intersected by an inclined plane that does not cut through its base. This intersection yields a closed, symmetric curve characterized by distinctive geometric properties. Most notably, an ellipse is defined as the collection of all points in a plane for which the combined distances to two fixed points—called the foci—remain constant.The ellipse features two principal axes: the major and the minor axes. The major axis is the longest diameter,...
Kepler's First Law of Planetary Motion01:10

Kepler's First Law of Planetary Motion

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. He formulated his first two laws based on the observations of his forebears, Nikolaus Copernicus and Tycho Brahe.
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Dynamics of Circular Motion01:30

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An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed acceleration is called centripetal acceleration. This acceleration acts along the radius of the curved path (thus is also referred to as radial acceleration).
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Kepler's Second Law of Planetary Motion01:29

Kepler's Second Law of Planetary Motion

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. His first law states that all planets orbit the Sun in an elliptical orbit, with the Sun at one of the ellipse's foci. Therefore, the distance of a planet from the Sun varies throughout its revolution around the Sun.
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Dynamics Of Circular Motion: Applications01:17

Dynamics Of Circular Motion: Applications

Suppose a car moves on flat ground and turns to the left. The centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. For this, a minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway. Let's now consider banked curves, where the slope of the road helps in negotiating the curve. The greater the angle of the curve, the faster one can take the curve. It is common for race tracks for...

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Related Experiment Video

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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Dynamics of elliptical galaxies.

D Merritt

    Science (New York, N.Y.)
    |March 26, 1993
    PubMed
    Summary

    Elliptical galaxies are now understood to be triaxial, not flattened, due to slow rotation. This triaxial shape is stable, supported by conserved quantities in galactic dynamics.

    Area of Science:

    • Astronomy and Astrophysics
    • Galactic Dynamics
    • Galaxy Formation

    Background:

    • Historically, elliptical galaxies were modeled as rotationally flattened systems, akin to stars.
    • Newer findings reveal slow rotation in elliptical galaxies, challenging previous structural and dynamic assumptions.
    • This discrepancy necessitates a revised understanding of their internal mechanics.

    Purpose of the Study:

    • To re-evaluate the structural and dynamic models of elliptical galaxies.
    • To explain the observed slow rotation rates in elliptical galaxies.
    • To investigate the stability and formation mechanisms of these galactic systems.

    Main Methods:

    • Theoretical modeling of self-consistent triaxial equilibria.
    • Analysis of conserved quantities (integrals of motion) in non-rotationally symmetric potentials.

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  • Review of observational evidence for galaxy shapes and central mass concentrations.
  • Main Results:

    • Elliptical galaxies are characterized by fully triaxial shapes, not flattened structures.
    • Self-consistent triaxial equilibria are long-lived, supported by integrals of motion.
    • Instabilities in some equilibria may explain the limited axis ratios (≤3:1) observed in elliptical galaxies.
    • Evidence suggests central mass concentrations, potentially massive black holes, exist in some elliptical galaxies.
    • Recent observations indicate elliptical galaxy formation via mergers of spiral galaxies.

    Conclusions:

    • The triaxial model provides a more accurate representation of elliptical galaxy dynamics.
    • Galactic potential symmetries and conserved quantities are crucial for stable triaxial equilibria.
    • Galaxy mergers are a significant pathway for the formation of elliptical galaxies.