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16933 results

Page 6 of 847

  • 4 - Tides

  • Barbara Ryden, The Ohio State University
  • Book:
    Celestial and Stellar Dynamics
    Published online:
    16 January 2025
    Print publication:
    30 January 2025, pp 63-80

  • Summary

    A Frenchman who arrives in London, will find Philosophy, like every Thing else, very much chang’d there… In France, ’tis the Pressure of the Moon that causes the Tides; but in England ’tis the Sea that gravitates toward the Moon. Letters Concerning the English Nation [1733] Letter XIV: On Descartes and Sir Isaac Newton, Voltaire (1694–1778)

  • 7 - Orbits

  • Barbara Ryden, The Ohio State University
  • Book:
    Celestial and Stellar Dynamics
    Published online:
    16 January 2025
    Print publication:
    30 January 2025, pp 138-156

  • Summary

    When night comes I stand on the steps and listen; the stars cluster in the garden and I stand, out in the darkness. Edith Södergran (1892–1923) “Stjärnorna [The Stars]” [1916] (tr. David Barrett)

  • 5 - Exoplanetary Systems

  • Barbara Ryden, The Ohio State University
  • Book:
    Celestial and Stellar Dynamics
    Published online:
    16 January 2025
    Print publication:
    30 January 2025, pp 81-102

  • Summary

    The revival of the heliocentric model by Copernicus in the sixteenth century led to speculation about planets orbiting other stars. In a heliocentric model, stars must show annual parallax as the Earth moves around the Sun.

  • 6 - Many-Body Systems

  • Barbara Ryden, The Ohio State University
  • Book:
    Celestial and Stellar Dynamics
    Published online:
    16 January 2025
    Print publication:
    30 January 2025, pp 103-137

  • Summary

    The techniques of celestial dynamics are useful within the solar system and other planetary systems. However, techniques that are useful in a system containing a few mutually gravitating objects are not as useful in a system containing a hundred thousand million objects.

  • 1 - Newtonian Dynamics

  • Barbara Ryden, The Ohio State University
  • Book:
    Celestial and Stellar Dynamics
    Published online:
    16 January 2025
    Print publication:
    30 January 2025, pp 1-16

  • Summary

    The noun “dynamics” entered the English language in the eighteenth century, when natural philosophers, following the lead of Isaac Newton, began thinking of motion in terms of applied forces and the resulting accelerations. In 1788, the New Royal Encyclopaedia contained the definition, “Dynamics is the science of moving powers; more particularly of the motion of bodies that mutually act on one another.” This is still a useful definition. For the purposes of this book, we can define dynamics as the study of objects that move while interacting through mutual forces.

  • 3 - Resonances and Chaos

  • Barbara Ryden, The Ohio State University
  • Book:
    Celestial and Stellar Dynamics
    Published online:
    16 January 2025
    Print publication:
    30 January 2025, pp 41-62

  • Summary

    A gravitationally bound two-body system (if the two bodies are spheres of constant mass) shows simple periodic motion. We have seen that a three-body system, even if we install restrictions for computational simplicity, can show a rich variety of behaviors. Tadpole orbits, horseshoe orbits, and ZLK oscillations are just a sampling of what can happen.

Celestial and Stellar Dynamics
  • Barbara Ryden
  • Published online:
    16 January 2025
    Print publication:
    30 January 2025
  • Although the field of celestial dynamics – the application of Newtonian dynamics to systems with a relatively small number of celestial bodies – is centuries old, it has been reinvigorated by the discovery of thousands of exoplanetary systems orbiting other stars. This textbook uses the properties of planetary systems, including own Solar System, to illustrate the rich variety of behavior permitted by Newton's law of gravity. The textbook then expands its view to examine stellar dynamics – the study of systems containing a very large number of stars or other celestial bodies. The different techniques used for celestial dynamics and stellar dynamics are compared and contrasted. However, throughout the text, emphasis is placed on the underlying physics that applies on scales as small as the Earth–Moon system and as large as a cluster of galaxies. It is ideal for a 1-semester astrophysical dynamics course for upper-level undergraduates and starting graduate students.

Page 6 of 847