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4 results

  • 3 - 1pN Gravitoelectric Effects: Mass Monopole(s)

  • Lorenzo Iorio, Ministero dell’ Istruzione e del Merito, Bari, Italy
  • Book:
    General Post-Newtonian Orbital Effects
    Published online:
    28 November 2024
    Print publication:
    05 December 2024, pp 54-72

  • Summary

    The impact of the 1pN gravitoelectric mass monopole acceleration, both in the test particle and in the two-body system of finite, comparable masses cases, is calculated for different types of observation-related quantities (Keplerian orbital elements, anomalistic, draconitic, and sidereal orbital periods, two-body range and range rate, radial velocity curve and radial velocity semiamplitude of spectroscopic binaries, astrometric angles RA and dec., times of arrival of binary pulsars, characteristic timescales of transiting exoplanets). The results are applied to a test particle orbiting a primary, a Sun–Jupiter exoplanet system, and to a S star in Sgr A*.

  • 5 - 1pN Gravitomagnetic Effects: Spin Dipole(s)

  • Lorenzo Iorio, Ministero dell’ Istruzione e del Merito, Bari, Italy
  • Book:
    General Post-Newtonian Orbital Effects
    Published online:
    28 November 2024
    Print publication:
    05 December 2024, pp 84-118

  • Summary

    The impact of the 1pN gravitomagnetic Lense–Thirring acceleration, generalized also to the case of two massive spinning bodies of comparable masses and angular momenta, is calculated for different types of observation-related quantities (Keplerian orbital elements, anomalistic, draconitic, and sidereal orbital periods, two-body range and range rate, radial velocity curve and radial velocity semiamplitude of spectroscopic binaries, astrometric angles RA and dec., times of arrival of binary pulsars, characteristic timescales of transiting exoplanets, and their sky-projected spin-orbit angle). The results are applied to a test particle orbiting a primary, a Sun–Jupiter exoplanet system, and an S star in Sgr A*.

  • 7 - Newtonian Effects: Mass Quadrupole(s)

  • Lorenzo Iorio, Ministero dell’ Istruzione e del Merito, Bari, Italy
  • Book:
    General Post-Newtonian Orbital Effects
    Published online:
    28 November 2024
    Print publication:
    05 December 2024, pp 123-145

  • Summary

    The impact of the Newtonian quadrupolar acceleration, generalized also to the case of two bodies of comparable amsses and quadrpole moments, is calculated for is calculated for different types of observation-related quantities (Keplerian orbital elements, anomalistic, draconitic and sidereal orbital periods, two-body range and range rate, radial velocity curve and radial velocity semiamplitude of spectroscopic binaries, astrometric angles RA and dec., times of arrival of binary pulsars, characteristic timescales of transiting exoplanets and their sky-projected spin-orbit angle). The results are applied to a test particle orbiting a primary, a Sun-Jupiter exoplanet system, and to a S star in Sgr A*.

  • Appendix - Mathematical details

  • Todd Timberlake, Berry College, Georgia, Paul Wallace
  • Book:
    Finding our Place in the Solar System
    Published online:
    18 March 2019
    Print publication:
    28 March 2019, pp 307-336

  • Summary

    This appendix provides mathematical details to supplement the ideas presented in the main text. Topic covered include: angular measurement, apparent diameter, trigonometry, finding the Sun’s altitude from the length of a shadow, determining the relative distances of the Sun and Moon, and finding the distance to an astronomical object using parallax measurements. In addition, this appendix shows how to calculate the sizes of epicycles in the Ptolemaic theory and the periods and sizes of planetary orbits in the Copernican theory. Mathematical details are also provided for Kepler’s Laws of Planetary Motion, Galileo’s measurement of mountains on the Moon, Galileo’s studies of falling bodies and projectiles, Newton’s universal gravitational force, and Bradley’s theory of the aberration of starlight.