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How could I determine the distance from the Earth to the moon by using the method of simultaneous parallax? I know the right ascension and declination as seen from two different points on earth. I also know the right ascension and declination of a distant star.

I have location 1 in Buenos Aires and location 2 in Shanghai, with both observing the moon at the same time. The moon has a different right ascension and declination in each location.

Knowing the right ascension and declination of the star Sirius, how might I calculate the distance to the moon? None of the equations I have tried gives me the correct answer.

  • Moon Right Ascension from Buenos Aires: 0.0363099165337 Radians
  • Moon Declination from Buenos Aires: 0.220376340654 Radians
  • Moon Right ascension from Shanghai: 0.0366537040004 Radians
  • Moon Declination from Shanghai: 0.197477937143 Radians
  • Sirius Right Ascension (same from the entire globe): 1.76780036611 Radians
  • Sirius Declination (same from the entire globe): -0.291750983093 Radians
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    $\begingroup$ You need the precise time of the observation also. The location of sirius isn't needed. The basic idea is: compute the geocentric xyz coordinates of the observers; rotate those coordinates based on the sidereal time of the observations; represent the RA/Dec from each site as lines, and compute the intersection of the two lines. $\endgroup$ Feb 2, 2023 at 2:35
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    $\begingroup$ Welcome to Astronomy SE! "None of the equations I have tried gives me the correct answer." Please show or at least link to all of the equations you have tried. It is possible you have chosen the wrong ones, or the right ones but used them incorrectly. The more information about what you have tried so far, the better an answer can address your situation. Thanks! $\endgroup$
    – uhoh
    Feb 3, 2023 at 21:52
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    $\begingroup$ i calculated the angular separation using that from skythisweek.info/angsep.pdf $\endgroup$ Feb 4, 2023 at 23:55
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    $\begingroup$ You can get data for Solar System bodies (including some spacecraft) from JPL Horizons $\endgroup$
    – PM 2Ring
    Feb 4, 2023 at 23:59
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    $\begingroup$ (Edit) I calculated the angular separation from the moon to the star from both locations using the equation from skythisweek.info/angsep.pdf I then subtracted one from the other to get the parallax angle. As shown in mccarthyobservatory.org/pdfs/pm020102.pdf Page 4. I then used equation Distance to moon = (Distance between two points/ (2*sin(parallax angle/2)) $\endgroup$ Feb 5, 2023 at 0:04

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