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I'm trying to calculate moon's parallax in it's altitude depending on the day I need and I followed this formula by geoastro.de Basics of Positional Astronomy and Ephemerides

but I need to calculate it's distance first and I don't know how to calculate it.

So is there formula or resource can help me.

moon's parallax formula

horParal = 8.794 / (moonDistance / 149.59787E6);
p = arcsin[cos(altitude)*sin(horParal/3600)];

Notes: altitude = 36.1° & moonDistance is in meters.

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  • $\begingroup$ The average distance to the moon is 384.4 million metres $\endgroup$
    – James K
    Commented Jun 7 at 21:06
  • $\begingroup$ The distance between the Moon and Earth varies from day to another, so I need it's formula to calculate the distance depending on the day I need $\endgroup$
    – Ahmed Dyaa
    Commented Jun 7 at 21:13
  • $\begingroup$ The author gives a few references, the Meeus algorithm he refers to is available here: celestialprogramming.com/meeus-elp82.html $\endgroup$
    – Greg Miller
    Commented Jun 7 at 22:07

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As per wikipedia (source)

$$ \begin{alignat}{3} \frac{d}{\mathrm{km}} = 385000.5584 & \ -\ 20905.3550 \cdot \cos(G_M) \\ & \ - \ 3699.1109 \cdot \cos(2D - G_M) \\ & \ - \ 2955.9676 \cdot \cos(2D) \\ & \ - \ 569.9251 \cdot \cos(2G_M) \\ & \ \pm \ \dotsc \end{alignat} $$

where $G_M$ is the mean anomaly (more or less how far the moon has moved from perigee) and $D$ is the mean elongation (more or less how far it has moved from conjunction with the Sun at new moon). They can be calculated from

$$G_M = 134.963 411 38° + 13.064 992 953 630° · t$$

$$D = 297.850 204 20° + 12.190 749 117 502° · t$$

where $t$ is the time (in days) since January 1, 2000

The number of decimal places given in that quote is a little ridiculous, but I shall let you prune them as you please.

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  • $\begingroup$ I tried This equation and these are the results date: 1991/5/19 JD: 2448396.04166667 T: -0.0862137805156328 GM: 133.810028945057 D: 296.799193631263 d (distance): 392792.08838494 km which totaly wrong it supposed to equal 370614 km $\endgroup$
    – Ahmed Dyaa
    Commented Jun 9 at 13:02
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    $\begingroup$ Discuss it with wikipeida. Why is T=-0.086? what about "t"? $\endgroup$
    – James K
    Commented Jun 9 at 15:35
  • $\begingroup$ T=-0.086 means roughly 10pm on December 31st 1999, not 1991-05-19 $\endgroup$
    – James K
    Commented Jun 10 at 17:14
  • $\begingroup$ It's still not clear to me what you're asking. Will you have a way to find the moon's equatorial coordinates? There's no simple formula that's better than interpolating almanac values, or an online lookup. If you know those coordinates, your source would likely also give the distance to the moon. $\endgroup$
    – stretch
    Commented Jun 10 at 22:43

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