I originally went to math.stackexchange.com and they suggested I try here as well.

I'm trying to figure out how to calculate times of moonrise and moonset for a given position on the earth on a particular date. I'm using Vallado's Fundamentals of Astrodynamics and Applications because there is an example in the book that lays out a simplified process. I'm stuck at the point where I'm trying to calculate Longitude of the ecliptic for the Moon. The formula is below where T = -0.013634497.

λEcliptic = 218.32° + 481,267.8813T + 6.29Sin(134.9 + 477,198.85T) - 1.27Sin(259.2 - 413,335.38T) + 0.66Sin(235.7 + 890,534.23T) + 0.21Sin(269.9 + 954,397.70T) - 0.19Sin(357.5 + 35,999.05T) - 0.11Sin(186.6 + 966,404.05T)

The expected answer is -0.8412457°. However, I'm unable to figure out how to get this answer. My calculations are below:

1) 218.32° + 481,267.8813T = -6343.525

2) 6.29Sin(134.9 + 477,198.85T) = 5.963779

3) -1.27Sin(259.2 - 413,335.38T) = -0.900843

4) 0.66Sin(235.7 + 890,534.23T) = -0.292285

5) 0.21Sin(269.9 + 954,397.70T) = -0.126871

6) -0.19Sin(357.5 + 35,999.05T) = 0.138211

7) -0.11Sin(186.6 + 966,404.05T) = 0.054722

Simply adding or subtracting gets me -6338.688731. How can I get the value -0.8412457° from this. My trigonometry is rusty and I'm not sure how to get the right answer. Any help would be greatly appreciated. Thanks.

  • $\begingroup$ It would help a lot if you have more context. As it is now, it is hard to figure out what you are trying to accomplish. $\endgroup$ Apr 2, 2016 at 11:31
  • $\begingroup$ I'm not familar with the term "longitude of the ecliptic". Do you mean the longitude of the ascending node, (or perigee?), in ecliptic coordinates? $\endgroup$
    – James K
    Apr 2, 2016 at 17:14
  • $\begingroup$ I'm using the term that came straight from the textbook. I'm assuming that Longitude of the Ecliptic refers to the time when the moon is passing the ecliptic but I don't know if it refers to the ascending node or the plane of the ecliptic for the sun. I would think it's the former but this is the term the book uses. Really all I'm trying to figure out is how to arrive at the -0.8412457° result mathematically. From the comments on math.stackexchange.com the answers I have above are correct but they imply that there is also some way to arrive at the desired term from the textbook. $\endgroup$
    – ZachC
    Apr 2, 2016 at 21:53

1 Answer 1


There's a mistake in the book (see page 280 on google books): the values for $\lambda_{ecl}$ and $\phi_{ecl}$ should be swapped. Your result is correct: $$ -6338.688^\circ\text{ mod } (360^\circ) = -218.688^\circ, $$ which is the value that is erroneously listed under $\phi_{ecl}$.

  • 1
    $\begingroup$ Okay, thank you. That clarifies things greatly. $\endgroup$
    – ZachC
    Apr 5, 2016 at 11:03

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