<p>There's a mistake in the book (see page 280 on <a href="https://books.google.be/books/about/Fundamentals_of_Astrodynamics_and_Applic.html?id=PJLlWzMBKjkC&amp;redir_esc=y" rel="nofollow">google books</a>): 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 $\phi_{ecl}$.</p>

CC BY-SA 3.0
2016-04-04T02:25:43.263Z
2016-04-04T02:25:43.263Z
Pulsar
<p>I originally went to math.stackexchange.com and they suggested I try here as well. </p>

<p>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.</p>

<blockquote>
  <p>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)</p>
</blockquote>

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

<blockquote>
  <p>1) 218.32° + 481,267.8813T = -6343.525</p>
  
  <p>2) 6.29Sin(134.9 + 477,198.85T) = 5.963779</p>
  
  <p>3) -1.27Sin(259.2 - 413,335.38T) = -0.900843</p>
  
  <p>4) 0.66Sin(235.7 + 890,534.23T) = -0.292285</p>
  
  <p>5) 0.21Sin(269.9 + 954,397.70T) = -0.126871</p>
  
  <p>6) -0.19Sin(357.5 + 35,999.05T) = 0.138211</p>
  
  <p>7) -0.11Sin(186.6 + 966,404.05T) = 0.054722</p>
</blockquote>

<p>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.</p>

CC BY-SA 3.0
2016-04-02T11:31:48.867Z
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.
SE - stop firing the good guys
CC BY-SA 3.0
2016-04-02T17:14:16.327Z
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?
James K
CC BY-SA 3.0
2016-04-02T21:53:52.393Z
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.
ZachC
<orbit><the-moon><rotation><ecliptic>
Longitude of the Ecliptic
ZachC
# Longitude of the Ecliptic

(Asked by: username_0 on 2016-04-02)

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.

**Tags:** orbit, the-moon, rotation, ecliptic

> **Comments:**
> **username_1**: 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.  
> **username_2**: 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?  
> **username_0**: 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.  

---

## 1 answers

### Answer by username_3 on 2016-04-04. Score: 1 | Accepted answer

There's a mistake in the book (see page 280 on [google books](https://books.google.be/books/about/Fundamentals_of_Astrodynamics_and_Applic.html?id=PJLlWzMBKjkC&redir_esc=y)): 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 $\phi\_{ecl}$.


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