How can I calculate moon phase and height?

  • How could I know what phase the moon is in when it's high in the sky during sunrise?

    How could I tell in general what its height in the sky will be at any given time?

    Are you looking for a program to do this, or are you looking for an equation?

    i want to understand the movement. i have stellarium for example but i didn't quite got it from it...

    the sun is high in the sky at the summer & low at winter, right? the same with the moon... i just don't understand what determinate its height.

    Might try the US Naval Observatory website: IIRC, they used to have a fairly detailed account of how phase is calculated, but the site's been rearranged and I 'm not finding that today. The USNO site's internal search engine was down when I tried it.

    How accurately do you need this? There are tools in several computer languages to do this. A simple approximation is to note there are 29.530589 days between full moons. More accurate more difficult are the Epact calcuations: The "official" software to compute moon phase is at:

  • The first question is quite simple if you imagine how the Earth is looked from above. To help you with that I've added a little drawing below.

    Probably you know that the Sun rises on the East and sets on the West. Imagine now how the sun illuminates the Earth: Europe is in the afternoon when the East cost of US is waking up. Imaging this you can see that the Earth is turning anti-clockwise if looked from the north.

    Now, imagine you are somewhere in US (so we can use the drawing from below), the sun is rising (on the East) and the moon is above you (something close to the zenith). This means the moon the configuration of the Sun-Earth-Moon system is something like in the drawing. As you can see in the drawing I've kept in white what's illuminated from the Sun. In Spanish we use to say that the moon is a bit of a liar, this comes because it shows a C shape when is waxing (decreciente) and a D shape when is crescent (creciente), so just the opposite letter of its action (don't know if there's a similar expression in other languages, and notice that the moon is not a liar for the Spanish speakers in the Souther hemisphere). So, coming back to the drawing, you can imagine that from the red-star position you will see the moon with a C shape, therefore is waxing... which means in 7 days or so would be new moon so is going to move between the Sun and Earth.. and we can see how the moon rotates around the Earth in the same direction than the earth rotates around itself.

    Earth Moon Sun system - not in scale

    I don't really understand your second question, so I cannot help much with that. But, if you mean to get a roughly calculation as on where the moon is at a certain time knowing its phase you can calculate it by knowing that the Earth spins 15°/hour and that the moon positions for each phase. Therefore, new moon the moon will be closer to the zenith at noon (local solar time), 6am for waxing moon, 12 am for full moon and 6pm for crescent moon. However, this is just a roughly approximation as the moon movement happens on a plane which is 5.14° inclined from the ecliptic plane which corresponds to positions between 18.29° and 28.58° latitude on Earth. So the same phase moon can be at different heights at different times of the year at the same hour.

  • This really isn't as simple as you may think, the moon does not orbit the Earth at a constant speed just like how the Earth doesn't orbit the sun at a constant speed. The phases repeat an average of every 29.53 days. The amount of time between the new moon can very.

  • I highly recommend picking up a copy of Astronomical Algorithms by Jean Meeus. Chapter 49 covers the calculation methods that are used by many (if not most) online calculators.

    The somewhat dated page at has a link to "moon.js", the javascript that does its lunar calculations. The calculations you need are in that file.

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Content dated before 7/24/2021 11:53 AM

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