Sun and moon rise/set project

Javascript: Moon and Sun rise and set

Sun, Moon rise and set times and times for twilight for any latitude. See further down this page for the method being used. Dates don't display properly in Safari 1.2 - investigating!

Year : Answers believed to be useable for 50 years either side of 2000
Month : No error checking on correct months, days and leap years yet.
Day :
Longitude : Decimal degrees west longitudes must be negative
Time Zone : Decimal hours west of or 'behind' Greenwich negative
Latitude : Decimal degrees south negative
Number of days : How many lines in the table? (keep below about 100 days on Mozilla browsers)
Click to run : : Use reset to clear table to calculate for a new location
Results :
Copy and paste!


This page contains an implementation of the Montenbruck and Pfleger sunrise / moonrise / twilight algorithm in JavaScript. The algorithm is described in detail lower down the page and should work for all latitudes even within the (ant) arctic circles. There will be a 'fuzzy zone' at around latitude 67.43 as a result of using approximate Sun postion routines - and a similar zone around the 'lunar arctic circle' - but real rise and set times depend strongly on your local horizon anyway. Treat any 'days' or 'nights' shorter than about 20 minutes with caution.

View the source of this page to see the Javascript code. Save this page to your computer to run the code offline - you don't need to visit this Web address to be able to use the page! This page has been tested on Netscape 4.7x, Netscape 6.2, MS Internet Explorer 6 and Opera 7. The dates don't print properly in Safari - the function caldat(), the loop or the cast to string method I'm using must be causing trouble for Safari.


This page describes an algorithm that will enable you to calculate the time of Moon rise and set and Sun rise and set, as well as the twilight times, for any latitude on the Earth's surface. The algorithm presented here will warn you if the Moon or Sun remains above or below the horizon all day (a definite possibility above latitudes of 66.5 degrees North), or if the object does not rise or set within the day chosen (the Moon will exhibit this behaviour on one day in each lunar cycle). The algorithm is taken from Montenbruck and Pfleger's Astronomy on the Personal Computer second English edition, section 3.8.

If you just want the results for your observing location, then I recommend the Web page based programs provided by the US Naval Observatory. One of these programs will give you a compact yearly calendar style printout of rise and set times at a given location on a single sheet of paper. I use a set of printouts in my own observation planning - its easier than switching on the computer!

In the implementation of the algorithm on this page, I have used approximate routines to calculate the coordinates of the Sun and Moon. You can choose latitudes where the program will predict a very short day when the Sun really remains below the horizon all day - this inaccuracy affects latitudes close to 67.43 degrees North, and you can imagine a 'fuzzy zone' around the Earth at this latitude (and a mirror image one in the South) where the program may be in error. The situation for moonrise and set is more complex as the 'lunar arctic circle' changes as the Moon's orbit changes its orientation. I suspect that more accurate position routines and better approximations for topocentric parallax, refraction and the diameter of the Sun and Moon would shrink this 'fuzzy zone', at the cost of increased complexity. The program will give meaningful results above latitude 70 degrees where methods based on iteration cannot.

The algorithm was implemented in QBASIC, a well structured interpreted basic available free for Windows computers, and easily adapted to Visual Basic syntax. The implementation is based very closely on PASCAL routines taken from Montenbruck and Pfleger. this page contains a Javascript implementation - view the page source to see the code.

Definitions and the problem

The rising and setting of the Sun and Moon is defined here to be the instant when the upper limb of the object is seen to cross a mathematically flat horizon by an observer at sea level. Real observing situations on land rarely approach this idealised model, and for my uses calculating rise and set times to the nearest minute or so is fine.

The following factors need to be addressed

In Montenbruck and Pfleger's approximate implementation, the last three points above boil down to subtracting a single correction term from the geocentric altitude of the Moon or Sun when looking for rise or setting events.

The large difference between the Moon and the Sun correction reflects the much larger parallax effect on Moon positions - roughly 1 degree for the Moon compared to 9 arc seconds for the Sun.

Different algorithms

Possible algorithms include:-

I used the 'single position and calculate as for star' method on a programmable calculator - the results for the Sun at moderate latitudes were 20 minutes or so wrong. Given the state of the local horizon, this was not much of a problem. This 'method' was very poor for the Moon, almost worse than guessing from the number of days since New Moon.

The 'trial and improvement' method with allowance for refraction, parallax and disc size is much better, and can give good results for the Sun for latitudes below 65N. The method will mostly converge after a few iterations - see Paul Schlyter's page.

Tral and improvement methods get fiddly in situations where the object remains above or below the horizon for a number of days, or where the object does not set one day or the next.

A table based method could be very simple - just calculate the altitude of the Moon for each minute of the day and find when the altitude changes sign. There is your rising or setting event.

This simple table based method could detect the 'always above the horizon' or 'always below the horizon' situations as the (corrected) altitude would never change sign over the day. The method could also cope with the Moon missing a rise or set each lunar cycle, but 'grazing' situations, where the Sun never quite dips below the horizon, would be more difficult as there would be no sign change in the altitudes. A real program based on this system would be really slow, requiring at worst case 1440 calculations of altitude for each object for each day to reach an accuracy of one minute of time.

Quadratic interpolation method

Interpolation based methods use a shorter table of altitudes - in my implementation we use a table with a maximum of 25 rows - and fit a quadratic function to each set of three altitudes in turn. We then use some GCSE algebra to find the times when the quadratic crosses the X axis - has zero altitude - and these times are candidates for a rising or setting event. This system can also deal with the situation when the rising and setting occur within the hour - the quadratic then has two zeros. Finally, if the two zeros are the same, then there must be a 'grazing' event in that interval, and the algorithm can detect the event.

The steps in the procedure are

  1. Calculate the sine of the altitude (corrected for refraction, parallax and the limb radius) for the first three hours in the day. Using the sine of the altitude saves some calculation and means that the values will always be within the range +1 to -1.
  2. Save sign of the altitude at 0h
  3. Take the values of the sine of the altitude for each set of three consecutive hours, correct for the refraction, parallax and fit a quadratic curve through these three points. See Montenbruck and Pfleger for algebra.
  4. Calculate the 'discriminant' for the quadratic, and classify as
    • No roots within the 2 hour interval - move onto the next 2 hour range and start from step 1
    • Two roots, one root within the interval - classify as rising or setting event and appropriate flag
      • If two flags set, i.e. rising and setting events both found, go to step 5
      • If one flag set, then return to step 1 for next two hour interval, to search for remaining event.
    • Two roots, both within the interval - set the rising and setting flags and go to step 5.
    • One root (i.e. both roots same) within interval - set both rising and setting flags and go to step 5.
  5. If neither rise nor set flag is set, then warn user that object is 'always above' or 'always below' horizon depending on the sign of the altitude in step 2, and move onto next object or quit.
  6. Print rise and set times, or message if one event missing in current day.
  7. Move onto next object or quit.

Test data

Below are some samples of program input and output tested using an earlier QBASIC program, together with accurate results from Chris Marriott's SkyMap Pro 6.0 and with a year 2000 calendar for the Sun, Moon and Nautical Twilight generated from the USNO web based program.

Case 1

Rise and set times for today in Birmingham UK - simple case with no ambiguities. Below is the dialogue with the QBASIC program. Times of events are given in form hhmm, and are UT times.

   Rise and set for Sun and Moon

   Year (yyyy) - - - - - - - - :2000
   Month  (mm) - - - - - - - - :1
   Day    (dd) - - - - - - - - :3
   Time zone (East +) - - - -  :0
   Longitude (w neg, decimals) :-1.91667
   Latitude  (n pos, decimals) :52.5



   Nautical twilight

Skymap Pro gives the following times for the Sun and Moon on 2000 Jan 3 - agreement is fine to nearest minute, except for Moonrise that rounds the wrong way to give a result one minute different from the USNO tables.

Sunrise and twilight
Date           Rise        Set         Naut Twi E    Naut Twi B
03 Jan 2000    08:18:11    16:05:50    17:30:56      06:53:06

Rise: 5h 0m 23s
Set: 14h 9m 18s

Case 2

For 1999 December 25th at a made up location of 0 Longitude, 67.43 latitude, the QBASIC program gives a 'day' lasting 8 minutes:
   Rise and set for Sun and Moon

   Year (yyyy) - - - - - - - - :1999
   Month  (mm) - - - - - - - - :12
   Day    (dd) - - - - - - - - :25
   Time zone (East +) - - - -  :0
   Longitude (w neg, decimals) :0
   Latitude  (n pos, decimals) :67.43



   Nautical twilight

Skymap Pro shows that the Sun remains below the horizon for the whole of that day at the latitude given. SkyMap Pro gives the altitude of the (centre of) Sun at transit for this day as roughly 53 minutes below the horizon. This implies an error of roughly 30 minutes in Sun position at that time for the QBASIC program. This seems rather large and I will be puggling about with this a bit more.

The Moon times and times for twilight are within a minute of those produced by SkyMap Pro. You might treat output from the QBASIC program presented here with caution for locations with latitudes between 67 and 68 North.

Case 3

For Narvik in Norway (further North), the program gives correct results give or take a minute:-

   Rise and set for Sun and Moon

   Year (yyyy) - - - - - - - - :2000
   Month  (mm) - - - - - - - - :1
   Day    (dd) - - - - - - - - :3
   Time zone (East +) - - - -  :1
   Longitude (w neg, decimals) :17.42
   Latitude  (n pos, decimals) :68.43


    always below horizon

   Nautical twilight
SkyMap Pro gives
Rise: 6h 27m 59s
Set: 11h 57m 47s

Date           Rise        Set         Naut Twi E    Naut Twi B
03 Jan 2000    --:--:--    --:--:--    16:07:06      07:42:21

Javascript page

Javascript version (this page) I have 'wrapped up' the main calculation loop in a function and this makes the program easier to handle. I have separated the moonrise and the sun related events (twilight and sunrise) in different functions so as to allow different tabulation intervals.

Sunrise times change relatively slowly, and a weekly listing is fine for a year. Moonrise times change by 50 minutes a day on average and so a daily listing is needed.

The Javascript page works fine on Safari 1.2+, Netscape 4.7+, MS Internet Explorer 6 and Opera 7.


Oliver Montenbruck and Thomas Pfleger,
Astronomy on the Personal Computer
1994, 3rd edition
ISBN 3-540-63521-1

Section 3.8 of this book is the basis of the QBASIC listing here. I have translated the PASCAL routines into QBASIC one by one. This book does not contain an exhaustive explanation of the quadratic fit method, and the test data the authors provide will not test all branches of the code. This book comes with a software disc with all the PASCAL routines - but does not cover all the ground in, say, Meeus' Astronomical Algorithms.

Sky and Telescope's software pages contain listings in 'spaghetti basic' that implement a similar method for the Sun and the Moon - there is a clever fix used to avoid re-calculating positions for the Sun and Moon up to 12 times each day at the cost of some increase in the 'fuzzy zone' when the programs may predict a Sunrise and set when there is none. The links below are to the BASICA listings.

Seidelmann, P. Kenneth (ed)
Explanatory Supplement to the Astronomical Almanac
University Science Books
1992, completely revised
ISBN 0-935702-68-7

Definitive reference on all aspects of the ephemeris and associated calculations. No hostages taken, no example calculations and modern vectoral notation used throughout. Sections 9.311 (p484) and 9.33 (p486) present the iterative algorithm for Sunrise for moderate latitudes.

Duffett-Smith, Peter
Practical Astronomy with your calculator
Cambridge University Press
3rd edition 1988
ISBN 0-521-35699-7

Good treatment of the basics of coordinate systems. Presents the formulas for rise and set time of a star, and presents an interesting linear interpolation scheme for Moonrise. Keith Burnett 3rd Jan 03 (It's snowing!)

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