Is there any url that can give me data of ecliptic line that i can plot in a map. i.e i need earth's latitude and earth's longitude of ecliptic line for a specific time and date. Right now i only have Sun's declination data and its longitude, with which i can plot only one point, but ecliptic line is like sine wave as i read on the internet. How can i get the data of complete ecliptic line for a given day and time. I am kind of new to this, kindly apologise if my question is wrong and show me the right way.

  • $\begingroup$ I think what you might be looking for is the "subsolar point", the point on Earth where the Sun is directly overhead. Google around for that and you should find several resources. Also, astronomy.stackexchange.com/questions/13488 might help $\endgroup$
    – user21
    Nov 22, 2019 at 2:39
  • $\begingroup$ @barrycarter thanks for the reply, Sub solar point, which is only one point, is what i have right now, i want to have the complete ecliptic line that can be plotted on earth. $\endgroup$
    – Rasika
    Nov 22, 2019 at 2:52
  • $\begingroup$ Not sure this answers your question: every point between the Tropic of Cancer and the Tropic of Capricorn will be a subsolar point sometime during the year. In other words, every location between those two lines will have the sun overhead at least once a year (and usually twice) $\endgroup$
    – user21
    Nov 22, 2019 at 3:48
  • $\begingroup$ If you know the subsolar point, then you have everything you need to know to plot the entire ecliptic. Use my equation to find the longitude where the ecliptic crosses the equator. Once that is known, all other points can be plotted for every X degrees of longitude. Note that I am updating my original answer. $\endgroup$
    – JohnHoltz
    Nov 23, 2019 at 14:07
  • $\begingroup$ The projection of the ecliptic on the Earth changes minute by minute as the Earth rotates "inside" the plane. Out of curiosity what is the purpose of projecting the ecliptic at a specific date and time? $\endgroup$
    – JohnHoltz
    Nov 24, 2019 at 17:18

1 Answer 1


The ecliptic is a plane that is inclined 23.43 degrees (approximately, insert your more accurate value as needed). One position on the ecliptic is 0 hours Right Ascension, 0 degrees Declination (0,0). If you plot that on the Earth at the date and time you have, the rest of the ecliptic's path on the Earth can be calculated as follows: $$\tan(23.43) \sin(longitude-longitude_{equatorcrossing}) = \tan(latitude)$$

where $longitude_{equatorcrossing}$ is the longitude where the ecliptic at 0 hours Right Ascension crosses the equator.

As a check, the latitude should be 23.43 degrees when the longitude is 90 degrees east of the (0,0) longitude point, and the latitude should be -23.43 degrees when the longitude is 90 degrees west of the (0,0) longitude point. In other words, if (0 Right Ascension, 0 Declination) corresponds to 15 degrees east longitude, then 105 east longitude is where the ecliptic is at the maximum northern latitude, and 75 degrees west longitude is where the ecliptic is at the maximum southern latitude.

  • $\begingroup$ Thanks for the reply, can you please give me any example calculation, if you dont mind, for today perhaps and the values i get from this will be in lat and long? $\endgroup$
    – Rasika
    Nov 21, 2019 at 17:23
  • $\begingroup$ Sorry for bugging you, can you please give me an example calculation wrt the sun's declination data of today, which will help me immensely. $\endgroup$
    – Rasika
    Nov 22, 2019 at 2:33
  • $\begingroup$ @rasika. I do not have time at the moment to go into details. The short answer is that you need to calculate the GMST (Greenwich Mean Sidereal Time) which is probably given somewhere on this site. This gives the Right Ascension (RA) at 0 longitude. From this, you can calculate what longitude corresponds to the known RA (0 RA). Then you are done. :-) $\endgroup$
    – JohnHoltz
    Nov 22, 2019 at 22:58
  • $\begingroup$ for some reason i am not able to understand this :( ..sorry for the trouble $\endgroup$
    – Rasika
    Nov 23, 2019 at 5:23
  • $\begingroup$ @Rasika a good recommendation for you would be to have a look at the book Astronomical Algorithms by Jean Meeus; also check out the spherical coordinate system because this is used in astronomy, where right ascension increases eastward from the vernal/spring equinox (RA = celestial longitude) and declination (Dec) corresponds to celestial latitude $\endgroup$
    – jmarina
    Oct 5 at 13:09

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