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How to Calculate Ecliptic Longitude

Ecliptic longitude (celestial longitude) is an important term in astronomy because it is used to find the position of an object within the solar system. Ecliptic longitude is calculated based on the ecliptic coordinate system. Ecliptic is the path that the sun moves across the sky in an annual period. Ecliptic longitude is the angular distance measured eastward from the vernal equinox to the intersection of the ecliptic, with a circle drawn through the object and the poles of the ecliptic. Vernal equinox is the point of intersection of celestial equator and ecliptic.

Things You'll Need

Tables to calculate Julian Day Number

Instructions

- 1
  Calculate the sun's mean anomaly (M) using the formula: M = 357.528 + 35999.050 (T0) + 0.04107H degrees. (T0) is the time in Julian centuries from 12.00 Universal Time on January 1, 2000, to 12.00 Universal Time on the day in which the calculation is made. (T0) can be calculated using tables. H is the time in hours since that preceding midnight.
  
  For example, if you want to calculate the ecliptic longitude of the sun on May 13, 2013, use the three Julian Day Number tables. From Table 27 (see Resources), you have to take the corresponding value of 2000, which is equal to 2451544. Now, take the year of the century, which is 13, and the corresponding value from Table 28, which is 4749. The day of the year is May 13, for which the value from Table 29 is 133. Adding these three values, you get (T0) as 2456426. Suppose you do the calculation at 2.00 a.m., then the value of H is 2. Now you get the value of M using the above formula as 88429002752.91014.
- 2
  Calculate mean longitude (Lambda) using the formula: Lambda = 280.460 + 36000.772 T0 + 0.04107 H degrees. You get the value of Lambda as 88433232641.41414.
- 3
  Calculate ecliptic longitude (lambdaO) using the formula: lambdaO = Lambda + (1.915 - 0.0048 T0) sin M + 0.020 sin 2M. You get M and Lambda from Step 1 and Step 2, respectively. Now ecliptic longitude = 88433231464.23 (rounded to 2 decimal points). This formula is derived from the Almanac for Computers published by the U.S. Naval Observatory every year.

Astronomy