How To Calculate Longitude From Right Ascension

Longitude and right ascension both start on the Greenwich meridian, which simplifies converting from one coordinate system to another. Meridians are imaginary lines along which a coordinate has a constant value and run north to south. Right ascension meridians fall on the celestial sphere, while those for longitude fall on the earth. Right ascension is measured eastward and is in hours, minutes and seconds, with values ranging from 0 to 24 hours. Longitude runs both eastward and westward and is measured in degrees, with a value of zero at Greenwich up to -180 degrees westerly and +180 degrees easterly. The 180-degree line is called the International Date Line.

Step 1

Convert the right ascension into decimal form using the following formula: hour + minute/60 + second/3600 = decimal value. For example, if the right ascension is 2 hours, 30 minutes and 45 seconds, then this time in decimal form is 2 + 30/60 + 45/3600 = 2.5125.

Step 2

Multiply the decimal time by 15 degrees. For example, 2.5125 x 15 = 37.6875 degrees. This value corresponds to the degree equivalent of 2 hours, 30 minutes and 45 seconds.

Step 3

Subtract 360 degrees from the result in Step 2 if the result is greater than 180 degrees, and this will give you the correct number of degrees longitude west. If the number calculated in Step 2 is less than 180 degrees, leave it alone. It correctly gives you the number of degrees east. For example, a right ascension of 13 hours in decimal form is 13.0, and multiplying this by 15 degrees gives 195 degrees. This value is greater than 180 degrees, so subtract 360 from it as follows: 195-360 = -165. The coordinate in longitude is -156 degrees, and it is referencing a location west of Greenwich.