# How to calculate Longitude from Right Ascension?

Considering that a star of certain declination is crossing the local meridian at the observer's zenith at an unknown location on the earth. Here, the declination of the star is equal to the observer's latitude. Knowing the Right Ascension of the star, how could the observer calculate his longitude?

Example: The star Miaplacidus (Dec: -69° 42' and RA: 9h 13m) crossing at the observer's zenith!

Latitude = 69° 42' S

[ Longitude= RA(Decimal Conversion) X 15° ... I'm not sure how to proceed from here ... ]

• You need a clock. Do you have one for this exercise? Dec 12 '13 at 10:45
• Nope :/ Perhaps proceed with a time or consider september 21 midnight... ST=LT
– Ken
Dec 12 '13 at 16:28

In other "words", the connection between the time of transit $t_\mathrm{tr}$ of an object, its right ascension $\alpha$ and the geographical longitude of an observer $l$ is the (apparent) siderial time at Greenwich $\theta_0$ (if you know your local siderial time $\theta$, you don't need $\theta_0$ or $l$): $$t_\mathrm{tr} = \alpha - \theta_0 - l = \alpha - \theta.$$