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How can I determine right ascension and declination of a star in the sky?

  1. Oct 11, 2014 #1
    I have a location of approximately 35 deg 14' S and 149 deg 4' E, and I have measured the position of the star Antares to be at an altitude of 27 deg 00' using an inclinometer, and direction 247 deg using a compass.

    Using this information can I calculate the direction of the star on the celestial sphere in terms of right ascension and declination? Or do I need more information?
  2. jcsd
  3. Oct 12, 2014 #2


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    You need a date and time during which you made your observation, since the star will move around the sky depending on the time of day, and season (and on the precession of the equinox).
  4. Oct 12, 2014 #3
    Sorry left that part out, the time I took the measurement was at 20:45 on the 25/09/2014, which I think is around 7:01.15 in sidereal time according to an online converter
  5. Oct 12, 2014 #4


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    going from AL/Az to RA and Dec is a little more difficult than the other way around

    from this site ....

    Hour Angle (HA) and Declination (DE) given the Altitude (AL) and Azimuth (AZ) of a star and the observers Latitude (LA) and Longitude (LO)
    1. Convert Azimuth (AZ) and Altitude (AL) to decimal degrees.
    2. Compute sin(DE)=(sin (AL)*sin (LA))+(cos(AL)*cos (LA)*cos (AZ)).
    3. Take the inverse sine of sin(DE) to get the declination.
    4. Compute cos (HA)=(sin (AL)-(sin (LA)*sin(DE)))/(cos (LA)*cos (DE)).
    5. Take the inverse cosine of cos (HA).
    6. Take the sine of AZ. If it is positive then HA=360-HA.
    7. Divide HA by 15. This is the Hour Angle in decimal Hours.
    Hour Angle to Right Ascension
    1. Convert Local Sidereal Time and Hour Angle into decimal hours.
    2. Subtract Hour Angle from Local Sidereal Time.
    3. If result is negative add 24.
    4. This is the Right Ascension in decimal hours.

  6. Oct 12, 2014 #5


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    The fastest way of making that coordinate conversion is to use a web page or a formula. But it's more instructive (and transparent) if you make a sketch of the celestial sphere, such as this one I'm supplying. You still need formulas, but you know what you're doing with them...

    The latitude of the place from where you have made the observation is phi (the altitude of the pole). And h is the altitude of the star that you have measured. The angle comprised by the two sides is 180º-a, where a is the azimuth of the star, measured from the south (ZS is the meridian of the place).

    At the right side, I've isolated the relevant spherical triangle. You need to find a formula, in the internet or elsewhere, in order to find the side 90º-delta (delta is the declination to be found) for the spherical triangle with two known sides, 90º-h and 90º-phi, and the angle comprised, 180º-a.

    Thus, you get the declination delta. Now, you need the right ascension: RA = sidereal time - hour angle. As the three side are now known, you can use another formula to find the angle APZ, comprised between 90º-phi and 90º-delta. Its value is the same as that of side t, the hour angle...

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