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  • Trigonometric Parallax

    Reggie Jones

    As a new astronomer / astro imager, one question you'll have is just how we know the distances to the stars and deep sky objects we observe and image from our planet.  All of these astronomical objects are well beyond any of the instruments we might normally use to measure the physical distance between us and any star or galaxy.  Well fortunately, we have a method to use to determine distances to stellar and deep sky objects and it’s called the Trigonometric Parallax method.  

    Hold a finger out at arms length, close your left eye and view it with your right eye.  Now keep the finger in the same place but close the right eye and view it with your left.  What you notice is that the position of your finger changes relative to the background behind it.  This phenomena is called parallax.  As our planet moves around its orbit with our star, the stars closer to us will appear to move to a different position relative to the background stars when viewed at different times in our orbital position.   The reason for this is our visual perception changes as our position around the sun changes.

    There is some math involved to derive this and that I’m avoiding in this post to keep things brief, but we know what the radius of our orbit around the sun.  Suffice it to say that the professional astronomers defined the distance that a star’s parallax is for 1 arc second of orbital distance along our orbital path to be 1 parallax-second, or a parsec.  As the distance to a star increases, the parallax shift decreases inversely.  The distance then to a star that we’re observing the parallax shift of at 2 different points in our orbit is then defined as d = 1/p, where:

    p is the parallax angle in arc seconds

    d is the distance in parsecs

    Once you know the distance in parsecs, you can convert it to light years since 1 parsec is equivalent to 3.26 light years.

    So how is this actually done in practice?  We observe a particular star at a point in time and note the angle the star makes relative to the sun’s position.  6 months later we do the same measurement again.  As we see the star, it will appear to move through an angle as shown in the attached image.  By definition, 1/2 of the total angle of apparent movement is the parallax, p.  All you need to do then is calculate the distance using the formula.

    As with everything, there are some caveats to note.  If the star you’re measuring is really far away, the parallax angle measured will be quite small and the measurement will be much less accurate.  As a general rule, the farther away the object is, the smaller the parallax will be and increases the risk of an inaccurate measurement.

    As seems to be the general case in astronomy, we also have a catalog of ground based parallax measurements of stars that have been taken through November 1995.  This is The General Catalogue of Trigonometric Stellar Parallaxes and it was compiled and edited by American Astronomer William Foster Van Altena, although it appears there were other astronomers involved with this effort but I haven’t been able to identify them.   This catalog contains parallax measurements of more that 8,000 stars.  Since then, the European Space Agency’s (ESA) HIPPARCOS (High Precision Parallax Collecting Satellite) space astrometry mission, ESA’s Gaia spacecraft and the Hubble Telescope have been involved taking parallax measurements of local neighborhood and deep sky stars.


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