How astronomical distances are measred
The Sunday Nation
Nairobi,
08 January 2012
The article about the newly discovered planet has elicited some
interesting reactions from readers. Charles Muchui writes: “When talking
of 600 light years. Is this an estimate or a fact? If [it is] a fact do
you mean this light was projected around [the year] 1400. Was that
possible by then or what is this light year you are talking about? I am
confused.”
Before I had started writing a reply to Charles’ question, Maths and
Physics teacher, Samuel Muchori sent in his comment: “This newly spotted
planet is 600 light years away…. So the image we are seeing is that of
the planet 600 years ago… Am I right?”
There is your answer, Charles.
Now the reason astronomers express distances in light years (LY) is that
the number of kilometres is too large. 9,460,800,000,000km makes one LY,
so 600LY is equivalent to 5,676,480,000,000,000km! Now are those
billions, trillions or what?
Light years are not the only units used in expressing distances in
astronomy. The one commonly used for objects within the solar system is
the so-called Astronomical Unit (AU). It is equivalent to the mean
distance from the Sun to Earth. That is
149,597,870km. Thus the outermost planet ( Neptune ) is only about 30AU
(4.5 billion km) from the sun.
Another unit used in astronomy is called the parsec. It is very
convenient because it is directly related to the way distances to other
stars are measure.
Suppose you locate a star in the sky today and you adjust your telescope
to position it right at the centre of the viewing eye-piece. Now wait
exactly six months later (timed down to the second); do you think the
star will still be at the centre?
Obviously not. This is because the earth has moved halfway around the
sun. Consequently, you will need to adjust the direction that the
telescope is pointing in order to bring the star back to the centre.
Now picture that: you have formed a triangle whose three points are (1)
the initial position of the earth, (2) its final position after six
months and (3) the star under observation.
Since the distance to the star is very large, the angle of adjustment is
bound to be extremely small. And the farther away the star is, the small
the angle.
Normally angles are measured in degrees – a full circle has 360 degrees.
Degrees are divided into minutes and seconds of an arc. One degree has
60 minutes and one minute has 60 seconds (obviously!). Thus, one second
of arc is a 3,600th fraction of a degree (60 x 60 = 3,600).
Now going back to the imaginary triangle; we can divide it into two
equal halves by drawing a line from the distant star to the sun. Knowing
the angle of adjustment, we can apply high school trigonometry to
calculate the distance from the sun to the star – in kilometres.
But we don’t have to: if the angle from the Earth-to-star-to-sun is one
second of arc, we can simply say that the distance is one parsec. Since
the angle decreases as the distance increases, then the number of
parsecs is simply the inverse of the angle (measured in arc-seconds).
If you do the math, you will find that one parsec is about 3.26LY, or
206,000AU, or 30,851,668,800,000km. Picture that in your mind as you
enjoy your Christmas.
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