Determining Stellar Distances
How can you tell how far away stars are from earth?
The nearby stars are done using parallax, taking images of the star
relative to other stars while Earth is on either side on its orbit
of the Sun. There are lots of basic astronomy books that explain this.
For farther objects, new yardsticks are required, like Cepheid variables.
On a basic level, we can do triangulation (much in the same way that
surveyors or cartographers used to measure distances of objects on
Earth). In this process, two spots (spot A and spot B) of known
distance from each other are chosen, the target object is sighted
from these spots, a triangle is thus formed between the target
object, spot A and spot B. If we know the angle made between
target-spot A-spot B, the distance between spot A and spot B, and
the angle formed by target-spot B-spot A, then we can calculate the
distance of the target from the midpoint between spot A and spot B
by simply calculating the height of the triangle formed (we can also
calculate spot A to target, or spot B to target distances).
To make more accurate measurements of the angles formed, you want to
make the distance between spot A and spot B as great as possible, so
often, the angle of the telescope looking at the target object will
be measured at some time of the year. We then wait for the Earth to
move around the Sun for a bit, so that at a later time of the year,
when some known distance has been covered in the Earth's orbit
around the Sun, the angle to the object is again measured, and the
triangulation can again be done.
Greg (Roberto Gregorius)
The basic concept of measuring these very large distances is called
Parallax. The easiest way to understand parallax is to put one
finger up a few inches in front of your face. Now close one
eye. Switch back and forth between opening your left eye and
closing your right and closing your left and opening your
right. When you do this, do not look at your finger, but at the
background--the wall, trees, whatever. When you do this, you will
see your finger apparently move. You know in fact that your finger
is not actually moving, but since your eyes are a couple inches away
from each other, each eye sees a slightly different position of your
finger when compared to the background. In fact, you can create a
triangle from your left eye, to your right eye, to your finger, back
to your left eye. Since you can measure the distances between your
eyes, you already know one of the distances of the triangle. Using
geometry you can solve for the internal angles of the triangle and
determine the distance to your finger.
You can do the same thing with stars! Now look at something very
far away and alternate blinking your eyes, just as before. You
should notice that you do not observe parallax anymore. The
distance between your eyes is so small compared to the distance to
very far objects that you would now have to use a second person many
yards or miles away to observe the parallax. The same thing applies
to stars! So how do we measure the parallax of stars? We use the
Earth's orbit to create the distance "between your eyes". Every 6
months, the Earth is approximately on the other side of its orbit
around the Sun--186,000,000 miles away from where you were 6 months
ago! This is quite a bit bigger of a distance than between your
eyes. Since we know this distance, we can use the same math as
before to determine the distance to stars.
Below is a link to a much more detailed explanation of parallax,
though it might be a little too complicated for you to understand
without an extensive math background. There are still a few
paragraphs and pictures that would be useful for you to look at though.
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Update: June 2012