How far is that star? - NRC Publications Archive

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How far is that star?
Tapping, Ken
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Skygazing: Astronomy through the seasons, 2016-08-30
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HOW FAR IS THAT STAR?
Ken Tapping, 30th August, 2016
How far away is that star? How did we determine
that galaxy is a billion light years away? This
process has taken us thousands of years and
involves several different methods. However, they
all depend upon one basic foundation – parallax.
If you close one eye while looking at a scene, then
close that eye and open the other, you will notice
that foreground objects move against the
background of more distant objects. This
phenomenon is called parallax, and is how our
brains assess distance. In surveying, this process
is called triangulation, where we observe distant
objects from two ends of a carefully surveyed line.
So the first step in measuring the Cosmos is to
measure the Earth. That will give us our initial
surveyed base from which we can push outwards.
The first accurate determination of the size of the
Earth was made around 200 BCE by the Greek
philosopher Eratosthenes. He noticed that on the
summer solstice, the Sun shone straight down a
well at Syene, now called Aswan, in Egypt,
meaning the Sun passed overhead. In Alexandria,
where he worked, he knew this was not the case.
The Sun never got within a few degrees of the
zenith. Greek scientists already believed the Earth
was spherical, and this led to Eratosthenes
proposing that the relationship between that angle
of a few degrees and a circle would be the same
as that between the distance between Syene and
Alexandria and the circumference of the Earth.
The angle was a 1/50 of a circle, so the distance
between Alexandria and Syene was 1/50 of the
circumference of the Earth. However, how far was
Syene from Alexandria? Many accounts suggest
he paced out the distance himself. However, since
he was a senior philosopher, it is more likely he
paid or cajoled someone else to do it, perhaps one
of his students. He then calculated the
circumference of the Earth, and got the right value.
Once we could establish the precise relative
positions of two well-separated places on Earth,
we could measure the distance and size of the
Moon. At as close to the same time as possible,
we observe at both locations the Moon's position
against the distant background stars. From this we
can estimate the Moon’s parallax and determine its
distance. Knowing how far away it is and
measuring how big it looks in the sky, we can then
find how big it is. This method also works for the
Sun. However, beyond that it gets difficult.
If space is filled with stars, some of them will be
much nearer to us than others. However,
measurements made from different places on
Earth showed no stars having different positions
against the other stars. The parallax was too small
to measure, indicating the stars are very far away.
However, it is possible to have a triangulation
baseline bigger than the Earth. The Earth orbits
the Sun at a measured distance of about 150
million kilometres, and takes a year to do so. If we
take pictures of the sky six months apart, we are
taking them from opposite ends of a 300 million
kilometre baseline. It worked. Some stars showed
small parallaxes. However, even those stars
turned out to be enormously far away – so far that
expressing those distances in kilometres was not
really practical, the light year is a better unit (a light
year is almost 10,000,000,000,000 km).
Thanks to improvements in our instruments, we
have used parallax measurements to determine
star distances out to about 1600 light years.
However, the Universe extends way beyond that.
We had to find other methods for measuring
distance, but without parallax they could never
have been developed. Moreover I think we would
not have much trouble explaining them to
Eratosthenes, or the unknown person who paced
out the distance between Syene and Alexandria.
Mars and Saturn lie low in the southwest after
dark. Saturn is above Mars, fainter and to the right.
The Moon will be New on the 1st.
Ken Tapping is an astronomer with the National
Research Council's Dominion Radio Astrophysical
Observatory, Penticton, BC, V2A 6J9.
Tel (250) 497-2300, Fax (250) 497-2355
E-mail: [email protected]