- Stretch your arm forward and extend your thumb, so that
your thumbnail faces your eyes. Close one eye (A') and move your thumb so that
your thumbnail covers the landmark A.
- Then open the other eye (A') and close the first (B'),
without moving your thumb. You may find that your thumbnail is now in front of some
other feature in the landscape, at about the same distance as A, marked B.
- Estimate the distance AB, by comparing it to the estimated
heights of trees, widths of buildings, distances between power-line poles,
lengths of cars etc. The distance to the landmark is 10 times the distance AB.
Why does this work? Because even though people vary in size, the
proportions of the average human body are fairly constant, and for most
people, the angle between the lines from the eyes (A',B') to the
outstretched thumb is about 6°, close enough to the value 5.73°
for which the ratio 1:10 was found in an earlier part of this section.
That angle is the parallax of your thumb, viewed from your eyes. The
triangle A'B'C has the same proportions as the much larger
triangle ABC, and therefore, if the distance B'C to the thumb is
10 times the distance A'B' between the eyes, the distance AC
to the far landmark is also 10 times the distance AB.
How far to a Star?
When estimating the distance to a very distant object, our "baseline"
between the two points of observation better be large, too. The most distant objects
our eyes can see are the stars, and they are very far indeed: light which moves at
300,000 kilometers (186,000 miles) per second, would take years, often many years,
to reach them. The Sun's light needs 500 seconds to reach Earth, a bit over 8
minutes, and about 5.5 hours to reach the average distance of Pluto, the most
distant planet. A "light year" is about 1600 times further, an enormous
The biggest baseline available for measuring such
distances is the diameter of the Earth's orbit, 300,000,000 kilometers.
The Earth's motion around the Sun makes it move back and forth
in space, so that on dates separated by half a year, its positions
are 300,000,000 kilometers apart. In addition, the entire solar system also
moves through space, but that motion is not periodic and therefore its effects
can be separated.
And how much do the stars shift when viewed from two points
300,000,000 km apart? Actually, very, very little. For many years
astronomers struggled in vain to observe the difference. Only in 1838 were
definite parallaxes measured for some of the nearest stars--for Alpha
Centauri by Henderson from South Africa, for Vega by Friedrich von Struve
and for 61 Cygni by Friedrich Bessel.
Such observations demand enormous precision. Where a circle is
divided into 360 degrees (360°), each degree is divided into 60
minutes (60')--also called "minutes of arc" to distinguish them from
minutes of time--and each minute contains 60 seconds of arc (60"). All
observed parallaxes are less than 1", at the limit of the resolving
power of even large ground-based telescopes.
In measuring star distances, astronomers frequently use the
parsec, the distance to a star whose yearly parallax is 1".
One parsec equals 3.26 light years, but as already noted, no star is
that close to us. Alpha Centauri, the sun-like star nearest to our solar
system, has a distance of 4.3 years and a parallax of 0.75".
Alpha Centauri is not a name, but a designation. Astronomers designate stars in
each constellation by letters of the Greek alphabet--alpha, beta, gamma, delta
and so forth, and "Alpha Centauri" means the brightest star in the
constellation of Centaurus, located high in the southern skies. You need
to be south of the equator to see it well.