104 PART 1^ |^ EXPLORING THE SKY
objective. A lens or mirror with a large area gathers a large amount
of light. Th e area of a circular lens or mirror is πr^2 , or, written in
terms of the diameter, the area is π(D/2)^2. To compare the relative
light-gathering powers (LGP) of two telescopes A and B, you can
calculate the ratio of the areas of their objectives, which reduces
to the ratio of their diameters (D) squared.
LGPA
_____
LGPB (^) (
DA
DB
(^) )
2
For example, suppose you compared a telescope 24 cm in diam-
eter with a telescope 4 cm in diameter. Th e ratio of the diameters
is 24/4, or 6, but the larger telescope does not gather six times as
much light. Light-gathering power increases as the ratio of diam-
eters squared, so it gathers 36 times more light than the smaller
telescope. Th is example shows the importance of diameter in
astronomical telescopes. Even a small increase in diameter pro-
duces a large increase in light-gathering power and allows
astronomers to study much fainter objects.
Th e second power, resolving power, refers to the ability of
the telescope to reveal fi ne detail. Because light acts as a wave, it
produces a small diff raction fringe around every point of light
in the image, and you cannot see any detail smaller than the
fringe (■ Figure 6-8). Astronomers can’t eliminate diff raction
fringes, but the larger a telescope is in diameter, the smaller the
diff raction fringes are. Th at means the larger the telescope, the
better its resolving power.
If you consider only optical telescopes, you can estimate the
resolving power by calculating the angular distance between two
stars that are just barely visible through the telescope as two sepa-
rate images. Astronomers say the two images are “resolved,”
meaning they are separated from each other. Th e resolving
power, , in arc seconds, equals 11.6 divided by the diameter of
the telescope in centimeters:
(^) 11.6____
D
For example, the resolving power of a 25.0 cm telescope is 11.6
divided by 25.0, or 0.46 arc seconds. No matter how perfect the
telescope optics, this is the smallest detail you can see through
that telescope.
Th is calculation gives you the best possible resolving power
of a telescope of diameter D, but the actual resolution can be
limited by two other factors—lens quality and atmospheric con-
ditions. A telescope must contain high-quality optics to achieve
its full potential resolving power. Even a large telescope reveals
little detail if its optics are marred with imperfections. Also,
when you look through a telescope, you are looking up through
miles of turbulent air in Earth’s atmosphere, which makes the
image dance and blur, a condition called seeing. A related phe-
nomenon is the twinkling of stars. Th e twinkles are caused by
turbulence in Earth’s atmosphere, and a star near the horizon,
where you look through more air, will twinkle and blur more
than a star overhead.
On a night when the atmosphere is unsteady, the images are
blurred, and the seeing is bad (■ Figure 6-9). Even under good
seeing conditions, the detail visible through a large telescope is
limited, not by its diff raction fringes but by the air through
which the telescope must look. A telescope performs better on a
high mountaintop where the air is thin and steady, but even there
Earth’s atmosphere limits the detail the best telescopes can reveal
to about 0.5 arc seconds. You will learn later in this chapter
about telescopes that orbit above Earth’s atmosphere and are not
limited by seeing.
Seeing and diff raction limit the amount of information in an
image, and that limits the accuracy of any measurement made
based on that image. Have you ever tried to magnify a newspaper
photo to distinguish some detail? Newspaper photos are made up
of tiny dots of ink, and no detail smaller than a single dot will be
visible no matter how much you magnify the photo. In an astro-
nomical image, the resolution is often limited by seeing. You
can’t see a detail in the image that is smaller than the resolution.
ab
■ Figure 6-8
(a) Stars are so far away that their images are
points, but the wave nature of light surrounds each
star image with diffraction fringes (much magni-
fi ed in this computer model). (b) Two stars close to
each other have overlapping diffraction fringes and
become impossible to detect separately. (Computer
model by M. A. Seeds)