Optical telescopes use either lenses or mirrors to gather and focus light, allowing astronomers to see objects that are too faint or distant to view with the naked eye. Refracting telescopes use lenses to bend and focus light, while reflecting telescopes use curved mirrors. Spectroscopy reveals properties of astronomical objects like temperature, velocity, and composition by separating light into its component wavelengths. Astronomers use several techniques to measure the vast distances to stars and galaxies, including trigonometric parallax for nearby stars, and variable star properties like period-luminosity relationships for more distant objects.

2. Methods of Observational
Astronomy
Mercado, Emmar Joy P.
Bachelor of Elementary Education
ASTRONOMY

3. Introduction to Telescopes
The first manner in which people learned
about the stars and the planets was, of course,
with their naked eyes, and it was with the eyes
alone that the modern constellations were
conceived and the first five of our planets
(Mercury, Venus, Mars, Jupiter, and Saturn) were
revealed.

4. Optical telescopes (which come in two types:
reflectors and refractors) are designed mainly to
gather light and reveal more detail than can be seen
with the naked eye. Other types of telescopes include
the much larger radio telescopes as well as space
telescopes including infrared (IR), ultraviolet (UV),
x-ray and gamma-ray telescopes.

5. Optical Telescope

6. Dr. Edwin Hubble
(1889-1953) peering
through the Hooker
telescope (near
Pasadena, California),
one of the oldest and
largest observatory
telescopes still in
operation today.
(Courtesy: NASA)

7. The basic principle of upon which lenses
work is their ability to refract light, a fact
outlined by a mathematical relationship many
of us learned in high school:
n1 sinq1 = n2 sinq2

8. where n is a dimensionless constant called
the index of refraction (and the 1 and 2
subscripts refer to the medium through
which the ray of light is traveling);q1 is the
angle of incidence; and q2 is the angle of
reflection

9. The refractive index, n, of a vacuum is exactly
1, while that of air is approximately 1.0003,
although this value changes with temperature.
The refractive indices for glass vary from 1.5 to
1.8. Someone who is spear-fishing can witness
an example of refraction: in order to catch a fish,
one must aim at a spot slightly below where the
fish is seen because the light rays coming off of
the fish are refracted when they travel from the
water to the air. Another example would be the
way a pen placed on a clear glass of water gives
the appearance of being bent due to the
refraction of the light.

10. Refraction of light
through a medium
like glass or
acrylic.

11. This principle of refraction when applied to lenses
results in the formation of images. The geometric
shape of lenses either results in light traveling
parallel to the lens to either converge (i.e., a double
convex lens) or diverge (i.e., a double concave lens).
Each type of lens has a focal point, a value that
depends on the amount of curvature the lens has.
This focal length can be closely estimated by
assuming a thin lens that is, a lens where the
thickness is small compared to the object distance,
the image distance, or the radii of curvature of the
lens.

12. Unfortunately, the spherical lenses produced in the
real world are not the same as the ideal thin lenses of
physics, resulting in a flaw called spherical
aberration. Spherical aberration results in less than
perfectly sharp images because the light rays that are
parallel to the optic axis but at different distances
from the optic axis fail to converge to the same
point.

13. Another related problem is chromatic aberration, and it
is the result of light of different wavelengths (that is, colors)
refracting differently and thus also focusing at different focal
distances. These problems can and do have an impact on the
quality of images that refracting telescopes produce.

14. The other principle of optics used in
telescopes is reflection, specifically the kind
of reflection that results from curved mirrors.
As with lenses, the rays will either converge
or diverge depending on whether the mirror
surface is convex or concave and both types
of mirrors have focal lengths that depend on
the amount of curvature of the lens.

15. It was in 1608 when a glass-maker named Hans
Lipperhey announced the invention of the telescope
when he applied for a patent in the Netherlands for a
certain device by means of which all things at a very
great distance can be seen as if they were nearby, by
looking through glasses. Although Lipperhey was
denied a patent on the grounds that the telescope was
too easy to copy, he was commissioned and well
paid to make some binoculars. Soon afterward the
news about this new technology spread throughout
Europe.

16. The principle
of reflection.

17. Optical telescopes require at minimum
two lenses, the objective and the eyepiece.
The simplest kind of telescope is called a
refractor. In a refracting telescope, the light is
collected through the objective lens and then
enlarged with the eyepiece, which basically
acts as magnifying glass that enlarges the
image produced by the objective lens.

18. Unless corrected for with another lens or a prism, this
image will appear inverted. The amount of magnification is
dependent on the ratio of the focal lengths of each lens that
is, the ratio of the distance from each lens to the focused
image. Written as an equation:

19. m = -fobj / feye
where m is the magnification, fobj is the
distance from the objective lens to the focal
point and feye is the distance from the eyepiece
to its focal length.

20. Although one might consider magnification as
the most important factor in a telescopes performance,
several other numbers are equally vital. Light gathering
power determines how bright the objects appear and is
very important for proper viewing of galaxies and other
faint objects. Making the objective larger in diameter
can increase the amount of light a lens can gather.

21. Another factor in a refracting telescope is
the resolving power, which concerns how well it
can discern two distant objects whose angular
separation is small, like a pair of twin stars. In
addition, the field of view must be considered,
since if an astronomer wants to view meteors she
would want a wider field of view than if she were
attempting to find galaxies.

22. Despite the use of refracting telescopes throughout
the centuries, all modern optical telescopes used by
professional astronomers are reflectors, and for good
reason: when using a reflecting telescope to view the
night sky there is no chromatic aberration; only one
mirror needs to be precise (instead of two or more
lenses); and the mirrors (unlike lenses) do not sag
because they can be supported not only on the sides
but on the back as well. The largest reflecting
telescope is the Subaru-Japan National Large
Telescope located at the dormant volcano Mauna
Kea in Hawaii.

23. The other principle of optics used in
telescopes is reflection, specifically the kind
of reflection that results from curved mirrors.
As with lenses, the rays will either converge
or diverge depending on whether the mirror
surface is convex or concave and both types
of mirrors have focal lengths that depend on
the amount of curvature of the lens.

24. Reflecting telescopes take advantage of the fact that
concave mirrors cause light to converge and convex
mirrors cause light to diverge. The kinds of reflectors
that the amateur astronomer can buy come in two
main types: Newtonian and Cassegrain. Newtonian
reflectors (named after their inventor, Sir Issac
Newton) reflect the rays of light back up the tube to
another smaller flat mirror and into an eyepiece on
the side of the tube. This is somewhat more
convenient for viewing than the Cassegrain reflector,
which has the eyepiece at the end of the tube. In both
cases the size of the image depends on the focal
length of the mirror.

25. Other, non-optical telescopes are also used to
reveal the mysteries of our universe: among these are
radio telescopes. Radio telescopes are much, much
larger than the ones described above because of the
longer wavelength of radio. Since a reflecting
surface cannot have irregularities greater than about
1/5th the wavelength of the radiation being collected,
radio telescopes are easier to configure since radio
waves are about 100,000 times longer than light. For
example the Arecibo Radio Observatory in Puerto
Rico has a 305 meter reflecting surface.

26. Another type of telescope is a space telescope.
Why bother putting a telescope in space?
There are several reasons for spending
millions of dollars putting one in orbit. First,
from space one can view the part of the
electromagnetic spectrum obstructed by the
Earths atmosphere (infrared, ultraviolet, x-
rays, and gamma-rays). Second, there is no
light pollution in space. Third, the lack of an
atmosphere results in a lack of light distortion
due to atmospheric turbulence.

27. Besides the familiar Hubble Space Telescope,
other space telescopes include the CHANDRA X-ray
Observatory, launched in July 1999 to get high
resolution X-ray images from high energy regions of
the universe, such as the remnants of exploded stars
and the Compton Gamma RayObservatory, which
was removed from orbit by NASA in June 2000
bringing to an end to a successful 9-year mission. In
2002 the SIRTF (Space Infrared Telescope Facility)
will be launched, allowing unprecedented infrared
images of our galaxy and the far reaches of the
Universe.

28. The Hubble Space
Telescope being
serviced by NASA’s
Space Shuttle
(Courtesy: NASA)

29. Spectroscopy and Stars

30. Spectroscopy
 Spectroscopy is the study of “what kinds” of light we see from
an object. It is a measure of the quantity of each color of light
(or more specifically, the amount of each wavelength of light).
It is a powerful tool in astronomy. In fact, most of what we
know in astronomy is a result of spectroscopy: it can reveal the
temperature, velocity and composition of an object as well as
be used to infer mass, distance and many other pieces of
information.
 Spectroscopy is done at all wavelengths of the electromagnetic
spectrum, from radio waves to gamma rays; but here we will
focus on optical light.

31. A spectroscope is an instrument that
consists of a prism or a grating spreads the
incoming beam of radiation into its different
wavelengths and some kind of screen to
project the spectrum:

33. • Spectra come in several types:
1. Continuous spectra: a smooth gradient of
electromagnetic radiation without any gaps
e.g., the spectrum of incandescent solids.

34. 2. Absorption spectra: an incomplete spectrum
with missing gaps (which appear as dark
lines) due to the absorption of a continuous
electromagnetic radiation by a cooler medium,
like a gas. Such absorbed energy can be re-
emitted, but the absorbed energy is essentially
removed from a telescopes view. Since the
cooler, outer gaseous surface of a star tends to
absorb the radiation produced in the hotter,
inner part, the spectra of most stars are
absorption spectra.

35. 3. Emission spectra: a spectrum that
represents all the wavelengths emitted by
atoms or molecules

36. Astronomers take advantage of
something from physics called Wiens
Displacement Law, a mathematical
relationship that basically says that the
hotter a body (like a star) is, the shorter
the wavelength of light will be emitted
from it:
λpeak T = 2.898 x 10-3 m K

37. where λpeak is the peak (i.e., maximum)
wavelength that the star emits and T is the
stars surface temperature. Hence, a red star,
with a maximum wavelength of 966
nanometers, has a surface temperature of only
3000 Kelvin while a blue star, emitting at a
maximum wavelength of 290 nanometers, has
a surface temperature of 10, 000 Kelvin!

38. In addition, the stars have been classified into
spectral classifications (labeled by a letter)
based on their surface temperature. These
spectral types also organize the stars by their
chemical make-up and their main sequence
lifetimes, that is, the lifetime of the star based
on calculations of its available fuel and the
rate at which it is consuming that fuel (as
interpreted by its luminosity).

39. Measuring Distances to Stars

40. Astronomers use several techniques for
discovering how far away an object is. The first
is called trigonometric parallax and is based on
geometry, but it is only good for up to about 500
light-years. The principle behind this method is
elegantly simple: Earth orbits the Sun at a
known radius and when the Earth is at opposite
ends of its orbit it results in a star appearing in a
slightly different positions against distant
background stars that allow us to use simple
trigonometry to calculate how far away it is

41. The parallax (symbolized by the Greek
letter, Θ) is defined as the angular size of
an elliptical arc that the star seems to
trace against the background of space.
Since,
tan Θ = r/d

42. where tan refers to the tangent of a triangle, r
is the radius of the Earth’s orbit (equal to 1
A.U.), and d is the distance to the star. Since
an astronomer can determine the parallax by
comparing photographs taken in, say, June
and December and the Earth's radius is well-
established value, calculation of the distance
follows easily!

43. You can quickly demonstrate the idea behind
trigonometric parallax to yourself by placing one
finger in front of you and keeping it in that position.
Close your right eye and make a mental note of your
fingers position against the background. Now close
your left eye and view your finger again note how
the position against the background has changed!
This is the same principle behind the trigonometric
parallax method used by astronomers. Just like your
finger seems to move based on which eye is open, a
star appears to move against the background of space
due to the Earth’s movement around the Sun.

44. For stars beyond 500 light-years away the techniques for
determining distances must get more complicated because of the
limits of measuring tiny changes in a stars apparent change in
position. The first such technique, called spectroscopic parallax,
makes use of a known relationship between a stars color and its
magnitude (i.e., its brightness). A stars magnitude can be measured
in two ways: by its apparent magnitude (that is, the brightness we
measure from Earth, which is dependent not only on its temperature
but also on how far away it is from us) and by its absolute
magnitude (that is, the brightness as measured from an arbitrary
standard distance of 10 parsecs (= 32.6 light-years), which is only
dependent the stars temperature).

45. We can determine a stars absolute magnitude by
virtue of the fact that back in the early 1900s, two
astronomers, Ejnar Hertzsprung and Henry Norris
Russell, made a graph relating the absolute
magnitude of the ordinary stars in our galaxy (called
main sequence stars) to their color/temperature.
Since most stars fall on a narrow line, called the
main sequence, astronomers can deduce a stars
absolute magnitude to within about one magnitude.
Such main sequence stars represent about 90% of the
stars (including our Sun), with the other 10% being
white dwarf and red giant stars.

46. Since it is known that a stars absolute
magnitude decreases by a square of its
distance from Earth, one can simply calculate
the distance to Earth by the following equation:
m = M/ d2
where m is the apparent magnitude, M is the
absolute magnitude, and d is the distance to
Earth. Spectroscopic parallax works for stars as
far away as 150,000 light-years away just about
beyond the Milky Way Galaxy.

47. For measuring the distance to stars in other galaxies
(the Large Magellanic Cloud is the nearest at
160,000 light-years away) astronomers must
measure the magnitude of stars that vary a little in
their brightness, called Cepheid Variables. Cephied
Variables are main-sequence stars in old age just
prior to death. Such pulsating variable stars have a
period over which they go from maximum
brightness to minimum brightness and then back to
maximum brightness. In addition, the stars period is
directly related to its absolute magnitude (i.e., the
greater its absolute magnitude, the longer its period),
as discovered by Henrietta Leavitt (1868 to1921).

48. Since Cephied variable stars are rather
abundant in space, astronomers simply measure the
stars period, determine its absolute magnitude and
then, together with the relative magnitude that can
also be measured, use the equation above to
determine distance. For the sake of brevity, some of
the details about measuring very far away stars and
galaxies have been omitted. For instance, at a certain
point astronomers must include the expansion of the
Universe into their calculations of distances.
However, this discussion of the techniques used by
astronomers to determine distances should give you
a general idea of how such measurements are
possible.