Methods of Observational

Astronomy

Mercado, Emmar Joy P.

Bachelor of Elementary Education

ASTRONOMY

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.

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.

Optical Telescope

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)

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

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

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.

Refraction of light

through a medium

like glass or

acrylic.

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.

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.

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.

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.

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.

The principle

of reflection.

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.

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:

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.

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.

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.

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.

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.

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.

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.

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.

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.

The Hubble Space

Telescope being

serviced by NASA’s

Space Shuttle

(Courtesy: NASA)

Spectroscopy and Stars

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.

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:

• Spectra come in several types:

1. Continuous spectra: a smooth gradient of

electromagnetic radiation without any gaps

e.g., the spectrum of incandescent solids.

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.

3. Emission spectra: a spectrum that

represents all the wavelengths emitted by

atoms or molecules

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

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!

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).

Measuring Distances to Stars

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

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

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!

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.

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).

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.

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.

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).

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.