SpectroscopyOfDeepSpaceObjectsUsingHomemadeDobsonianTelescope by ConleyDitsworthJr Fall2004

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SPECTROSCOPY OF DEEP SPACE OBJECTS USING A HOME-BUILT

DOBSONIAN TELESCOPE

Conley W. Ditsworth, Jr.Department of Physics, University of Illinois at Urbana-Champaign

1110 West Green Street, Urbana, IL 61801-3080

You-Hua Chu

Department of Astronomy, University of Illinois at Urbana-Champaign

1002 West Green Street, Urbana, IL 61801

ABSTRACTEver-present, the heavens have been a source of wonderment and curiosity

throughout the history of mankind. In a never-ending quest to understand the

universe we inhabit, past and present generations have devised ingenious methods

of analyzing the meager information received by Earth-bound observers.

Spectroscopy, the splitting of light into its component wavelengths, is one of themost ingenious and useful of these methods ever devised. In this paper, I explore

the feasibility of modifying a home-built telescope to perform basic spectroscopyon deep space objects using a digital camera. This involved building the

telescoping, devising a method for splitting light for analysis, then finally using

the equipment in the field to analyze the spectrum from selected astronomical

sources. Ultimately, the goal of this exercise is to examine the feasibility of designing an undergraduate astronomy course around this concept.

I. INTRODUCTION

In the larger world of scientific research, building a home-made telescope and using it toperform crude spectroscopy provides no new theories or ground-breaking discoveries, nor do Iexpect it to. Instead, my purpose in performing this work is educational. Nothing excites the

mind better than hands-on experience; by building this telescope and showing it may be used for

some basic science, all within the given time constraints, I hope to prove the viability of

designing an undergraduate astronomy laboratory course around this concept. Such a coursepromises to spark interest in students who might otherwise show no desire to pursue an

education in astronomy. As any laboratory researcher knows, assembling an experiment from

the ground up instills an understanding of the subject matter that cannot be achieved throughtraditional textbook education alone. A course in telescope assembly and use may inspire a

whole new generation of astronomers who previously had little interest in the subject.

II. GENERAL THEORY

Several options exist for the amateur astronomer who wishes to build his own telescope. Theoptics come in two primary configurations: refracting lens systems and reflecting mirrors. Each

of these also has many different methods of guiding light to the observer and ways of mountingthe completed telescope. For this project, I went with the style that is by far the most popular

among amateur astronomers: a Newtonian reflecting mirror system using a Dobsonian mount.

- 1 -



The Newtonian design, shown in figure 1, uses a primary mirror to redirect the incominglight to a smaller, secondary diagonal mirror. The diagonal then deflects the light rays

perpendicularly so that they focus on the eyepiece system where the observer can comfortably

view the resulting image.

Figure 1: Design of a Newtonian reflecting telescope

In the paraxial theory of geometric optics, light arriving from a distant source will take theform of plane waves. As illustrated in figure 2, plane waves reflecting from a parabolic mirror

will converge at the mirror’s focal point. For a spherical surface, the focal length equals half the

center of curvature as measured from the mirror’s face. Conveniently, any light source underconsideration in the night (or daytime, for that matter) sky is far enough away to be a source of

plane waves, making the parabolic reflecting mirror an ideal telescopic instrument.

Figure 2: Ray tracing of a parabolic mirror

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There are several advantages to using a mirror configuration versus a lens system, the mostimportant involving a mirror’s superior optical properties. A mirror focuses light through

reflection, whereas a lens uses refraction. According to Snell’s law, a lens changes the path of a

light ray according to r r ii nn θ θ sinsin = , where n represents the index of refraction of the

medium in which the light is traveling, and θ represents the angle the incoming or outgoing light

makes with the normal to the lens surface. The i and r subscripts indicate the incident andrefracted quantities, respectively; figure 3 gives a pictorial representation of refraction through aconverging lens.

Figure 3: Refraction through a converging lens for parallel light (i.e., plane waves)

The principle difficulty in using lenses arises from the frequency dependence of the lensmaterial’s index of refraction. A quantum mechanical treatment of the dispersion of

electromagnetic waves through a medium of N contributing electrons per unit volume gives the

following dispersion relation:

⎟⎟ ⎠

⎞⎜⎜⎝

⎛

−+=

22

00

2

2 11)(

ω ω ε ω

e

e

m

Nqn ,

where n is the index of refraction, qe is the charge of an electron, ε0 is the permittivity of free

space, me is the mass of an electron, ω0 is the electron’s resonant frequency, and ω is the

frequency of the incident radiation (Hecht 70). This frequency dependence leads to theundesirable property of lenses known as chromatic aberration, in which the focal length of the

lens changes for different colors of light, causing blue light to converge at a shorter focal length

than other colors. This effect can be partially (but never completely) eliminated through the useof a complicated lens system dubbed an achromatic lens, but already the system grows more

complicated (and expensive) than desired for an amateur telescope.

Mirrors, on the other hand, do not suffer chromatic aberration since they work on the

principle of reflection. The focal length depends only on the radius of curvature, so all light rayswill converge at the same point regardless of wavelength. There are other so-called third-order

aberrations, such as spherical aberration, coma, astigmatism and distortion, that arise from higherorder terms in the binomial expansion used in the derivation of the paraxial approximation, but

- 3 -



these properties are relatively unimportant in the choice of optics used for building a telescopesince they are commonly shared by both lenses and mirrors. These aberrations can be minimized

by altering the shape of the mirror or lens to restore the desired convergence.

The next major advantage of reflecting telescopes is portability. Figure 4 details thenecessary configuration of a lens system for a refracting telescope. In its simplest form, this

telescope requires two lenses: the primary objective and the eyepiece. To work properly, thelenses must be spaced a distance equal to the sum of the two lens’ focal lengths (actually, it’stypically spaced slightly off this distance to reduce noise effects, i.e., imperfections and dirt on

the objective being focused into the eyepiece and interfering with the desired image, but that’s

unimportant to this comparison). Contrasting this configuration to that in figure 1 for the

reflecting telescope, the refractor obviously necessitates a much longer tube than the reflectorsince the reflector tube depends on only one focal length, that of the mirror. Even then, the

Newtonian design deflects the light at a right angle prior to reaching the mirror’s focal length, so

the tube length doesn’t even have to accommodate the entire focal length of the mirror. Thisdifference allows reflecting telescopes to be built with relatively large primary mirrors while

maintaining a size conducive to easy transportation.

Figure 4: Optics of a refracting telescope

Finally, reflecting telescopes cost much less to fabricate. This primarily stems frommanufacturing differences between lenses and mirrors. Since the light passes through a lens,

creating as perfect a lens as possible is critical to limit distortions in the image. Minor

imperfections, such as bubbles and small changes in the refractive index, can drastically alter theconvergence of the plane waves at the focal plane of the eyepiece. Mirrors, on the other hand,

only require perfection on the reflecting surface. Since this surface is typically the top side of the

mirror, the inside is relatively unimportant and any bubbles or other imperfections will have noeffect on the optical properties. This makes manufacturing mirrors much less expensive than

lenses, and the difference in price for the same aperture size can become several thousand dollarsfor larger diameters.

As far as disadvantages to reflecting systems, only one comes to mind: intensity loss due to

light blocked by the secondary mirror. The diagonal mirror’s position above the primary causes

some loss in the light intensity of the final image since it blocks some of the reflecting surface.

However, this loss in brightness is pretty minor; for my telescope, I chose an 8” diameter mirror,and the secondary subtends a circular cross-sectional area of approximately 1.5” in diameter.

This means the secondary blocks a fraction of the reflecting surface equal to:

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%52.30352.0"8

"5.122

==⎟ ⎠

⎞⎜⎝

⎛ =

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ =

p

s

p

s

D

D

A

A

Therefore, only about 3.5% of the incoming photons are lost due to this geometry, making this a

pretty insignificant disadvantage for the reflecting system. There are ways to counter even thissmall amount of loss; the mirror can be arranged so that it focuses light off the central axis,

allowing the secondary mirror to be placed outside the line of sight of the primary, but this

requires high precision in designing and assembling the telescope, and the minimal loss doesn’t justify the additional work involved.

Since the advantages to reflecting systems far outweigh those of refractor telescopes, my

choice of optics clearly makes sense. The next step, then, is to gather the necessary materialsand build the telescope.

III. BUILDING THE TELESCOPE

It would be senseless to try and design the telescope from scratch; that would be tantamountto “reinventing the wheel” as the old saying goes. Instead, amateur astronomers have been

refining and perfecting the art of home-built telescopes for several decades, and many populardesigns are freely available. I chose one of the most popular, an easy to build and operate style

called a “Dobsonian” after its inventor, John Dobson, also co-founder of the San FranciscoSidewalk Astronomers Association (see the references for links to the Sidewalk Astronomers and

the plans for the Dobsonian telescope). Figure 5 is an illustration of the design of the Dobsonian

taken directly from the instruction plans.

Figure 5: Basic design of the Dobsonian telescope; part letters indicate pieces on the plywood cut pattern

Assembly of the telescope requires three main steps: 1) building the tube assembly (typically

referred to simply as the “telescope”), 2) constructing the body, or the “rocker box,” to hold andposition the telescope, and 3) aligning (“collimating”) the mirrors and all optical components.

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Building the telescope tube is the most time-consuming and sensitive part of the entireproject. Accurate measurements are necessary to ensure the incoming light is properly focused

to converge at the focal plane of the eyepiece. Aside from the optical components, construction

of the tube requires only the tube itself, a small piece of plywood for the tailgate and blocksholding the primary mirror, and collimation bolts for the tailgate. The tube turned out to be the

most difficult component to find; I ended up having to order it online since nobody locally hadany cardboard forms that were 10” in diameter. The material used is called “Sonotube” (note:Sonotube is a brand name) and is primarily used for concrete forms in the construction industry.

It’s a very sturdy ¼” thick cardboard tube that is well-suited for telescopes since it is light-

weight and doesn’t warp under changing temperature extremes. The tube is painted gloss black

on the outside and flat black on the inside; black is the preferred color because it keeps the tubecooler, thereby minimizing thermal currents within the tube that can distort the light rays,

warping the final image.

The critical part in preparing the tube is finding the position for drilling the eyepiece hole.As previously discussed, the total distance from the face of the primary mirror to the diagonal

and then from the diagonal to the eyepiece must equal the true focal length of the primary mirror

to enable the observer to focus an image in the eyepiece (see figure 1). To accomplish this, thetrue focal length of the mirror must be determined. For my telescope, I purchased an 8” f/6

mirror, where the f/# property is the ratio of the focal length to the mirror diameter.

Theoretically, therefore, the focal length of my mirror should be given by multiplying the f/# by

the mirror diameter; in this case the focal length should be 48”. However, manufacturingprocesses don’t necessarily provide a perfectly-formed mirror, and the true focal length may be

off as much as a couple inches. The way to determine the true focal length is to use the

geometrical property that the focal length is one-half the radius of curvature. Examining the ray-tracing in figure 2, a light source placed at the center of curvature will return an image to the

same location. Armed with this knowledge, I used a small flashlight and a piece of cardboard toact as a screen; placing the mirror against a wall, I positioned the cardboard so it was next to the

flashlight’s filament and moved them together back and forth in front of the mirror until a perfect

image of the filament formed on the cardboard. I then measured this distance to be 93.5”;dividing this distance by two provided a true focal length for my mirror of 46 ¾”.

Figure 6: Finding the location to drill the eyepiece hole

Knowing the true focal makes the rest of the procedure fairly simple; I drilled the eyepiece

hole at (what I thought) was the proper length and mounted the diagonal mirror so that it lined up

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with the eyepiece hole. Later, at the completion of most of the work, I found that I hadmistakenly placed the eyepiece about 5” short of the true focal length and had to re-position it.

The final step in the process is making the tailgate and mounting blocks needed to hold the

primary mirror in place at the base of the tube. Figure 7 shows the basic plan for this; thetailgate is simply a piece of plywood with three holes drilled into it for the collimation bolts,

which are used to make small adjustments to the positioning of the mirror so that the lightconverges properly to the eyepiece. To protect the back of the mirror, a piece of cardboard is cutand placed over the end of the collimation bolts and small pieces of masonite are then glued to

the cardboard directly over the ends of the bolts.

Figure 7: Tailgate assembly (left) and end view of tube showing the mirror mounting blocks

For some unknown reason, the four mounting blocks shown in the right diagram in figure 7

turned out to be the most troublesome and time-consuming part of the entire project. Theseblocks are nothing more than four pieces of ¾” plywood cut to 1”x 4”, painted flat black and

then positioned as shown in the diagram. I attached rubber furniture glides to these blocks; these

glides serve to hold the mirror in place so that the mirror edge and front face is protected from

damage (figure 8). The difficulty came in getting these four blocks to line up properly inside thetube. It took several attempts and re-cutting these pieces three times before I was finally able to

get a perfectly aligned mount for the mirror. I checked the alignment by placing the mirror onthe mounts; if it wobbled the alignment was off. I also verified leveling to ensure the mirror

wasn’t mounted crooked, which would make aligning (collimating) the primary and diagonal

mirrors difficult.

Figure 8: Mirror mounting blocks

- 7 -



With the telescope complete, the rocker box was next on the construction list. This partconsisted mainly of carpentry work, cutting and assembling different pieces of plywood to make

the configuration shown in figure 9. To control azimuthal motion (i.e., left-to-right) of the

completed telescope, the box and ground board are constructed separately. The two pieces areconnected using a ½” lag bolt, but to ensure smooth operation, several pieces of Teflon were

attached to the ground board. On top of these Teflon pieces I positioned one of my oldphonograph records (it was nice to finally find a use for one of them!); this combination allowsthe rocker box to rotate smoothly on top of the ground board while not being so loose that the

telescope moves too freely. Figure 10 illustrates the assembly of the rocker box and ground

board.

Figure 9: Rocker box and ground board assembly

To hold the tube in place on the rocker box, I cut two cradle boards with triangular notches at

about 60 degree angles and attached them as shown in the right sketch of figure 10. A simplesquare box, also shown in the right diagram of figure 10, attaches to the telescope tube so that the

center of mass of the assembly is centered over two 6” diameter circular pieces of plywood. I

positioned the cradle boards at a height that allows the telescope to easily rotate into a verticalposition with a couple inches clearance from the bottom of the rocker box. For elevational

motion (i.e., up and down), I nailed two pieces of Teflon onto each of the notches in the cradle

boards at the points of contact of the plywood disks. The Teflon allows the telescope to rotateeasily, yet maintains sufficient friction to keep it from rotating freely. Getting the telescope

positioned in the tube box so that the center of mass is properly placed over the pivot helps

ensure the telescope doesn’t move after it’s been aimed at an object in the sky.

I made one modification to this procedure to improve the final product: instead of only using

two plywood disks on the tube box, I placed one on every side for a total of four. Thismodification allows me to rotate the telescope by 90 degrees in the rocker box if desired for

more comfortable viewing of objects located in awkward positions in the sky. Other than that,the final design matches the instructions and diagrams as given in the Sidewalk Astronomers’

website.

- 8 -



Figure 10: Assembly of rocker box to ground board (left) and rocker box with cradle boards showing

positioning of the tube box that holds the telescope in place (right)

To complete the telescope, the optics must be properly aligned to get an image to form in thefocal plane of the eyepiece. Rather than building everything from scratch, which the instructions

make possible, I purchased the optical components in a kit from e-Scopes (formally known as

Coulter Optical; website http://www.e-scopes.cc/). The kit consisted of the primary and

secondary mirrors, a 50mm Plossl eyepiece, a 1 ¼” mounting tube for the eyepiece, the spiderassembly for mounting the diagonal mirror, a finder scope for quick location of objects, and a

section of tube guard to fit over the end of the tube. The mounting block on the spider assembly

that holds the secondary mirror came equipped with five plastic screws that move the diagonal inall directions for proper alignment. The first step in collimating the mirrors involves adjusting

the screws (with the primary mirror and tailgate removed) so that, from the eyepiece hole, the

entire bottom of the tube appears perfectly centered in the diagonal.

Figure 11: Aligning the primary mirror

Once the secondary is properly lined up, a small decal (I used a paper hole reinforcementsticker) gets placed exactly in the center of the mirror. This sticker can remain in place

permanently; it will not affect the optical qualities of the mirror since it is positioned below the

- 9 -



shadow of the secondary mirror and will not focus into the eyepiece. The mirror and tailgate arethen replaced at the bottom of the tube. To get as perfect an alignment as possible, I used the

eyepiece tube as a bull’s-eye; imagine the end of the tube closest to the observer and the opposite

end inside the main tube as two concentric circles. With the eyepiece removed, the eyepiecetube, spider assembly and primary mirror will appear as in figure 11. By making small

adjustments to the collimation bolts on the tailgate, the mirror is slowly repositioned until thedecal becomes exactly centered in the bull’s-eye formed by the eyepiece tube. When the decal iscentered, the telescope is ready for use!

The final step in the assembly process is entirely aesthetic. With everything now operational,

the telescope can be sanded and painted or stained to taste. Prior to sanding, I used wood putty

to completely fill in any gaps and defects in the plywood (and my rusty craftsmanship). At thetime of this writing, the finishing work is partially complete; I still have to complete sanding of

the rocker box and staining the entire thing, but all the puttying and most of the painting is done.

Since I had originally placed the eyepiece in the wrong position, I also need to patch the originalhole, which I can easily accomplish by using the section I cut out from the new location and

patching it into the old hole using automotive bondo. Afterwards I plan to repaint the entire tube

with a final coat of gloss black. Then, the telescope will be completely finished.

IV. MODIFYING FOR SPECTROSCOPY

The first goal of this project involved construction of the telescope; the next goal is to modifyit so that it can be used for spectroscopy of deep-space objects. The concept is relatively simple;

a method of separating the incoming light into its spectral components at the eyepiece hole needs

to be developed. The separated spectrum then gets captured on a charged coupled device (CCD)assembly in a common digital camera; the resulting digital images can then be analyzed as

desired.At this point I need to explain that this section of the project, and the remaining sections, still

need to be completed. Telescope construction filled the entire time allotted for the project,

delayed somewhat by poor weather conditions that kept me from testing and perfecting thetelescope optics with enough time left for the actual spectroscopy part of the experiment. All is

not lost, however, since the project time only consisted of half the semester and the primary goal

is to see if this work can be feasible for a full semester course. I plan to continue working on thisproject throughout the winter break to fulfill the original goals.

Three primary means exist to split light for spectral analysis: prisms, diffraction and

reflection gratings. A prism uses refraction according to Snell’s law to separate light; this works

because of the frequency dependence of the index of refraction (figure 12). A reflection gratingseparates light using a system of angled reflecting surfaces (figure 13), and a diffraction grating

works on the principle of Fraunhofer diffraction through multiple slits to form the component

spectrum. For simplicity, I decided upon diffraction film as the method of choice for myattempts at separating light. Figure 14 gives a good representation of ways to separate light for

capturing spectral images in a camera; the image using a prism shows why I decided against that

method. Constructing a mount to hold the prism and camera configuration near the telescope’seyepiece seemed to be a daunting task, especially since the prism would need to be accurately

adjusted to aim the spectrum directly into the camera’s aperture. The reflection grating, although

a popular method of performing both amateur and professional spectroscopy, also seemed more

- 10 -



complicated than I cared to attempt since it involves reflection and would require another systemof mirrors to direct the light into the camera.

Figure 12: Wavelength-dependent dispersion of light through a prism

Figure 13: Wavelength-dependent dispersion of light by a reflection grating

Figure 14: Photographing spectra using diffraction gratings and prisms

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There are two main considerations to make in choosing the size of diffraction grating film to

use: resolution and dispersion. Both of these concepts are intimately related; a higher resolution

spreads the spectrum out wider so that lines closer together may be resolved, but in the processlines that are farther away will move completely out of the field of view due to dispersion. The

dispersion of a grating is given by:

θ λ

θ

cosd

m

d

d = ,

where m is the order of the spectral line, d is the spacing between the lines in the grating, and θ is

the angle the line makes with the central axis. This formula is derived by differentiating the

grating equation: λ θ md =sin . The resolution of a grating is given by:

Nm R =∆

=λ

λ ,

where λ ∆ is the difference in wavelength from the central wavelengthλ and N is the number of

illuminated slits in the grating; note that N = width of illuminated region/slit spacing d , so the

resolution formula may easily be written as a function of the slit spacing.

Obviously, the choice of diffraction grating to be used depends on the intentions of theobserver. For high resolution spectra, for instance to separate closely-spaced lines associated

with hyperfine energy levels in elements, gratings with a large number of slits would be

necessary. But if instead the observer wished to sample the entire first order spectrum of anobject the resolution, and therefore the dispersion, must be reduced, necessitating a grating with

a smaller number of slits. My goal is to sample a wide variety of spectra, so I will attempt to

construct numerous diffraction filters at several different values of the slit spacing.To make a feasible mechanical system for using the diffraction filters I plan to modify

several normal camera filters by mounting pieces of diffraction grating film into them; these

filters should then mount simply to the camera or telescope eyepiece. For placing this set-up on

the telescope, I found a universal camera mount at Orion Telescopes and Binoculars (availableonline at http://www.oriontel.com); figure 15 shows a picture of the mount from Orion’s website.

This very simple device attaches directly to the eyepiece with a clamp and to the tripod adaptor

on the camera. It is designed so that it is simple to adjust and the camera easily slides back andforth so the image should be fairly simple to focus into the camera.

Figure 15: Universal camera mount

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Probably the most important choice to make in this whole modification is the camera itself. I

did careful research and found that there are several critical features to look for. The main

features necessary are manual shutter and aperture settings, the ability to turn off the flash, aremote control (which I still have to purchase), a liquid crystal display (LCD) screen and optical

zoom settings. I found that amateur astrophotographers have a special fondness for the NikonCoolpix line of cameras, especially some of the older models; after some searching I was able tofind a factory refurbished Nikon Coolpix 995. In addition to the other features listed, it also has

a wonderful noise reduction mode for long exposures. In this setting, the camera adjusts for the

dark current interference inherent in CCD systems by taking two photos, first the normal

exposure and then an additional exposure with the shutter closed. The camera subtracts the dark current image from the first picture to reduce the noise. I was thrilled to find such a popular

camera; unfortunately, however, it appears to have been incompletely refurbished and refuses to

accept any memory cards I place into it, so I am in the process of returning my new purchase forwarranty work and hope to have it back for use before too long.

Figure 16: Nikon Coolpix 995 digital camera

After I am able to construct the diffraction grating filters and my camera returns in peak operating condition the telescope should be ready to provide spectral images of deep space

objects.

V. ANALYZING THE SPECTRA

The question naturally arises as to the use of these digital spectral images once they areobtained. Spectral lines form in several different ways and therefore provide a wealth of

information about their source. From these images, I hope to be able to perform a chemical

analysis on the objects in question, and, if the system works exceptionally well, I would like touse Doppler effects to derive mechanical information about the source’s radial velocity and

possibly its rotational velocity.The light a telescope receives can be formed in a few primary manners as shown in figure 17.

A hot body, such as a star, emits light in a continuous spectrum that depends on the source’stemperature according to the Planck blackbody function:

1

2

)(2

3

−=

kT h

e

ch

T Bυ υ

υ

,

- 13 -



where B is the intensity at a frequency υ, h is Planck’s constant, c is the speed of light, k isBoltzmann’s constant and T is the temperature of the blackbody. Accordingly, any hot source

will have a peak intensity at a certain frequency, or wavelength, that depends on its surface

temperature. A simple way of determining that peak wavelength is through Wien’s displacementlaw:

T K cm ⋅= 290.0maxλ

Wien’s law provides the first simple use of the obtained spectra: by determining the most intensewavelength in a continuous spectrum, the surface temperature of the object can be derived.

Figure 17: Astronomical sources of spectra

Usually, the light we receive passes through some intermediate material, which may be dust,planetary nebulae, or interstellar gas clouds. As figure 17 shows, the light interacts with atoms

and molecules in the interstellar medium, producing either absorption or emission spectra. When

the observer’s line of site is along the path connecting the hot source and absorbing molecule, wereceive an absorption spectrum. Absorption occurs when the energy carried by a photon

coincides with the energy spacing between energy levels of an electron; the electron will

preferentially absorb these photons and excite to a higher energy level, destroying the photons in

the process. The absorption spectrum therefore resembles a continuous spectrum, only withcertain wavelengths missing. The electron will not, however, remain in the excited state long,

but will decay back to its ground state and in the process release another photon with the same

wavelength as the one absorbed. In this case we receive an emission spectrum where instead of acontinuous spectrum the result is series of lines at specific wavelengths.

Since the emission and absorption lines correspond to energy spacings in atoms and

molecules, a mathematical description is much more involved and requires a quantum

- 14 -



mechanical treatment; in some cases even hyperfine energy levels must be considered. Forhydrogen, the simplest possible case, the Rydberg formula gives the emission lines as:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−=

22

11

i f nn R

λ ,

where R is the Rydberg constant and the values of n represents the initial and final energy states

of the electron emitting the photon. Of course, since this only represents hydrogen, and alsoignores any energy differences in angular momentum and spin states, it’s of little practical use

for this experiment. Instead, astronomers rely more upon laboratory work providing a catalog of

characteristic spectra associated with certain elements with which to compare observed spectra.Figure 18 provides a sampling of a few spectra associated with some common astrophysical

elements.

Figure 18: Sampling of emission spectra from several elements

A chemical analysis of all three of these types of spectra was the primary goal I hoped toaccomplish with this project, and if all works well this may still be possible.

- 15 -



In addition, if the chemical analysis works well and I’m able to achieve sufficiently highquality spectra, I hope to next attempt to derive the radial velocity of some deep space objects

using the Doppler effect. According to the Doppler effect, relative motion between two bodies

causes a shift in wavelength in the light received.

Figure 19: The Doppler effect

An object moving towards us causes a shortening in the wavelength of light it emits, called a“blueshift,” while an object moving away lengthens the wavelength, known as a “redshift.” The

nonrelativistic form of the Doppler effect is given by:

c

v=

∆

λ

λ ,

where emitted observed λ λ λ −=∆ , v is the radial velocity of the source and c is the speed of light.

The shift is pretty easily detected since the spectrum received will still appear like those seen in

figure 18 for a certain element, only the lines will appear uniformly displaced to the left or right

of where they would be if emitted by an element or molecule at rest with respect to Earth. Thenonrelativistic form suffices for the purposes of this experiment since a light source will only

move at relativistic speeds with respect to Earth if it is at cosmologically significant distances,

- 16 -



and the level of detection required for that kind of object is far beyond the expected capabilitiesof my simple telescope.

There are a couple caveats to this Doppler analysis. The first is that the Doppler effect only

reveals radial motion; the object will almost certainly not be moving directly towards or awayfrom us, but will have both radial and transverse velocity components. The Doppler effect will

detect the radial velocity, but other methods must be employed to detect the transverse motion(such as parallax if the object is close enough). The other item to note is that relative motion isnot the only way to cause a Doppler shift in a photon. Gravity and the expansion of the Universe

are also key sources of Doppler shifts. Photons being emitted from deep within a gravitational

well, such as a large star, a compact object, or maybe near the center of a galaxy, will experience

a redshift as they climb out of the potential well. The expansion of the Universe causes an

additional velocity effect in very distant objects according to the Hubble Law: , where

H

d H v 0=

0 is the Hubble constant (currently known with somewhat questionable accuracy) and d is the

distance to the object. Since this Hubble velocity component is due to the expansion of theUniverse, where the object is being carried along with the flow of spacetime rather than the real

motion of the object, it is not considered part of the true radial velocity. For the purposes of this

project, I expect the Hubble flow contribution to be insignificant since my telescope is unlikelyto detect objects at cosmologically significant distances, but it is possible that gravitational

redshifts may cause some interference. For anything I could detect with a home-built telescope,

however, the majority of any Doppler shift is likely due to the object’s radial motion relative toEarth.

One final possible use for these spectra, assuming all else went better than could ever be

hoped for, is to try and determine the rotational velocity of some selected objects. Of course, due

to the limitations of a home-built telescope, these would have to be objects large enough for thetelescope to be able to image the extreme left and right edges separately (possibly with the

addition of a slit to differentiate portions of the object); potential sources would be the Sun, the

Moon, and maybe the Andromeda galaxy or some other extended deep space object. The idea is

that one side of the object will be moving towards us, and therefore is blueshifted, and the otheraway from us and redshifted. By analyzing the separation between the shifts from eitherextreme, the relative radial motion can be eliminated, leaving the object’s rotational rate.

Obviously, this is a much more complicated procedure than either of the two previous analyses,

so I’m not too optimistic that it will be successful.So, with the telescope completed, prepared for spectral research, and the appropriate physical

theory in my arsenal, the next step is to actually identify some potential deep space targets and

start collecting data!

VI. SELECTING SOURCES

Choosing suitable targets for this project is as important as any of the previous steps. Since Iam dealing with a home-built telescope there are many complications to consider. First and

foremost is the long exposure time that would be required to get a good spectrum. Imaging

objects in the dark requires lengthy exposure times, as long as several minutes depending on thebrightness of the source. Unfortunately, the Earth doesn’t cooperate with our desires but instead

continues its steady rotation in its eternal repetition of the cycle of day and night. While deep

space objects are so vastly far away that their own motion is virtually undetectable under normalconditions, the Earth’s rotation causes all objects in the sky to appear to rotate in a direction

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opposite the Earth’s. Professional observatories have mechanical guidance systems thatcompensate for the Earth’s movement, and commercial telescopes can be purchased with similar

options, but for a home-built Dobsonian telescope the required components, while available, are

extremely expensive; with a student’s budget, it may as well be considered impossible.However, there are other ways to compensate for the Earth’s stubborn defiance of our objectives.

The apparent motion of an object in the night (or day) sky depends strongly upon itsdeclination, which is the angle it makes on the celestial sphere with respect to the celestialequator (which is simply the Earth’s equator extended into space). Referencing the geometry

shown in figure 20, any object in space is considered a point on the celestial sphere; for

simplicity, this sphere is assumed at an arbitrary unit distance. The object’s velocity is given by:

srad xhr shr T

Rv / cos1027.7cos / 360024

2cos

2cos 5

δ δ π

δ π

δ ω ω −=

⋅====

Figure 20: Apparent motion of a deep space object

Therefore, an object located at the celestial equator will move in the sky with an apparentangular velocity of 7.27 x 10-5 radians/second, but the velocity slows as the declination

approaches the North Celestial Pole (NCP) at a latitude of 90 degrees, at which point the velocity

is zero (of course, this also occurs at the South Celestial Pole, but since I don’t plan on headingtowards Australia anytime soon this point is irrelevant). The obvious solution to the exposure

time dilemma is to choose objects located as close to the NCP as possible.

Another way around this difficulty is to limit the required exposure time by choosing brighterobjects. The visual magnitude of astronomical objects is given by the formula

⎟ ⎠

⎞⎜⎝

⎛ −=−=

24log5.2log5.2

R

L F m

π ,

where F is the photon flux received at Earth, L is the luminosity, or power output, of the source,

and R is the distance from the source to Earth; note that brighter objects will have a smaller

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visual magnitude. This formula implies that an object has to either have an incredible poweroutput or be really close in order to have a bright enough magnitude to positively affect the

required exposure time. To give the formula some perspective, under perfectly dark skies for a

person with perfect vision, the limit of human resolution is a magnitude of about six. For atelescope, the limiting magnitude (in general, not counting atmospheric effects) is given by

for an 8” diameter mirror. This limit is for visualobservation; for photographic purposes the limit would typically be a couple magnitudes higher.

( ) 0.14log55.7 =+= cminapertureml

Theoretically, considering the above arguments, the optimal situation is to choose bright

objects close to the NCP. Realistically, deep space objects outside of our solar system will not

be especially bright, and objects within our solar system are not going to be close to the NCP.My goal is to sample as wide a variety of objects as possible; therefore, my objective is to find

deep space objects near the NCP with a visual magnitude no greater than approximately 8. For

local objects, I plan to take a solar spectrum, lunar spectrum and those of a couple planets,

probably Venus and Jupiter since they are the brightest. My expectations are that all local solarsystem objects will result in something close to a continuous solar spectrum since the planets and

their moons primarily shine from reflected light. In addition to the solar spectrum, there may be

some identifiable absorption lines due to the chemical compositions of these objects at theirsurfaces or within their atmospheres.

The selection of extra-solar objects is more subjective. Since I haven’t yet performed this

part of the project, I’m not sure of the limitations of my equipment. However, for the purposesof this paper I have selected a couple deep space objects as potential targets for my future

observations, a galaxy and a nebula.

The first object is the spiral galaxy M81 (the M stands for Messier, a standard catalog for

astronomical objects), known as Bode’s galaxy. Located at a declination of 69° 04’ with a visualmagnitude of 6.9 and apparent dimensions of 21x10 arcminutes, Bode’s galaxy should be well

within the capabilities of my telescope.

For my nebula, I chose NGC 6543, more popularly known as the Cat’s Eye Nebula. At a

declination of 66° 38’ and visual magnitude of 8.1, the Cat’s Eye will likely prove a moredifficult target, but it’s properties are easy to verify since it’s a favorite observational subject.

VII. RESULTS

Obviously, the project as a whole is incomplete and therefore the results are inconclusive.

The first part of the project, building the telescope, was successful. I managed to build and test a

Dobsonian reflecting telescope within half a semester, the time constraints of the project, butdidn’t have enough time, or cooperation from the weather, to actually use the telescope for its

intended purpose before the project was due.

However, during my research I have learned that it is possible to perform spectroscopy at an

amateur level. Although I didn’t find anyone who had practiced it quite the way I’m proposing, Ihave found several who use home-made spectrometers in conjunction with digital cameras to

take very good spectral images. Figure 21 shows a solar spectrum taken with a digital camera I

found on an amateur website; the hydrogen and helium absorption lines from elements in thesolar atmosphere are clearly visible.

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Figure 21: Sample solar spectrum captured with a digital camera (Gavin)

Although incomplete, there’s still time for success in the primary goal of this experiment.

Since the work to date has taken only half a semester, the idea of turning this project into anastronomy laboratory course is definitely feasible. More work will show whether spectroscopy

is also a reasonable goal, but even if it doesn’t work out, there’s plenty of other uses for a home

built telescope. Spectroscopy was more of a personal curiosity; for an undergraduate course, the

goal could be at a simpler level, like honing observational skills, classifying stars or maybeastrophotography. Therefore, overall, I believe this project was a success!

VIII. REFERENCES

1. Carroll, B., Ostlie, D. 1996, An Introduction to Modern Astrophysics, Addison-Wesley

Publishing Company, Inc.

2. Cash, R., Complete Plans for Building a Dobsonian Telescope, Available

http://members.aol.com/sfsidewalk/cdobplans.htm

3. Fowles, G. 1989, Introduction to Modern Optics, 2nd Ed., Dover Publications, Inc.

4. Gavin, M. 2000, Spectroscopy – A Practical Beginner’s Guide, Available

http://www.astroman.fsnet.co.uk/begin.htm

5. Griffiths, D. 1995, Introduction to Quantum Mechanics, Prentice Hall.

6. How Stuff Works, Available http://science.howstuffworks.com/

7. John Dobson: The Official Site, Available http://www.johndobson.org/

8. The Many Colors of Sunlight , Available http://www.phy6.org/stargaze/Sun4spec.htm

9. The Physics Classroom: Refraction and the Ray Model of Light , Availablehttp://www.glenbrook.k12.il.us/gbssci/phys/Class/refrn/u14l1a.html

10. Students for the Exploration and Development of Space, Available http://www.seds.org/

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SpectroscopyOfDeepSpaceObjectsUsingHomemadeDobsonianTelescope by ConleyDitsworthJr Fall2004

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