Download Do It Yourself Telescopes

ASTR 1030
Fall 2005
Kyle Willett
Joey Espejo
DIY Telescope
SYNOPSIS: We will be assembling and using refracting telescopes that you will be able
to take home and use after the completion of our lab. We will be using them to observe a
variety of objects, as well as gaining familiarity with celestial coordinates.
EQUIPMENT: Telescope kit, resolution targets, planetary images, setting circles,
equatorial mounts
LENGTH: One lab period, plus some night time on your own.
In the previous optics lab, we discussed the basic principles of how telescopes are made
and what happens to the light as it travels from its original source all the way to your eye.
In particular, we examined both refracting (bending the light using lenses) and reflecting
(bending the light using mirrors) telescopes and looked at the various advantages and
disadvantages of each design.
The exercises in this lab are intended to show you that it doesn't HAVE to be as difficult
as many of you remember from assembling your Cassegrains – if you're willing to
sacrifice some space (having a longer telescope) and gathering power, excellent small
telescopes can be made from relatively simple materials without the alignment headaches
that arise with a Cassegrain.
This is also intended to give you some historical perspective on early astronomy – the
telescopes that we will be assembling and using are very similar to the ones used by
Galileo in his early explorations of the solar system and the night skies. Galileo, while he
was not the first to invent the telescope (contrary to popular belief), used a similar
refracting telescope with which he made the first observations of the largest Jovian
satellites, the phases of Venus, and resolving clusters into individual stars. His telescope
used plano-convex and plano-concave lenses (similar to those used here) and had an
objective focal length of about 30-40 inches. Our telescopes will be smaller, but the
quality of the lenses supplied really does more than make up for what Galileo worked
with! (and hey – he revolutionized astronomy as we know it. No pressure, though).
I. Assembly
The kits we have provided include all parts and can be assembled without the need for
glue or adhesives of any kind. You should have a set of two sliding cardboard tubes (one
within the other), and a small plastic bag containing:
1 red plastic cap
1 cardboard washer
1 large lens (objective)
1 small lens (eyepiece)
1 foam eyepiece holder
1 cardboard space (small tube)
Note before starting – DO NOT touch either lens with your bare hands, as
fingerprints are extremely difficult to get off the lenses! Use a piece of cloth or a
tissue at all times.
Lay the red cap on the table with the lip of the cap downwards (open end up). Place your
cardboard washer inside the cap (this will be what keeps the objective from getting
scratched, as well as defining our aperture size). Holding the objective BY THE
EDGES, look at your lens edgewise. You should see that one side is curved outwards
and that the other is flat – this is a plano-convex lens. Plano-convex lenses are used to
reduce geometrical aberrations. The curved side should face the outside of the telescope;
the flat side should be on the inside. Still holding it by the edges, place it in the cap so
that the curved edge is downwards.
Insert the larger end of your two sliding cardboard tubes into the cap – it should fit snugly
and keep the objective firmly in place.
Lay the black foam eyepiece holder on the table and push your tiny cardboard spacer into
the foam so that it is flush with the table. Using a piece of cloth or tissue, push your
eyepiece into the foam and resting on the spacer so that the curved side faces upwards.
Now, push the eyepiece holder into the smaller end of the cardboard tubes so that the
curved side faces inside the tubes (ie, the flat side of the eyepiece should be closer to your
eye and the cardboard spacing should be in between). Your telescope is complete!
II. Solar Observing
Scientists for many years have been looking at the sun through a variety of scopes
(although not with their own eyes!) in order to study solar behavior. While most images
taken of the sun nowadays are multi-wavelength (the Sun emits detectable light from Xray all the way through radio), visual images are especially useful for viewing sunspots
and prominences like flares and coronal mass ejections.
The main features we expect to see on the Sun with our telescope are sunspots.
Sunspots are caused by variations of the magnetic field lines within the Sun. Although
the causes are not fully understood, we do know that at certain points the magnetic field
lines of the Sun get “tangled” due to differential rotation of the various layers of the Sun.
If a field line breaks the photosphere of the Sun, then energy flux from the interior of the
Sun will go down and the temperature will decrease. The nominal temperature of these
sunspots is about 5000K – still blindingly hot! (they only look darker compared to their
surroundings at ~5770K). Sunspots come in cycles of 22 years – as of 2005, we’re
nearing an intensity minimum, unfortunately, although a few should still be visible.
Solar observing is normally done with special solar telescopes like our heliostat
here at SBO, where the image is projected onto a screen (rather than looking directly at
the source). Simple refractors like the one we've just assembled, though, can also be used
to observe the sun – we can spare our own eyes from looking at the blinding solar
radiation using a method called eyepiece projection.
CAUTION! NEVER LOOK AT THE SUN THROUGH THE TELESCOPE!!!
II.1. Take your telescope and a sheet of white paper out to the observing deck. Focus
your telescope on a distant object (such as the crest of the mountains or a far-off
building). Make a pencil mark on the smaller tube of your telescope so that you have a
reference the next time you want to focus.
II.2. Place your sheet of white paper on the ground (or you can tape it to a wall if the
Sun is approaching the horizon). Align your focused telescope with the sun until you
see a projected image of the sun on your paper – try to get a nice, crisp edge. Move
the telescope back and forth along your line of sight to the Sun. Does the
sharpness/focus of the image change? What about the image size?
II.3. Once you have the Sun located and focused, have one member of your group
trace the Sun on your paper, preserving its size and shape. Be sure to include any
individual features that you notice, such as sunspots or flares.
II.4. Estimate the size of the sunspots you sketched using your projection in terms of
solar diameters. The diameter of the Sun is approximately 1.39 x 10^6 km. What is
the diameter of the sunspots that you measured in Earth diameters? (Surprised?)
II.5. (for afternoon labs only) Sunset around November 25th takes place at about 3:30
pm MST. Use your eyepiece projection method to view the projection of the sun as it
sets. Once it starts to dip below the horizon, time the total duration of the sunset. How
long did it take?
II.6. The apparent size of the Sun as seen from the Earth is about 1/2 degree. The
Earth rotates through one degree in approximately four minutes. Your value is
probably slightly greater than this – what causes this difference in total time of the
sunset?
III.
Resolution and Aberration
In the Optics lab, we measured the resolution of our telescopes using targets at a known
distance to view the separation between lines. The same technique can be used with these
refractors to determine their resolving power.
III.1. Place the telescope on the equatorial mounts we've provided and attach it firmly
with the rubber bands. Point it at the resolution target at the other end of the deck and
focus the telescope. What is the distance to the target?
III.2. Focus in on the smallest grouping of lines in which you can distinguish
individual lines (the white space in between the lines). Using the conversion table on
the back of the chart, what is the smallest spacing (in lines/mm) that you can
distinguish with your scope?
III.3. The angular resolution of your telescope can be found using the spacing between
lines and the distance to the target:
 = (180 degrees / π radians)* (3600 arcsec/degree) * (line spacing)
(target distance)
What is the angular resolution of your telescope?
III.4. Now, let's compare this to the diffraction limit – the theoretical maximum of your
telescope's resolving power. The diffraction limit of a telescope (in visual
wavelengths) is given as  = (120/D) arcseconds, where D is the diameter of the
aperture measured in millimeters. What is the diffraction limit of your telescope?
III.5. Typical results for the refractors we built in the optics lab had an angular
resolution of about 21 arcsec for a 10mm aperture. How does your telescope compare
to the refractors we built?
III.6. Posted next to the resolution targets are some of the images we used in the
Planetary Geology lab of the Galilean satellites and the Moon. What features can you
make out on these?
III.7. The telescopes we’ve assembled use plano-convex lenses, which reduce the
geometrical aberration in the image. Point the scope again at the resolution target and
look carefully toward the edges. Describe the geometrical distortion (if any) that you
see.
IV. Telescope Alignment, Navigation using Setting Circles, and Daytime Observing
Celestial Coordinates
The need for a coordinate system is obvious: it’s a way of pinpointing the exact
locations of celestial objects in the sky. The first thing to get used to, as a skywatcher, is
that the Earth is the center of your universe, though not of the real one. That is, you are
always standing on the Earth, and that’s what everything seems to revolve around.
It is convenient to think of the sky as a gigantic celestial sphere, a globe
surrounding the Earth. The sphere is assumed to be infinite in size; the planets and stars
are so far away that their distances don’t matter. When you step outside and look up, the
sky appears as a dome, a hemispherical bowl. It isn’t, of course, but the illusion works for
our purposes. As the Earth rotates, this bowl seems to twirl around. The Earth rotates
from west to east, which causes the sky seemingly to rotate from east to west, once every
23 hours and 56 minutes (one sidereal day). The stars stay in fixed positions on the
celestial sphere (because they’re so far away); the Sun, Moon, and planets gradually
move around it in their orbits, so it takes four more minutes (making a total of 24 hours)
for the Sun to get back to the same position.
Latitude and Longitude, Astronomy Style
On the celestial sphere, astronomers use lines similar to those of latitude and longitude on
the Earth. The astronomical equivalent of latitude is declination, measured in degrees (°)
of arc, positive for north and negative for south. Each degree is divided into sixty minutes
('), and each minute is divided into 60 seconds (''). (Seconds are used only when great
precision is needed.) “Declination” comes from a Latin word for “bending” or “angle.”
The celestial equivalent of longitude is right ascension (a rather clunky term, for sure). It
is measured in hours (0 to 24), minutes, and seconds, rather than degrees, for reasons
we’ll get to presently. For example, the pole star, Polaris, is at right ascension 2 hours 32
minutes, declination +89° 16'. The Table below shows the right ascensions and
declinations of some other bright stars.
Positions of some bright stars (Epoch 2000.0)
Star
Right Ascension
Declination
Sirius (in Canis Major)
6h 45m 09s
-16° 42' 58''
Regulus (in Leo)
10h 08m 22s
+11° 58' 02''
Arcturus (in Boötes)
14h 15m 40s
+19° 10' 57''
Altair (in Aquila)
19h 50m 47s
+8° 52' 06''
Fomalhaut (in Piscis Austrinus)
22h 57m 39s
-29° 37' 20''
The strange name “right ascension” has to do with the rising of a star as viewed
from the Earth’s equator, where stars with low declinations rise (ascend) vertically
(straight up). The right ascensions and declinations of stars are essentially fixed, although
they shift very slowly because of precession, a gradual change in the direction of the
Earth’s axis. The reason most star charts say “Epoch 2000.0” is that they show star
positions for the beginning of the year 2000. Earlier, we had Epoch 1950 and Epoch 1900
charts. The rate of precession is 1° every 72 years, but different parts of the sky are
affected to different extents.
Contrary to stars and galaxies, objects in our Solar System (the Sun, Moon,
planets, comets, and asteroids) are not fixed relative to the stars. They move around. You
have to look up their right ascension and declination for a particular date. The declination
of Polaris, +89° 16', is almost 90° north, which means Polaris is less than a degree away
from the north celestial pole. That’s the point around which the stars appear to twirl (for
Northern Hemisphere viewers). You can line up the polar axis of an equatorial mount by
sighting on Polaris. If you live south of the equator, you can’t see the north celestial pole;
instead, you see the south celestial pole, which is not marked by a bright star (although
Sigma Octantis is close). An old astronomers’ joke is to report the discovery of some
interesting object “about ten degrees south of Sigma Octantis” — there’s no such place,
because declinations range only from +90° to -90°.
The point directly over your head, the zenith, has a declination the same as your
latitude on Earth. The point directly south of you on the horizon has negative declination
of 90° minus your latitude; for example, declination -50° if your latitude is 40 north.
That’s why objects such as the Magellanic Clouds, at declination -65°, are never visible
from the continental United States.
We mentioned already that right ascension is measured in hours (0 to 24) rather
than degrees (0° to 360°). The two are interconvertible, of course; one hour equals 15
degrees of arc. If you want to give right ascension in degrees, you can; celestial
navigators do, and they call it sidereal hour angle (SHA). The reason right ascension is
measured in hours is of course that the celestial sphere seems to rotate as the Earth turns.
Its rotation period is called one sidereal day, or 24 hours of sidereal time, which runs
slightly faster than mean solar time. If a particular star is directly above you, it will be
directly above you again 24 sidereal hours later, or 23 hours and 56 minutes later by the
ordinary clock. The sidereal time at any moment is the right ascension of the point
directly overhead, as well as points directly north and south of it (along a line called the
meridian).
At the same mean solar time — midnight, for instance, or 10 p.m. — the sidereal
time will be 4 minutes later each successive day. That’s because the Earth orbits the Sun.
The celestial sphere seems to “slip” relative to the Sun (actually, the Sun is moving on
the celestial sphere), and that’s why we see different constellations at different seasons.
Most objects rise in the east and set in the west. Along the way, they follow lines of
declination, which are circles centered on the north celestial pole.
Some objects near the celestial pole are always above the horizon; they just whirl around
and around without setting. They’re said to be circumpolar. Above the Arctic Circle, the
circumpolar region is so large that the Sun gets into it and doesn’t set, resulting in the
Midnight Sun.
What Does the Coordinate System Mean For Amateur Astronomers?
An object’s coordinates tell you where it is in the sky. If you have a telescope on
an equatorial mount, you can locate celestial objects to view by “dialing in” their right
ascension and declination coordinates using the mount’s setting circles. (We won’t go
into how to do it here.) The setting circles on most equatorial mounts, and the mounts
themselves, are not accurate enough to land you right on an object consistently, but
they’ll get you close; then you merely have to sweep the telescope a bit using the slowmotion controls until you spot the object.
Conversely, you can use the setting circles to identify objects you happen upon in
the sky. By noting the right ascension and declination values of an object your scope is
pointed at, you can then look up the values in a star atlas or catalog to find out what it is.
Other coordinates are useful for other purposes. The most obvious are altitude (distance
above the horizon, in degrees) and azimuth (compass direction; north = 0°, east = 90°,
south = 180°, west = 270°). Computer programs can convert right ascension and
declination into altitude and azimuth for a particular place and time.
Also important are ecliptic coordinates. The ecliptic is the line in the sky that
corresponds to the Earth’s orbit around the Sun. The planets are always near the ecliptic,
in a narrow band called the zodiac. Planetary orbits are always computed relative to the
ecliptic, and ecliptic coordinates take the ecliptic as their “equator.” Ecliptic latitude is
the distance of an object from the ecliptic, and ecliptic longitude is measured along the
ecliptic from the place where it passes through declination 0°.
(from telescope.com)
Finding the Sun’s Coordinates
The R.A. “clock” of the sidereal time begins on the vernal (spring) equinox,
March 21. At midnight on this date the sun’s location on the celestial sphere is 0 hours.
As the year goes on, the sun advances through R.A. time on the celestial sphere, much
like the hour hand on a clock. After one year (365.25 days) the sun has moved through all
the 24 hours of R.A. coordinates and is back at 0 hours R.A. on the next vernal equinox.
Thus, finding the sun’s R.A. coordinate at any time throughout the year requires knowing
how many days have passed since the last vernal equinox, and then converting these days
into R.A. coordinates.
solar R.A. = 24 hours x (days past equinox)
365.25 days
A little more conversion needs to be done in order to use this time coordinate. R.A. is
usually expressed as (hours) : (minutes) : (seconds). The number of fractional hours
needs to be expressed as minutes (we’ll round off and ignore seconds). Example: For a
time of 1.25 hours, 0.25 is the fractional hours. To convert this to minutes =
(0.25hours)x(60minutes per hour) = 15 minutes. So the proper R.A. time would be
1hour : 15minutes.
IV.1 What is the current date and time? How many days have passed since the last
vernal equinox? Remember to count fractional days (i.e. 11:30 AM = 11.5 / 24 days).
IV.2
What is the sun’s current R.A. coordinate?
IV.3 Using the chart of the ecliptic’s path provided, what is the sun’s current
declination coordinate?
IV.3 Now that you know where the sun is on the celestial sphere, what is the current
local sidereal time (R.A. coordinate that is passing through the zenith right now)? (Hint:
Remember, the sun passes overhead at noon? The local sidereal time will be the R.A. you
calculated for the sun at noon.)
IV.4 Which of the bright stars in the chart a few pages back are currently in the sky
(you will be looking for them in a bit)?
Telescope Alignment
Telescopes navigate through the sky using setting circles. Setting circles are the
two graduated circular scales provided on the right ascension and declination axes of a
telescope that aid in locating an object by its coordinates on the celestial sphere. The
declination scale runs from -90° to 90°. The R.A. scale goes from 0 hours to 24 hours,
subdivided into minutes. Setting circles are set up by first sighting on a star of known
right ascension and declination and adjusting the circles to those coordinates. Then the
observer need only maneuver the telescope to the coordinates of the desired target, which
should be in the field of view or very near it. For daytime observing, the only easily seen
bright star available is the sun.
It is very important that coordinates of your alignment star be correct. Otherwise
your alignment on the celestial sphere will be incorrect, and you will be lost. You can
double check the coordinates for the sun using a useful website at
http://www.heavens-above.com. Go to the website and enter Boulder, CO as your
location. Under the Astronomy heading, click the link for the sun data for today.
IV.5
What are the R.A. and declination of the sun, according to Heavens Above?
Now go back and click on the Planet Summary Data link.
IV.6 What are the coordinates of any planets that are currently in the sky? (Venus,
Jupiter, Mercury!!)?
How about the moon?
Now go out on the observing deck and attach your telescope to the equatorial mount.
CAUTION! NEVER LOOK AT THE SUN THROUGH THE TELESCOPE!!!
IV.7
Align the telescope with the sun using the method outlined in section II.1to II.4.
IV.8 Adjust the setting circles to the coordinates you found for the sun. Your telescope
is now aligned (for now). Since the earth is rotating, the alignment is going to slowly
drift. When this happens you will need to repeat this step to re-align your telescope.
IV.9 Now move to the coordinates of one of your object. If the moon or Venus is up,
go there first since they are easier to find (this will take some practice). Look through the
eyepiece. Do you see your object? If not, you can try scanning the telescope up-downleft-right by small amounts until you find it. If you’re still having trouble your alignment
may have drifted. Repeat V.7 and V.8 and try again.
V.10 View at least two objects in this manner. For each sketch the object and make
observing notes. How does it look? Did you have to scan to find it? (If so, what
coordinates did it end up being at?)
If the object is a planet, look for “phases” or moons.
V. Follow-Up Questions: Star-Hopping
You now have a telescope that is about as good as the one Galileo used. Why use
it some more? Go out on a clear night and use your telescope to view at least two
additional objects. Your telescope has a low enough magnification that you really don’t
need an equatorial mount with setting circles to find objects in the night sky. Instead you
can use a method referred to as “Star Hopping.”
To star hop, the observer uses well known or well charted bright objects to find
his way to a desired object. A predetermined path of bright stars is often drawn up before
the observing session. First, you must obtain a star chart so that you can compare with
what you see in the telescope. There are charts in your textbook, and others available
online (ex. www.SkyAndTelescope.com). The first object on your path should be a naked
eye star (one that you can see without the aid of a telescope) near the intended target
(bright stars such as Sirius or Vega are good choices for these, depending on the time of
night). Then pick a number of other objects that provide a clear stepping path toward
what you want to see. Things such as patterns of stars in geometrical shapes, pairs of stars
that can serve as pointers in a particular direction, and stars of different brightness are
acceptable steps to take. Galaxies and quasars are not acceptable as they will be too faint
for you to find with a telescope of this power. When your observing session begins,
locate your target star with your naked eye. Center the scope on this star. Then move the
telescope to the next object by comparing the view in the eyepiece or finder with the
drawings in the chart. This constitutes your first hop. Keep hopping until you get to the
object under study.
You will, however, need to come up with some method for mounting the
telescope so that is steady enough for you to view your object. A very crude method
would be resting one end of the telescope on a wall or the back of a chair. A very good
yet simple mount can be made if you have a camera tripod. Just use masking tape to
attach the telescope to the tripod. Equatorial mounts are best of all, if you’re able to use
one or adapt – try to orient your tripod surface so that “up” (the direction perpendicular to
rotation of the telescope) points directly at Polaris (an angle of 40 degrees).
V.1 View at least two objects, making sketches and notes for each. Also include a
description of your “hopping” method (your starting star, intermediate points, etc). Some
suggestions for objects are Mars and the Orion Nebula (very nice!).
Inclement weather
VI.
Solar System
Now, let's go back to the model Solar System that we used in the first lab. Typically,
some of the brightest objects we see in the sky are right in our own backyard,
astronomically speaking - not surprising, considering the range in distance between our
Solar System and even the nearest star. Many people are puzzled and confused, however,
when they ask to see large planets such as Uranus or Neptune through the telescope and
are disappointed to make out only a faint dot that looks no different from a star.
To predict what we might be able to see using our telescopes (without the benefit
of a clear night and a good star map), we can use the model Solar System to check our
available viewing.
Split up your lab group in two – have one group stay fixed at the Earth with the scope and
the other group roam around the Solar System. We can use the scaling of the Solar
System here to predict whether we could observe these objects on a clear night.
VI.1. Have the roaming group go to Venus. Using the size of Venus on the plaque as a
reference, draw a circle on a piece of paper of the same size. Next to that image, draw a
crescent of the same size (representing Venus during a crescent phase). Standing next to
the plaque, hold up your images so they can be seen by the group standing at Earth. Can
you make out the shapes with your naked eye? What about with the telescope?
VI.2. Now move to Mercury and repeat the process, drawing a circular and crescent
Mercury. Can you make out the crescent shape with your telescope?
VI.3. Moving on the other side, head out to Mars and draw a hollow circle of the same
size on your paper. Olympus Mons, the largest volcano on Mars (and in the entire solar
system!) , has a diameter approximately 1/12th of that of the entire planet. Make a mark
of that size inside your image of Mars. Could we make out Olympus Mons with our
telescope?
VI.4 Head out to Jupiter and draw a circle of the same size. Add the Galilean moons in
your drawing (Callisto has an orbital radius of about 10 Jupiter diameters, while Io has a
radius of about 3 Jupiter diameters). Can you make out the individual moons? How big
does Jupiter appear in your field of view?
VI.5. Head out to Saturn and draw its circle, complete with the ring system. Galileo
claimed in 1610 that he saw the “ears of Saturn” through his scope. Do you believe him?
What kind of features can you see?
VI.6. Finally, head to Uranus and repeat the process. You may have to move out to the
adjoining field to be seen from the Earth for this one. What kind of resolution do you
have for Uranus? Can you make out any kind of detail or shapes as compared to Jupiter
or Saturn?
VI.7. Back at Earth, take one last look at the sun. Remember (you can use the “hand
calculator” as a reminder) that the Sun has angular size of about 1/2 degree. Look at the
scale Sun through your telescope – based on that, what is the estimated size of your
telescope’s field of view? (the diameter, in degrees, that your telescope can see in a
single viewing)