Credit/Permission: For text, © David Jeffery. For figures etc., as specified with the figure etc. / Only for reading and use by the instructors and students of the UNLV astronomy laboratory course.
This is a lab exercise with observations that are essential: see Sky map: Las Vegas: current time and weather.
Sections
We do touch on the following topics:
Some of the
Tasks can be completed ahead of the lab period.
Doing some of them ahead of lab period would be helpful.
However, you can print a copy ahead of time if you like especially if
want to do some parts ahead of time.
You might have to compensate for updates in this case.
The Lab Exercise itself is NOT printed in the lab ever.
That would be killing forests
and the Lab Exercise is designed to be an active web document.
General remarks about quiz prep are given at
Quiz Preparation: General Instructions.
For DavidJ's lab sections, the quiz prep is doing all the items listed here and self-testing with the
Prep Quizzes and Prep Quiz Keys
if they exist.
Review the parts of the
Celestron C8 telescope
in the figure below
(local link /
general link: telescope_c8_diagram.html).
You should also review the
Observation Safety Rules.
However to complement and/or supplement the reading, you should at least
read the intro of a sample of the articles
linked
to the following keywords etc.
so that you can define and/or understand some keywords etc. at the level of our class.
A further list of keywords which you are NOT required to look at---but it would be useful to do so---is:
If the sky is going to be heavily clouded, then
an alternative lab exercise without observations (or for which observations are NOT essential) from the
Introductory Astronomy Laboratory Exercises.
Patchy cloud cover may be OK. You will have to make a judgment call based on visual inspection of the
sky.
You should call up groups of students one by one to run them through this task which
is NOT done in order of the
Tasks, but whenever you call a group up.
Note if the night is cloudy,
you can still do the lab with observations or without.
See Star Choices again.
Really this lab CANNO be postponed more than once.
Obviously, a full explication of optics
is well beyond our scope.
We only consider
Gaussian optics
which is
geometrical optics
in the limit of the
paraxial approximation:
i.e., when light rays
make small enough angles
to the optical axis
that the small angle approximation
for the trigonometric functions is valid.
Geometrical optics
itself is the limit of
physical optics in which
diffraction is neglected and
light is treating just as propagating
light rays.
The figure below
(local link /
general link: optics_lens_curved_mirror.html)
explicates what we need to know about
lenses
and curved mirrors.
A general discussion of
telescopes is beyond our scope.
A full explication of the
C8's
is also beyond our scope---thrash about before you crawl as they say.
The classic
Keplerian telescope
gives a simple case for understanding something
about telescopes.
Sub Tasks:
Sub Tasks:
The C8's are
Schmidt-Cassegrain telescopes.
The figure below
(local link /
general link: telescope_schmidt_cassegrain.html)
explicates the
Schmidt-Cassegrain telescope
to a limited degree.
Sub Tasks:
A telescope ideally should be
slewable to all points on the
celestial sphere.
The celestial sphere requires
two angular coordinates to locate objects.
The simplest way to do this is to use two perpendicular axes of rotation.
Therefore, usually telescopes
are designed to slew around
two perpendicular axes of rotation.
In practice, the first axis is fixed and the second axis rotates on the
first axis, but is always perpendicular to the first axis.
The axis setups are called telescope mounts.
There are two common
telescope mounts:
The second axis which rotates on the first gives
altitude
slewing.
The altazimuth mount
is conceptually simple and easily constructed.
The second axis which rotates on the first gives
declination (Dec or δ)
slewing.
The equatorial mount
is conceptually a bit trickier than the
altazimuth mount and
probably a bit harder to construct usually.
However, the equatorial mount
gives straightforward
clock-drive motion since
only the first axis has to slew
to keep the telescope
pointing at a point on the celestial sphere.
Pre-computer-controlled
telescopes
could only be build easily for
clock-drive motion
with the equatorial mount.
With computer-controlled telescopes,
either altazimuth mount
or equatorial mount
easily give clock-drive motion.
However, equatorial mount
may still be preferred since with it
clock-drive motion
probably gives less wear on the gear train
The Schmidt-Cassegrain telescope
does a point inversion
during image formation.
Recall that the Keplerian telescope
(which is refractor telescope recall)
does this too.
Point inversion in the figure below
(local link /
general link: optics_point_inversion.html).
But a C8
star diagonal
(which is a Porro prism
star diagonal:
see figure below:
local link /
general link: optics_prism_porro.html)
is ordinarily
attached and it causes a further inversion.
The star diagonal's purpose
is to bend the optical axis
and beam paths of light rays
through 90° from the main optical axis
of the telescope
in order to save the observer from krinking his/her neck.
To achieve its purpose (but NOT as part of its purpose),
a Porro prism
star diagonal
also causes
an plane reflection.
Plane reflection
is illustrated and explicated in the figure below
(local link /
general link: optics_reflection_plane.html).
But you can do it with a little thought.
Recall a star diagonal's purpose
is to bend the optical axis and
beam paths of light rays
through 90° from the optical axis
of a telescope
in order to save the observer from kinking his/her
neck.
For star diagonal images,
see the figure below
(local link /
general link: telescope_star_diagonal.html).
The bending is done by
total internal reflection.
The figure below
(local link /
general link: optics_prism_porro.html)
shows how
a Porro prism works
in our C8
star diagonals.
Each group member OR each group as specified by the
instructor
should print out the figure below
(local link /
general link: field_of_view_inversions.html)
and complete it
by drawing the point inverted
and axis reflected
(the 2-d analog of plane reflected)
versions of the field of view (FOV)
which contains the Alien.
The point inversion
can be done easily using two printouts and rotating one 180° and
tracing
on the other.
The axis reflection
is tricky to understand in a sense, but
it is just what happens in Image 1 of the figure above
(local link /
general link: optics_reflection_plane.html).
It's probably best to just to use your artistic skill to do the
axis reflection.
But it can be done with tracing
too plus some trickery.
Trace the
FOV without the
star diagonal (but with
the Alien
point inverted already drawn)
on the back of the printout.
That will effect the axis reflection.
Then trace that tracing
to a separate sheet of paper, and then
do the final tracing
from the separate sheet of paper to the printout
for the FOV with
the star diagonal.
But make sure the completed
FOV with
the star diagonal
has the
Alien in the RIGHT PLACE on
the reflection axis,
NOT shifted off the reflection axis,
etc.
Append the printout to your report form. Each group should have a printout.
Sub Tasks:
What is our
C8
finderscope specification
and what does it MEAN? HINT: Look at the
C8
on display in the classroom if there is one and click on
Wikipedia: Finderscope: Function and Design.
Complete the following procedure for centering an object in the
field of view (FOV) of
a C8:
We have to learn a bit about the
Earth's rotation
and unit conversions---they're fun.
The Earth rotates on its
axis.
Relative to the inertial frame
fixed stars
(which to sufficient accuracy is the same as
the local inertial frame
of the observable universe)
the Earth's rotation
(i.e., its angular velocity) is
360 degrees per 24 sidereal hours (h_s).
Note 1 unit of sidereal time
= 0.99726958 of the corresponding regular time units.
This is because it takes the Earth
a bit longer to compete an axial rotation relative to the
Sun than to
the inertial frame
fixed stars.
A unit conversion is just multiplying the value to be converted by 1
(i.e., a factor of unity) expressed in appropriate way so that you cancel out
the units you don't want. You can always multiply something by 1 without changing its value.
A general discussion is less clear that a few examples:
Now 1 m = 100 cm, and so the factor of unity is 1 = (100 cm / 1 m).
Behold: 7.2 m = 7.2 m * 1 = 7.2 m * (100 cm/ 1 m) = 7200 cm.
Sub Tasks:
Sub Tasks:
A field of view (FOV) of a
telescope is
a circular area on the sky.
The size of the FOV
is angular diameter of the
FOV.
This size is also called FOV in a second
meaning of FOV. As usual context decides
what meaning is meant.
Consider a star that
transits
(i.e., passes through) the center of a FOV as
the sky rotates
(i.e., does its
diurnal rotation).
The star's path is actually slightly
curved in general, but it approximates as a straight line to
very accuracy/precision.
The exact formula is obtained using
spherical trigonometry in
the file field_of_view_procedure.html.
And the reason for this if you track it back is that we want the
angular diameter
of the FOV from
the Earth where we
observe from rather than from the
celestial axis
where we do NOT observe from (except for
astronomical objects
of zero declination:
i.e., astronomical objects
on the celestial equator).
In tonight's observations, we will measure the
angular diameter of the
FOV
(i.e., its size)
by measuring the time t_m for a star to
transit
from the CENTER to the EDGE of
the FOV
and then using the
FOV timing formula to
calculate said
angular diameter from time t_m.
We'll just round off the declination
values to the nearest degree.
Our timing measurements are too imprecise to worry about fractions of a degree of
declination.
To prep for having real observations, let's apply the
FOV timing formula to some synthetic observations.
Remember, just round off the declination
values to the nearest degree.
Sub Tasks:
Look at the figure
local link: sky_swirl_polaris_ehrenbuerg.html
below and watch the accompanying
videos.
The star trails each take
the same time to form in the
long-exposure image
and have the same angle
around the celestial axis.
But the field of view (FOV)
angular diameter
is an angular diameter
subtended at the observer
and is the SAME for any
declination.
So as you go to higher in declination
(i.e., get closer to the
celestial axis)
it takes a longer star trail
and thus a longer
transit time
to transit the
FOV.
In fact, the transit time
is infinite at the
celestial axis.
Do you understand why now? Y / N
Some time before observations get the
instructor
to give your group a hands-on
intro to the C8's.
The instuctor could call you up for the intro or you could take the initiative in getting him/her to give
you the intro.
You or a group member has had the intro. Y / N
You or a group member has at least mostly covered all the sub tasks below. Y / N
Sub Tasks:
For more detailed information, see
Telescope
Operating Procedure for Instructors
or
Telescope
Operating Procedure for Instructors, pdf.
Each group will need a sky map
to help locate the star choices for tonight's observations.
Sub Tasks:
Recommendations for the instructor:
In fact, the students do NOT actually need to track the designated
star.
Any star in the vicinity of the
designated star will give virtually the same result.
Write down the two star choices for tonight's observations and their
declinations.
Sub Tasks:
This takes a little practice.
Time 1: _______ m _______ s = ______________ m with decimal fraction.
If NO observation, use: 1:20.
Time 2: _______ m _______ s = ______________ m with decimal fraction.
If NO observation, use: 1:22.
Time 3: _______ m _______ s = ______________ m with decimal fraction.
If NO observation, use: 0:22.
Average Time: ________________ m with decimal fraction
Note if any of the 3 timings differ from the others by more than 20 seconds,
then you probably have made some error.
Repeat the timing in this case or neglect the out-of-trend observation in the average time calculation.
Evaluate the FOV timing formula
(which is linked to its name)
to get
the FOV
angular diameter.
Remember to give the units, arcminutes (').
Result: _____________________
This measurement was done with our standard 40 mm
eyepiece.
Make sure that the first star
is very well centered before proceeding. The new
eyepiece has
a smaller FOV
and it is easy to lose the
star
and NOT find it again.
However, it doesn't really matter since any
star in the vicinity of
the first star will do as well
for the measurement.
Now remove the standard eyepiece just
loosening the screws NOT taking them out---if you take them out you will drop them
and they'll roll into the crevices and we'll NEVER get them out.
Put the standard eyepiece
in the box designated for doing that so it is safe.
But, if your
instructor
allows it, you can put it on the base right by the pillar
and the electrical connection in an upright position
so it is safe and will NOT roll off.
Put the new eyepiece
in and tighten the screws enough so that the
eyepiece is snuck---but don't
grind the screws in.
What is the focal length
of the new eyepiece?
_________________
Time 1: _______ m _______ s = ______________ m with decimal fraction.
If NO observation, use (i) 2:01, (ii) 1:21, (iii) 0:57, OR (iv) 0:40 as your
instructor designates.
Time 2: _______ m _______ s = ______________ m with decimal fraction.
If NO observation use (i) 1:59, (ii) 1:18, (iii) 0:56, OR (iv) 0:37 as your
instructor designates.
Time 3: _______ m _______ s = ______________ m with decimal fraction.
If NO observation use (i) 2:05, (ii) 1:25, (iii) 1:01, OR (iv) 0:43 as your
instructor designates.
Average Time: ________________ m with decimal fraction
Note if any of the 3 timings differ from the others by more than 20 seconds,
then you probably have made some error.
Repeat the timing in this case or neglect the out-of-trend observation in the average time calculation.
Evaluate the FOV timing formula
(which linked to its name)
to get
the FOV
angular diameter.
Remember to give the units, arcminutes (').
Result: _____________________
Time 1: _______ m _______ s = ______________ m with decimal fraction.
If NO observation use 4:05.
Time 2: _______ m _______ s = ______________ m with decimal fraction.
If NO observation use 4:00.
Time 3: _______ m _______ s = ______________ m with decimal fraction.
If NO observation use 3:55.
Average Time: ________________ m with decimal fraction
Note if any of the 3 timings differ from the others by more than 20 seconds,
then you probably have made some error.
Repeat the timing in this case or neglect the out-of-trend observation in the average time calculation.
Evaluate the FOV timing formula
(which linked to its name)
to get
the FOV
angular diameter.
Remember to give the units, arcminutes (').
Result: _____________________
At the end of the observing:
If you are the last section observing and NOT otherwise, you:
Have we have done all these things? Y / N
Complete the following table using your own calculated values
and values obtained from other groups.
Do the preparation required by your lab
instructor.
Keywords:
air mass,
angular resolution,
aperture,
plane reflection,
celestial sphere,
Celestron C8 telescopes,
clock drive,
cosine function,
crosshairs,
curved mirror
(concave mirror,
convex mirror,
spherical mirror),
declination (Dec or δ),
diurnal rotation,
Earth's rotation,
eyepiece,
field of view,
finderscope,
focal length,
focal point (AKA principal focus),
focal plane,
Keplerian telescope,
lens
(converging lens,
diverging (biconcave) lens),
light-gathering power,
light rays,
magnification
(telescope magnification),
observational astronomy
optical telescope,
optics
(Gaussian optics,
geometrical optics
physical optics),
primary mirror (AKA objective),
point inversion,
Rayleigh criterion,
real image,
Schmidt-Cassegrain telescope
(Cassegrain telescope,
Schmidt telescope,
Schmidt corrector plate),
sidereal time,
reflector,
refractor,
Schmidt-Cassegrain telescope,
Schmidt corrector plate,
secondary mirror,
seeing,
slewing,
star diagonal,
star pointer,
TheSky
(TheSky6,
TheSkyX,
List of Tricks for TheSky,
TheSky Orientation),
transit,
visual astronomy.
Hm.
Task Master:
EOF
We will now learn something about
optics,
telescopes,
and our
C8 telescopes.
The finderscopes on the
C8's
are,
in fact, Keplerian telescopes.
The figure below
(local link /
general link: telescope_keplerian.html)
explicates the
Keplerian telescope.
The
Celestron C8 telescope
can be mounted in either
altazimuth mount
or equatorial mount.
Currently, we use the equatorial mount.
Now point inversion
is what the C8's
give without a star diagonal attached.
Because of the inversions,
it's tricky relating the orientation of what you see in the
field of view to
the actual sky.
A Porro prism
star diagonal
contains a Porro prism
which causes the effective bending
of the optical axis and
beam paths of light rays.
In this section, we study the features/parts/characteristics of
the C8's, but
many of these features/parts/characteristics apply to other
telescopes.
In this section we will consider the
field of view (FOV)
of telescopes
and one way of measuring it.
1 acre-foot = 1 acre-foot * (1 mi**2 / 640 acres)
*( (1609.344m / 1 mi)**2)*(0.3048 m / 1 ft)
= 1233.48 m**3 .
27' = 27' * (1 degree / 60') = 0.45° .
The sky rotation rate for a fixed
Earth is exactly the
Earth's rotation rate rate
for a fixed sky. But you knew that without saying.
The angular diameter of the
FOV
to a accuracy/precision
1st order approximation
is given by the FOV timing formula
FOV = 2*(R*t_m)*cos(δ),
where
the 2 converts angular radius to angular diameter,
R = 15 arcminutes/m_sidereal = 15.041 arcminutes/m ≅ 15 arcminutes/m to sufficient
accuracy for this lab,
t_m is time in minutes for
the observed star to transit
from the CENTER
to the EDGE of the FOV,
and δ is the declination of the star.
Some points about this formula:
There are some things to do before observations.
The red laser dot is powered by
a little lithium battery
which is frequently dead.
The star pointer
can still be used, but you have stand a meter or so off from it and
get a little practice.
Some nights, yours truly can do this pretty niftily, other nights, no luck.
Mark the two star choices on your printed out
sky map in such a way that
you can see them easily outside.
Now for the observations.
Ah, back inside where it's cool/warm.
________________________________________________________________
Table: C8 telescope specifications for available eyepieces
________________________________________________________________
focal length magnification approximate
(mm) (X) fields of view
(arcminutes = ')
________________________________________________________________
40
25
18
12.5
9
________________________________________________________________