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 which are essential: see Sky map: Las Vegas: current time and weather.
Sections
We touch on the following topics:
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Do the preparation required by your lab instructor.
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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:
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Keywords:
air mass,
angular resolution
(resolving power),
apse line (AKA line of apsides),
astronomical seeing
(usually abbreviated to seeing),
binary
(close binary,
double-lined spectroscopic binary,
eclipsing binary,
visual binary,
single-lined spectroscopic binary,
spectroscopic binary,
wide binary),
Dawes limit,
double star
(best double stars),
interacting binary,
Kepler's 3rd law
(also the dynamical Kepler's 3rd law),
line of sight,
multiple star systems,
optical double,
orbit
(apparent relative orbit,
circular orbit,
elliptical orbit
true relative orbit),
orbital inclination (exo-systems)
(face-on inclination,
edge-on inclination),
parallax,
position angle,
radial velocity,
Rayleigh criterion,
semi-major axis,
Sirius
(Sirius A,
Sirius B),
sky map,
stellar parallax,
two-body system,
white dwarf.
Hm.
Therefore you should check the weather well in advance (e.g., using National Weather Service (NWS) 7-day forecast, Las Vegas, NV) and on the night of by visual inspection.
The weather and seeing have to be pretty good.
If they are NOT good enough, you should choose another lab preferably one from some other date in lab schedule. If nothing the lab schedule is suitable, then check the catalog of Introductory Astronomy Laboratory Exercises.
This is mostly because the students will need the clock drive on to observe the double stars adequately particularly when they switch eyepiece to increase telescope magnification.
The sky alignment is also good because it helps them find the double stars and gives them practice using the menus on the LCD keypad.
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EOF
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End of Task
A double star is often considered just as a single star when NOT resolved into two stars in naked-eye astronomy or telescopic visual astronomy.
There are two main classes of double stars:
However, optical doubles are observationally interesting: they are fun to look at and they can be used to test one's angular resolution and the astronomical seeing (usually abbreviated to seeing).
Actually, 2 gravitationally-bound stars that are labeled a double star may be part of multiple star system of more than 2 stars. The 2 stars labeled a double star are just the most prominent members of the multiple star system.
One shouldn't get too finicky in terminology.
An example of a famous pair of stars that are NOT considered a double star is Castor and Pollux.
But Castor, in fact, is itself a well known double star. For an explication, see the sky map in the figure below (local link / general link: iau_gemini.html).
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An example of another famous
double star is
Albireo which is illustrated in
the figure below
(local link /
general link: star_double_star_albireo.html).
You can roughly measure
angles
using your
hand.
Explication is given in the figure below
(local link /
general link: alien_angular.html).
What is the angular separation of
Castor and
Pollux in
fists? Explain how you got your answer.
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Sub Tasks:
RMI qualification: If you do NOT have access to a printer, you will have to hand-draw the sky map.
You will have to do a conversion from local time to Universal Time (UT) to update the time. How to do the conversion is explicated in the figure below (local link / general link: sky_map_current_time_las_vegas.html).
NOT all the double stars in the Observing Working Table for Double Stars are labeled on the printed-out sky map. You will have to click on the names of the unlabeled ones (on the printed-out sky map) in Observing Working Table for Double Stars to get a sky map with them located. Label the unlabeled double stars on your printed-out sky map.
RMI qualification: Whether you report your sky map in any way depends on the instructions for your particular semester of the Remote Instruction Course.
Sub Tasks:
Generally, you go down the list in order since the
generally the double stars get
harder to resolve going down the list, and so you gain experience as you go.
However, if a double star
is getting close to the
horizon or being threatened
to be clouded-out, you may have to observe it early.
Double stars
that may need to be observed early are marked with OE for "observe early".
Of course, if you can locate the
double star by eye using your
sky map,
you can just slew the
C8
to the vicinity of the double star
without using the LCD keypad location tool.
All the double stars
in the Observing Working Table for Double Stars
are bright enough to be seen with the
naked eye even in
Las Vegas though some barely.
You could ask your
instructor if you are doubtful.
Add a comment if needed: e.g., clouded-out, too close the
horizon,
the secondary star
in the double star too faint
to be seen compared to the primay star,
awesome.
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EOF
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A second meaning of angular resolution is the smallest angle that allows two point light sources to be resolved.
Context decides which meaning applies as usual.
Actually, there is almost never a hard limit to angular resolution (in both the first and second meanings).
However there usually a characteristic angular resolution limit (in the second meaning) that defines an angular size scale of marginal angular resolution (in the first meaning).
Below we consider three characteristic angular resolution limits that occur in astronomy
A first meaning of seeing is qualitatively "the amount of apparent blurring and twinkling of astronomical objects like stars due to turbulence in the Earth's atmosphere, causing variations of the optical refractive index of the Earth's atmosphere" (Wikipedia: Astronomical seeing: slightly edited).
If stars or other astronomical point light sources are too close together, you CANNOT resolve them because of the seeing: i.e., you do NOT have angular resolution (in the first meaning of the term) to resolve them.
The seeing in a second meaning is the smallest resolvable angular separation on the sky set by seeing in its first meaning: i.e., it is an angular resolution (in its second meaning).
Context decides which meaning of seeing applies as usual.
Seeing θ_S (in its second meaning) is usually determined empirically. You measure what it is when you observe.
Fiducial excellent seeing has θ_SE = 0.4'' (which is available at high-altitude mountaintop observatories) and fiducial good seeing has θ_SG = 1'' (see Wikipedia: Astronomical Seeing: The full width at half maximum (FWHM) of the seeing disc).
It has been claimed---by Diane Pyper Smith?---that θ_S ≅ 4'' is possible near the Las Vegas Strip. Yours truly will believe it when yours truly resolves the angular separation of Castor A and Castor B which currently is ∼ 5'': to be more precise, 4.87'' in 2013 (see Observer's Handbook, Royal Astronomical Society of Canada).
Believe it or NOT, let's write fiducial Las Vegas Strip value as θ_SL = 4''.
There is an intrinsic angular resolution
limit due to the
wave nature of
light.
As foreshadowed above in the preamble of this section
(i.e., section Angular Resolution), the limit is NOT sharp.
But there is a formula giving a fiducial
angular resolution limit that
for useful for most cases called the
Rayleigh criterion.
The Rayleigh criterion is
Recall the
visible band has fiducial range 0.4--0.7 μm.
So for visible band, a
human-fiducial
Rayleigh-criterion
limit is
The
human-eye
angular resolution
naturally varies significantly with person.
However, the typical and fiducial value is
θ_H = 1 arcminute (') = 60 ''
(see Wikipedia: Naked-eye astronomy).
Some sharp-eyed people may be able to do better.
In visual astronomy, this
human-eye
angular resolution limit
is enhanced via
telescope magnification.
Recall the magnification formula:
Since magnification
magnifies angles by M,
it effectively enhances (i.e., reduces)
the human-eye
angular resolution limit
θ_H by 1/M to θ_HT.
One can see this from by solving
Thus, the fiducial telescopic human-eye
angular resolution limit is
For the magnifications
available to our labs, see
Table: C8 Telescope Magnification and Field of View
below
(local link /
general link: telescope_c8_mag_fov_table.html):
In general, all three
angular resolution limits
discussed above
(see subsections
Seeing,
The Rayleigh Criterion,
and
Human Eye Angular Resolution)
are active.
There must be some valid way of combining them to get an overall
angular resolution limit.
However, usually one angular resolution limit
is dominant---the largest one.
Thus,
If the dominant
angular resolution limit is overwhelmingly the
largest, then it is essentially the
angular resolution limit.
If there is an
overwhelmingly
angular resolution limit,
there is little point in trying to reduce the
non-dominant
angular resolution limits
since that will NOT significantly improve the
angular resolution.
But if you can reduce the
dominant
angular resolution limit,
that will improve the
angular resolution.
Sub Tasks:
As an example of seeing,
consider the film in the figure below
(local link /
general link: star_seeing.html).
θ_R = (4.952'')*[(λ_μ/0.5 μm)/D_in] ,
where θ_R is the
Rayleigh criterion
angular resolution limit itself,
λ_μ is wavelength
in microns (μm),
and
D_in is the diameter of the
primary in
inches.
θ_RV ≅ 5''/D_in .
M = f_p/f_e ,
where M is angular magification,
f_p is primary
focal length,
and
f_e is eyepiece
focal length.
There is sometimes a minus which just indicates
the magnification involves
a point inversion, but the
minus sign is usually suppressed since inversions are finicky details which
are often altered by other optical devices
(e.g., star diagonals)
anyway.
M*θ_HT = θ_H to get θ_HT = θ_H/M .
θ_HT = θ_H/M = 60''/M .
So M = 60 gives θ_TH = 1'' which is the same as θ_SG = 1''
(i.e., fiducial good seeing:
see subsection Seeing above).
EOF
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θ_dominant = max( θS , θRV , θHT ) .
_________________________________________________________________________________
Table: Parameters to Equal/Surpass the Seeing Limit
_________________________________________________________________________________
Seeing θ_S D_in = 5''/θ_RV D_in = 5''/θ_RV M = 60''/θ_HT M = 60''/θ_HT
(θ_RV=θ_S) (θ_RV=θ_S/3) (θ_HT=θ_S) (θ_HT=θ_S/3)
('') (in) (in) (X) (X)
_________________________________________________________________________________
Poor 10
LV Strip 4
Good 1
Excellent 0.4
_________________________________________________________________________________
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Sub Tasks:
Sub Tasks:
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In isolation from all other sources of gravity, a a binary forms an exact two-body system in the limit of Newtonian physics.
Of course, in reality there are is NO complete isolation. There are always perturbations. Also, general relativity changes the behavior of the two-body system from Newtonian physics with the change increasing with the mass of the bodies and decreasing with their separation. Nevertheless, many binaries approximate exact two-body systems in the limit of Newtonian physics to high accuracy.
The more luminous member of a binary is called the primary star and the less luminous member, the secondary star.
Animations in the 2 figures below (local link / general link: orbit_elliptical_equal_mass.html; local link / general link: orbit_circular_large_mass_difference.html) illustrate exact two-body systems.
There are several common classes
of binaries.
The classes do overlap since one binary can fall into
more than one class.
The classes are:
The sense is often that
component stars interact significantly
by processes other than the
gravitational force between
spherically symmetric objects.
This means the binary systems
has
edge-on inclination
(i.e., are at nearly 90°
inclination).
Eclipsing binaries are
usually NOT
visual binaries.
Their eclipsing nature is known from dips in their light
curve as illustrated in the animation
in the figure below
(local link /
general link: star_binary_eclipsing.html)
of a
close eclipsing binary.
Visual binaries
are often NOT classed as
spectroscopic binaries
even though they usually have observed spectra---but one can always adapt the terminology to one's needs.
There are two sub-classes
spectroscopic binaries
(wouldn't you know it):
The periodic Doppler shifts
of the two spectra make the system an obvious
binary.
The periodic Doppler shifts
of the one spectrum make the system an obvious
binary.
Of course, whether
binary is
a visual binary or NOT
depends on what telescope
you are referencing.
Often one references the highest
angular resolution
telescope that has
looked at the binary.
The sense is often that
component stars do NOT interact significantly
by processes other than the
gravitational force between
spherically symmetric objects.
Wide binaries
are the opposites of
close binaries.
It could be a
compact object:
a white dwarf,
neutron star, or
black hole.
We still call the system a binary in this case.
In fact, self-gravitating systems of
two compact objects
are also usually called binaries.
If the companion object is a
brown dwarf
then yours truly
thinks??? the system is called a binary.
A two-body system
consisting of
2
brown dwarfs is probably also called
a binary???.
However, star and one or more
gravitationally-bound
planets
is called a
planetary system.
Sirius AB is an example of a
visual binary.
The figure below
(local link /
general link: star_sirius.html)
shows the orbit
of Sirius AB.
The animation in the figure below
(local link /
general link: star_binary_eclipsing.html)
illuatrates an
eclipsing binary which is
also a close binary.
Sub Tasks:
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Note that a
gravitationally-bound
companion object to a
star
need NOT be an ordinary star.
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Modifications to the sub tasks in General Task: Naked-Eye Observations below:
However, you should be able to find in the winter and spring not-too-late night sky Castor (α GEM) and Pollux (β GEM) which are "twin" stars even though NOT collectively a double star in the usual meaning. Their angular separation is 4°30'19.53'' at some epoch, maybe the J2000 epoch (see Distance between Pollux and Castor?). This angular separation is about half a fist at arm's length.
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Post mortem comments that may often apply specifically to
Lab 9: Double Stars:
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