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:
This binary system is a close binary because the relative mean orbital radius is NOT large compared to the stellar radii of at least one of the binary stars.
To be an eclipsing binary, the binary is seen nearly edge-on (i.e., at an inclination relative to the line of sight of nearly 90°).
If only one component star's spectral lines are seen the binary is a single-lined spectroscopic binary.
If spectral lines are seen from both component stars, the binary is a double-lined spectroscopic binary.
Visual binaries are those that can be resolved into two stars.
There may be some eclipsing binaries that are visual binaries, but yours truly knows of none.
All one can determine for a double-lined spectroscopic binary is the quantity m*sin(i)**3, where m is the stellar mass of a component star, i is inclination, and sin is the sine function. We know even less about the stellar mass of single-lined spectroscopic binaries (e.g., Shane Larson: Binary Stars).
However, for an eclipsing binary, we know inclination i ≅ 90°. So at least for double-lined spectroscopic binaries we can determine the component stellar masses to some accuracy.
One can, of course, determine mass for stars by modeling and stellar spectroscopic data, but those results are then model-dependent, of course.
The other method is the Doppler spectroscopy method.
Caption: Euclid (fl. 300 BCE) in a detail from The School of Athens (1509--1511).
The hair-challenged Euclid is giving the totally-engaged and luxurously hirsute students a lesson in geometry.
Hipparchus (c.190--c.120 BCE) and Ptolemy (c.100--c.170 CE) are about to drop globes on Euclid. A celestial globe by Hipparchus (c.190--c.120 BCE) and an Earth globe by Ptolemy (c.100--c.170 CE).
The model for Euclid was Donato Bramante (1444--1514) (see Wikipedia: The School of Athens: Program, subject, figure identifications and interpretations).
Credit/Permission:
Raphael (1483--1520),
1510--1511
(uploaded to Wikipedia by User:Cyberpunk,
2006) /
Public domain.
Image link: Wikipedia:
File:Euclid.jpg.
Local file: local link: euclid.html.
File: Ancient Astronomy file:
euclid.html.
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.
Caption: A diagram of the Celestron C8 telescope, a compact Schmidt-Cassegrain telescope.
Features:
See file telescope_schmidt_cassegrain.html for a fullish description of a Schmidt-Cassegrain telescope like the C8 with particular attention to the function of the Schmidt corrector plate and the effective focal length.
Credit/Permission: ©
David Jeffery,
2013 / Own work.
Image link: Itself.
Local file: local link: telescope_c8_diagram.html.
File: Telescope file:
telescope_c8_diagram.html.
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:
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.
The Tasks do sometimes have to be done out of order in order to accommodate observations.
Some Tasks can be done ahead of time as part of the preparation for the lab exercise.
The Tasks are NOT always the full instructions.
You need to read/work your way through the lab exercise to make sure you get the full instructions and to get the information you need to do the Tasks.
If you try to just do the Tasks without the reading lab exercise, then often you do NOT know what to do.
A few sections and Tasks are explicitly marked as "Optional at the discretion of the instructor." These sections and Tasks are the ones the lab author thinks might need to be omitted. However, the instructor is free to omit sections and Tasks as they find necessary.
In fact, the lab exercises are all designed to be complete explorations of their main themes, and therefore usually are a bit too long intentionally. Also some sections/tasks might be too difficult for some classes. So some omissions are almost always necessary. The instructor should NOT as a usual rule shorten the lab below about 2 hours (see Lab Duration).
That learning is what helps you in following courses and all the rest of your life.
That said, to get an acceptable/good/great grade complete the Report Form correctly, completely, neatly.
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).
Caption: Constellation Gemini (The Twins) (zodiac symbol ♊) on a sky map of a portion of the celestial sphere.
Features:
However, they are an obvious pair on the sky for naked-eye astronomy.
Their angular separation is 4°30'19.53'' at some epoch, maybe the J2000 epoch (see Distance between Pollux and Castor?).
To be specific, Castor is a sextuple consisting of visual triple (i.e., 3 apparent stars) each of which is spectroscopic binary (a binary system only identifiable as such via spectroscopy and the Doppler effect).
The two brightest members of the visual triple constitute a double star in small telescope observation: i.e., Castor A and Castor B (see Wikipedia: Castor: Physical properties) which are separated by 4.87'' in 2013 (see Observer's Handbook, Royal Astronomical Society of Canada).
It takes excellent seeing for near the Las Vegas Strip (∼ 4'') to resolve Castor A and Castor B.
Image 1 Caption: A image of double star Albireo AB (β CYG AB, V_mag 3.1,5.1, angular separation 35'') in the Northern Hemisphere summer sky constellation Cygnus (Swan) taken 2023 Jul07.
You need to click on Image 1 and click on Albireo to get an enlarged view.
To locate Cygnus on an all-sky sky map, see Sky map files sky_map_all_sky.html
Features:
Selected astronomical object named and unnamed in the sky map: Albireo AB (β CYG AB, V_mag 3.1,5.1, angular separation 35'') Cepheus (King Cepheus), Cygnus (Swan), Deneb (α CYG), Draco (Dragon), Hercules (Heracles), Lyra (Lyre), Messier objects (M27 (Dumbbell Nebula), M39, M56, M57 (Ring Nebula)), Milky Way (shown by the smudgy blue band), Summer Triangle (asterism formed by Altair, Deneb, Vega), Vega (α LYR, V_mag 0.03), Vulpecula (Fox).
You can roughly measure angles using your hand.
Explication is given in the figure below (local link / general link: alien_angular.html).
Caption: How to measure angles approximately using your hand---in the form of spread hand, fist, and finger.
Now everyone's combination of hand and arm is a bit different---we are all unique---but just approximately at arm's length:
1 finger ≅ 1° 1 fist ≅ 7--10° (depends on whether you count the protruding thumb or not) 1 spread hand ≅ 18--20° (all from yours truly's own measurements).The above results are convenient for judging angles on the sky.
You CANNOT expect high accuracy/precision.
Examples of astronomical angles are:
Note: An angular diameter is the angle subtended by the diameter of a spherical astro-body (or any spherical body) as measured from some observation point which is usually the Earth for astronomy.
Credit/Permission: ©
David Jeffery,
2003 / Own work.
Image link: Itself.
Local file: local link: alien_angular.html.
File: Alien images file:
alien_angular.html.
What is the angular separation of Castor and Pollux in fists? Explain how you got your answer.
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.
Caption: Sky map Las Vegas, Nevada for current date & time.
Features:
If you are NOT in Las Vegas, Nevada, you will have to use your local geographic coordinates (i.e., latitude and longitude).
Conversion from Universal Time to Local Time and Vice Versa:
The abbreviations above are explained by the following linked terms: Pacific Daylight Time (PDT), Pacific Standard Time (PST), Universal Time (UT).
If you are NOT in Las Vegas, Nevada, see World Time Zones Map for the world time zones. You add/subtract the time zone numbers at the bottom of time zones to go from UT/(local time) to (local time)/UT. Remember that +(-x)=-x and -(-x)=x. Also note the time zone numbers are for standard time (ST). To convert daylight saving time (DST) to ST requires the mnemonic spring forward, fall back---so during DST subtract an hour to get ST. For example, say it is X local DST. It's then (X-1) local ST. If the time zone number is -8 (as for Las Vegas, Nevada), then the UT is (X-1) - (-8) = X+7, and so you get the rule above for Las Vegas, Nevada: UT = PDT+7.
Of course, you could just google "Universal Time" to get the current UT wherever you are. Then just add/subtract from that UT go get the UT you want. Say 6 pm local DST googles to 1 am UT (which is tomorrow) and you want to observe at 9 pm DST, then that will be 4 am UT.
Here are the main Solar System astronomical symbols:
,
Neptune ♆,
ex-planet Pluto ♇.
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.
_____________________________________________________________________________________________ Table: Observing Working Table for Double Stars _____________________________________________________________________________________________ Summer & Fall Double Stars _____________________________________________________________________________________________ Double Star θ V Observed Resolved Comment ('') (y/n) (y/n) (Ours/Yours) _____________________________________________________________________________________________ Mizar/Alcor (ζ/80 UMA) (Col) 709 2.2,4.0 OE, θ ≅ 12' ζ-1 Lyrae (SAO 67321) (Col) 44 4.3,5.9 South-east of Vega (α LYR) and in the same finderscope FOV Albireo AB (β CYG AB) (RASC) 34.3 3.1,5.1 Polaris AB (α UMi) (RASC) 18.2 2.0,8.7 Mizar AB (ζ UMA) (RASC) 14.5 2.3,4.0 OE Achird (η CAS AB, SAO 021732) (Col) 12 3.6,7.5 Almach (γ AND) (RASC) 9.5 2.3,5.1 Rasalgethi (α HER AB) (RASC) 4.6 3.5,5.4 OE δ CYG (Rukh, SAO 48796) (RASC) 2.7 2.9,6.3 _____________________________________________________________________________________________ Winter & Spring Double Stars _____________________________________________________________________________________________ Double Star θ V Observed Resolved Comment ('') (y/n) (y/n) (Ours/Yours) _____________________________________________________________________________________________ Mizar/Alcor (ζ/80 UMA) (Col) 709 2.2,4.0 θ ≅ 12' Cor Caroli (α CVN) (Col) 19.4 2.9,5.6 Polaris AB (α UMi) (RASC) 18.2 2.0,8.7 Mizar AB (ζ UMA) (RASC) 14.5 2.3,4.0 Achird (η CAS AB, SAO 021732) (Col) 12 3.6,7.5 OE Sirius AB (α CMA) (RASC) 9.5 -1.4,8.5 Hard to see B Rigel AB (β ORI) (RASC) 9.2 0.1,7.0 OE Castor AB (α GEM) (RASC) 4.9 1.9,2.9 North of Pollux Algieba (γ LEO) (RASC) 4.6 2.6,3.8 _____________________________________________________________________________________________
_____________________________________________________________________________________________
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
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.
Recall the visible band has fiducial range 0.4--0.7 μm.
So for visible band, a human-fiducial Rayleigh-criterion limit is
θ_RV ≅ 5''/D_in .
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:
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.
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
M*θ_HT = θ_H to get θ_HT = θ_H/M .
Thus, the fiducial telescopic human-eye angular resolution limit is
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).
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):
________________________________________________________________ Table: C8 Telescope Magnification and Field of View Primary diameter = 8 inches = 20.32 cm Primary effective focal length = 80 inches = 2.032 m ________________________________________________________________ Eyepiece Magnification Approximate focal length (X) field of view (FOV) (mm) (arcminutes = ') ________________________________________________________________ 40 50.8 40 25 80.3 30 18 112.9 20 12.5 162.6 14 9 225.8 10 ________________________________________________________________
________________________________________________________________
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,
θ_dominant = max( θS , θRV , θHT ) .
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:
_________________________________________________________________________________ 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 _________________________________________________________________________________
As an example of seeing, consider the film in the figure below (local link / general link: star_seeing.html).
Caption: "Slow-motion film of the star ε Aquilae taken with the Nordic Optical Telescope on the morning of 2000 May13 for testing lucky imaging (which is one form of speckle imaging)." (Slightly edited.)
Features:
Yours truly will do their best to explicate, but caveat lector.
The turbulent motions constantly distort the wavefronts of light or, from geometrical-optics perspective, the paths of the light rays.
The seeing is good if the distortion is small, bad if it's NOT.
In longer exposure-time images, all one would see is a single larger fuzzy blob called the seeing disk which is the time-averge of the individual ones.
The human eye actually can marginally detect the individual blobs which we call twinkling (AKA scintillation). Nevertheless, we tend to judge the apparent size of star by region in which we see twinkling occurs.
Setting λ=0.5 μm (just guessing that the film effective wavelength is somewhere in the middle of the visible band (fiducial range 0.4--0.7 μm)) and using D_in=101 for Nordic Optical Telescope, we obtain an angular diameter for the blobs of about 0.05 arcseconds ('').
It has been claimed---by Diane Pypher Smith?---that ∼ 4'' seeing is available near the Las Vegas Strip. Yours truly will believe it when yours truly resolves Castor AB which currently have angular separation of 3.8''.
D_in(saturation) = (4.952'')*[(λ_μ/0.5 μm)/θ_seeing_disk('')] ,
where D_in(saturation) is the saturation diameter in inches,
λ_μ is wavelength
in microns (μm),
and θ_seeing_disk('') is the
seeing disk
diameter in
arcseconds.
From this saturation formula, it's clear that with good seeing ≅ 1'', the saturation diameter is about a measly 5 inches. With great seeing ≅ 0.4'', the saturation diameter is about a measly 12 inches.
However, light-gathering power grows as the square of the primary diameter, and so yes, the bigger the telescope, the better for going deep (i.e., for observing faint objects).
That's why we keep making bigger telescopes (e.g., extremely large telescopes (ELTs) such as TMT, GMT, and EELT).
Its angular resolution is typically about 1 arcminute (') = 60'', but some sharp-eyed people may be able to do better (see Wikipedia: Naked-eye astronomy).
Taking the human pupil as the circular aperture, one can use the Dawes limit to estimate human eye angular resolution.
There is considerable variation between individuals, but typically for scotopic vision the pupil diameter is in the range 4--9 mm ≅ 0.15--0.35 in (see Wikipedia: Pupil: Optic effects). With these values, the Dawes limit formula,
θ_DL('') = (4.56'')/D_in ,
suggests that
human eye
angular resolution
as small as 13'' is possible.
However, the Dawes limit and the Rayleigh criterion are probably only part of the story in determining human eye angular resolution.
In any case, human eye angular resolution is too big for seeing (if it isn't awful) to be a limitation in naked-eye astronomy.
These techniques include lucky imaging, speckle imaging, and, creme de la creme adaptive optics.
None of these are currently available in UNLV's intro astronomy labs.
Actually, adaptive optics have gone a long way to reduce the need for space astronomy, but there are still many observations that can only be done from space.
There is no immediate replacement for the HST when it dies sometime after 2020 (see Wikipedia: Hubble Space Telescope: Orbital decay).
Sub Tasks:
Caption: A simulated Airy diffraction pattern with intensity in grayscale.
Features:
If λ << L (where L is the characteristic length of the aperture or obstacle that cuts the wavefronts), then the diffraction pattern alternating dark and bright fringes are very tiny about the bright central fringe which approximates an ideal beam of light rays.
So the diffraction patterns at the edges of shadows are usually too minute to be observed by casual observation.
But actually, we'd notice them pretty often if they weren't generally partially averaged away as discussed above.
Sub Tasks:
Caption: Two overlapping Airy diffraction patterns (in some optical device with a circular aperture) for two identical monochromatic point light sources at optical infinity separated in angle θ. Going downward in the image, θ goes 2θ_R, θ_R, and (1/2)*θ_R, where θ_R is the Rayleigh criterion.
Features:
If there is no effective overlap, the two sources are cleanly resolved.
If θ = 0, the 2 point light sources will coincide exactly and CANNOT be distinguished at all.
θ_R = (1.21966989 ...)*(λ/D)
≅ 1.220*(λ/D) ,
where
So the Rayleigh criterion is NOT an absolute limit of angular resolution merely a fiducial one and often a practical one.
The 3rd panel in the image shows that case of θ = (1/2)*θ_R is distinguishable from complete overlap, and so does actually resolve the 2 point light sources.
However, if your measuring device was poor θ = (1/2)*θ_R may be effectively an unresolvable separation.
θ_R = (1.21966989 ...)*(λ/D) radians ≅ 1.220*(λ/D) radians standard form
= (25.16'')*(λ_μm/D_cm) = (9.905'')*(λ_μm/D_in) fiducial-value form
= (4.952'')*[(λ_μm/(0.5 μm))/D_in] fiducial-value form
≅ (5'')*[(λ_μm/(0.5 μm))/D_in] approximate fiducial-value form,
where θ_R('') is in arcseconds ('') (1° = 3600''),
λ_μm is wavelength in
microns (μm),
D_cm is aperture
diameter
in centimeters,
and D_in is aperture
diameter
in inches
(1 in = 2.54 cm exactly in modern definition).
For visible light (fiducial range 0.4--0.7 μm), one can often just use the last version of the above formula for crude calculations.
The Dawes limit was determined by an empirical study of what angular resolution humans could obtain when observing close binary systems (see Wikipedia: Angular resolution: Rayleigh criterion).
θ_DL('') = (4.56'')/D_in .
There is NO explicit wavelength dependence
since the formula was obtained for effective
human eye
wavelength-averagved
psychophysical sensitivity to
stars.
Actually, people often just conflate the Rayleigh criterion and the Dawes limit because they have such similar formulae, but they are really NOT the same thing.
The Dawes wavelength can only be considered a characteristic or average wavelength for psychophysical sensitivity for resolving stars assuming that the Dawes limit is, in fact, approximately the Rayleigh criterion.
But starlight is a mixture of spectral colors and, in fact, the mixture never looks blue to yours truly on the sky.
So if the Dawes limit is approximately Rayleigh criterion, it is NOT because starlight is pure blue.
Well, the two values are NOT so far apart, but NOT so close that we can say for sure that we've proven Dawes limit is approximately the Rayleigh criterion.
Credit/Permission: Spencer Bliven (AKA User:Quantum7),
2014 /
Public domain.
Image link: Wikimedia Commons.
Local file: local link: optics_rayleigh_criterion.html.
File: Optics file:
optics_rayleigh_criterion.html.
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.
The animations in the 2 figure below (local link / general link: orbit_elliptical_explication.html) illustrate exact gravitational two-body systems.
Image 1 Caption: An animation of a (gravitationally-bound) gavitational two-body system with two spherically symmetric, equal-mass astro-bodies orbiting in elliptical orbits around their common center of mass which marked by a red cross.
The star sizes are vastly exaggerated relative to the inter-star distances for most binaries---but NOT all---there are some very close binary systems.
Features of general gravitational two-body systems:
a=(1/2)*( r_periapsis +r_apoapsis ) ,where r_periapsis is the periapsis separation and r_apoapsis is the apoapsis separation.
Image 2 Caption: A gravitationally-bound gavitational two-body system with a large difference in mass between the two spherically-symmetric astro-bodies orbiting in circular orbits their common center of mass which marked by a red cross.
In this case, the more massive body center would effectively be the center of mass of the gavitational two-body system.
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.
Caption: The apparent relative orbit (right) and true relative orbit (left) of Sirius B around Sirius A.
Collectively Sirius A and Sirius B constitute the binary system Sirius AB.
Features:
Usually, the astro-body that acts as the origin is the more massive.
Sirius A is A1 V star (i.e., a main-sequence A1 star). It has apparent V magnitude -1.47, stellar mass 2.02 M_☉, and luminosity 25.4 L_☉.
Sirius A is, in fact, the brightest star on the sky (i.e., the star of highest apparent brightness).
However, one can also use Sirius to mean just Sirius A.
Context tells you what is meant
As the image illustrates, the angular separation of Sirius A and Sirius B is order of magnitude 10''
The human eye angular resolution has the typical and fiducial value 1 arcminute (') = 60'' (see Wikipedia: Naked-eye astronomy). Some sharp-eyed people may be able to do better.
A White dwarf is a post-main-sequence star that has ended its nuclear-burning lifetime, lost much of its original mass, and is now cooling off forever.
However, originally Sirius B was the larger, more luminous star.
The more massive one, and therefore brighter one, runs through all phases of its nuclear-burning lifetime faster than the less massive one.
Ergo, Sirius B was once the primary star.
It lost a large fraction of its mass due to strong stellar winds in post-main-sequence evolution.
The animation in the figure below (local link / general link: star_binary_eclipsing.html) illuatrates an eclipsing binary which is also a close binary.
This binary system is a close binary because the relative mean orbital radius is NOT large compared to the stellar radii of at least one of the binary stars.
To be an eclipsing binary, the binary is seen nearly edge-on (i.e., at an inclination relative to the line of sight of nearly 90°).
If only one component star's spectral lines are seen the binary is a single-lined spectroscopic binary.
If spectral lines are seen from both component stars, the binary is a double-lined spectroscopic binary.
Visual binaries are those that can be resolved into two stars.
There may be some eclipsing binaries that are visual binaries, but yours truly knows of none.
All one can determine for a double-lined spectroscopic binary is the quantity m*sin(i)**3, where m is the stellar mass of a component star, i is inclination, and sin is the sine function. We know even less about the stellar mass of single-lined spectroscopic binaries (e.g., Shane Larson: Binary Stars).
However, for an eclipsing binary, we know inclination i ≅ 90°. So at least for double-lined spectroscopic binaries we can determine the component stellar masses to some accuracy.
One can, of course, determine mass for stars by modeling and stellar spectroscopic data, but those results are then model-dependent, of course.
The other method is the Doppler spectroscopy method.
Sub Tasks:
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.
Sub Tasks:
The sky map is set to 9:00 pm for the Pacific time zone (PST/PDT).
If you are NOT in Las Vegas, Nevada or want a different Date & Time, you will have to update control panel fields below the sky map and then click on the Update button just below the sky map:
If you need help getting the Universal Time (UT), click on Conversion from Universal Time to Local Time and Vice Versa.
If you have NO printer, you will have to sketch the sky map. Sketch and label the major constellations, the named stars (e.g., Vega (α LYR) in the summer night sky and Betelgeuse (α ORI) in the winter night sky) and Polaris (α UMi) (which is just α UMi on the sky map), the planets, and, if in the sky, the Moon.
The planets are labeled on the sky map by the planet symbols: Mercury ☿, Venus ♀, Earth ⊕, Mars ♂, Jupiter ♃, Saturn ♄, Uranus ↑☉,♅, Neptune ♆, ex-planet Pluto ♇.
To use the sky map outside, you will probably need a flashlight or cell phone.
In the winter night sky, you should be able to see Orion (which is a recognized IAU 88 constellation).
Of course, if you are clouded out, there's nothing to see.
My Answer: I'd guess I'd identify lots. On 2020 Jun10, I should be able to see Mercury ☿ at about 8:30 pm about a spread hand above the horizon. One has to stare for awhile to see it leap out of the dim twilight.
Caption: Nott riding Hrimfaxi.
Nott is the goddess of night in Norse mythology. Hrimfaxi is her horse. She also has---as a Renaissance intrusion---a cherub (in the sense of putto).
Nott, night---you get it---you see you understand Old Norse when you really, really try. Indo-European languages are all pretty much the same thing.
Credit/Permission: Peter Nicolai Arbo (1831--1892),
2nd half of the 19th century
(uploaded to Wikipedia
by User:Florian Huber,
2005) /
Public domain.
Image link: Wikipedia.
Local file: local link: nott_riding_hrimfaxi.html.
File: Art file:
nott_riding_hrimfaxi.html.
Caption: Film poster for TheMummy (1932) starring Boris Karloff (1887--1969).
Credit/Permission: Employee or employees of
Universal Pictures
attributed to
Karoly Grosz (fl. 1930s),
1932
(uploaded to Wikipedia
by User:Crisco 1492,
2012) /
Public domain.
Image link: Wikipedia:
File:The_Mummy_1932_film_poster.jpg.
Local file: local link: the_mummy.html.
File: Art file:
the_mummy.html.
