Disclaimer: links to web sites are ever-changing.  It turns out to be a Sisyphus task to keep them updated all the time.  Therefore, either try a different "spelling" of the hyperlink, look for it on google.com and/or let me know about an outdated link by writing an e-mail to aveh@wncc.net .

 
F0  Parallax F5  Spectra of gases
F1  Constellations F6  Stellar Spectra
F2  Age and distance of a star cluster F7  Optics
F3  Starfinder (fall or spring ) F8  Telescopes
F4  Coordinates (fall or spring ) F9  Kepler's Third Law



Lab      F0    Stellar Parallax

These stars are part of the small constellation "Canis Miragelis" (the Miracle Dog).
Notice the big (i.e. bright) star Alpha Canis Mirageorum.  It seems to have shifted slightly when comparing the two pictures.  Just above the middle you see an isosceles triangle.  The star Gamma is to the left of this triangle in one picture and to the right in the other picture.  And just above the triangle is the variable V162 which shifted as well.
How come?  These stars do this once every year, shifting right to left and back.  The left-hand picture was taken in spring 98, the right-hand picture in fall 98.  Between the two pictures our own Earth has moved to the other side of our Sun, producing a baseline of 300 million km (180 million miles).  Different vantage points for our observations mean that close-by stars seem to have shifted.  The more the shift, the closer the star must be.  This is called parallax.  And the distance can be determined via triangulation.
The other stars are so far away that their parallax is not observable.

The method described above is correct and is really applied.  Measurements have been made since 1810 (first by F.W. Bessel) and have been improved upon.  The most accurate measurements were recently completed by Hipparcos .  Stars need to be very close (within 100 ly), otherwise parallax doesn't show up.
Nevertheless I cheated during the above description.  There is no constellation "Canis Miragelis" and stars do not shift as much as indicated.  The true apparent shift is smaller than a penny would appear at a distance of more than 1 km (1 mile).
The stars are instead "Glow in the Dark Stars" that I attached to the wall in my lab.  From the light fixture above these stars I extended a   1 m   beam into the room, on which I hung the 3 stars (that appear to shift).  It looks really neat when the lights are off.  Standing on the other side of the room (a = 6.80 m) and moving sideways then really gives the impression that these three stars that are closer seem to shift.  It mimics parallactic motion really well.
The stars are cream colored but have a greenish glow in the dark.  Exposure time was 1 min with the lights off.

Check here for a description of the parallactic method and triangulation (link temporarily offline).

The same images as negative prints (and bigger), so it's easier to evaluate them:

Objective: Determine the distance to the stars that appear to shift. For online students: usually I will just ask you to determine which star is closest and which is farthest.

Procedure:

  1. The baseline used was the front desk in my lab (b = 1.5 m).
  2. The stars on the wall don't shift, their angle of shift is a = 0 degrees.  In real astronomy we say that this corresponds to an infinite distance (d = b / tan 0), which, of course, is not true: but they're so far we can safely assume, for the sake of measuring the closer stars, that they are at infinity.  Anyway, in our case they're on the wall at d = 6.8 m .  That gives an angle of a _w= arctan (b / d) = arctan (1.5 / 6.8) = 12.4 degrees (this angle appears only here because we do this in my lab).
  3. As a reference we take the three wall stars above the middle that form an isosceles triangle.  The angle between the upper two stars is a_i = 0.9 degrees .  You need this value when using the simple proportions.  Measure in mm (or fraction of an inch) the distance  d_i  between these two stars.
  4. Check my calculations for star x.
  5. Measure the distance  d_x  by which the star  x  shifted (e.g. put one negative photo atop the other).  Determine its angle a_x  via   a_x =  a_i * (d_x / d_i).
  6. Determine its distance to us, the observer on the baseline (i.e. at the front desk), via  d = b / tan (a_x + a_w) = 1.5 m / tan ( a _x + 12.4).
  7. Do the same for stars y and z.

    8.  

     
     
     
     
     
     
     
    d_i = ...      (on my print-out it's  10 mm)

    		star x star y star z
    d_x 2 mm

    a_x  0.2 deg

      d 6.71 m

    true d 6.7 m 5.8 m 6.5 m



Lab        F1  Constellations

There are a total of 88 constellations, most of which got their names from Greek mythology, and a few, mostly in the Southern hemisphere where they were not accessible to the ancient Greeks (and neither to most of my students), got their names in the past centuries, named after creatures or new inventions.

This lab asks for your opinion and for your imagination.

Look at a few constellations and decide if they really do resemble a the ancient description or a more recent, but popular meaning.  You may invent your own descriptions, but keep in my mind that the ancient and more recent names are established.  Thus there would be very people who could agree with you.

Example: Delphinus, the dolphin is recognizable by many observers.  A former student suggested "knapsack".  Perhaps.  The problem is that that description doesn't communicate with other astronomers because for them it's a dolphin.  So although inventing new names is fun, communicate with me and the others by using the established names.

Fall semester:
Sagittarius = marksman, popular: teapot and milk dipper
Scorpius = scorpion
Cygnus = swan, popular: cross
Lyra = harp
Aquila = eagle
Bootes = herdsman, popular: kite (I heard ice cream cone before)
Corona Borealis = northern crown
Delphinus = dolphin (I heard knap sack before)
 

Spring semester:
Canis Major = big dog
Pegasus = winged horse, popular: great square, (baseball) diamond
Orion = hunter
Auriga = charioteer, popular: pentagon
Taurus = bull (snout and horns)
Leo = lion
 

Circumpolar:
Ursa Major = big bear, popular: big dipper, big wagon
Ursa Minor = little bear, popular: little dipper, little wagon
Cepheus = king, popular: house
Cassiopeia = queen, popular: celestial W
 



Lab         F2   Age and Distance of a Star Cluster
    1. Print the two HR-diagrams.  Lay them on top of each other.
    2. With the color index B-V values being aligned, shift the diagrams up and down only until they match.  The y-axes should show a difference V-M of 4, 5, or 6 magnitudes.
    3. Determine this difference V-M (apparent minus absolute magnitude).  Plug this value into this equation:   d = 32.6 ly * 10^(V-M/5).  This gives you an approximate distance to the Pleiades.  (The accepted value is 400 lightyears, but you're fine if you're in the ballpark range of that value.)
    4. Next determine the age of this cluster.  We do that by determining where the turn-off point of the cluster lies.  Turn-off means the point, where the hotter, bluer or whiter, brighter, and therefore more massive and short-lived stars have already left the Main-Sequence.  It appears that the Pleiades are so young that a turn-off point really doesn't exist yet.  So what you do is to take the brightest, hottest star still remaining on the Main Sequence, determine the its color index or temperature, then check my SEA-5 to determine its MS lifetime.  This can be taken as the maximum age of the Pleiades.  (The accepted value is 50-100 million years.)


    HR-diagram of the closest 100,000 stars.  (c) The Hipparcos Space Astrometry Mission, ESA - European Space Agency .


    This (not yet complete) HR-diagram of the Pleiades was created from the data of 24 stars that previous students (spring 97 - spring 98) analyzed with the CLEA labs on Photometry and Stellar Spectra .  These labs supply 79 stars, so ways to go.  Updated on January 5, 1999.

Lab         F3 I         Starfinder
 

  • Note: During Daylight's Savings Time, the time on the star finder trails by 1 hour.
  • Set the star finder to today's date at 8 p.m.
  • During the following exercises, turn the star finder slowly between 7 p.m. and 10 p.m., which is about our observation time.
  • Name three constellations that are setting in the West during this time.  Name 3 bright stars that are setting in the West.
  • Name 3 constellations which are rising in the East.  Name 3 bright stars which are rising in the East.
  • Redraw the constellations CASSIOPEIA, CEPHEUS, CYGNUS, URSA MAJOR, SCORPIUS (online students don't need to submit their drawings). These constellations are easy to find in the sky. What do their names mean?
  • AQUILA is a summer constellation. At which dates would it be directly in the south at 7 p.m., 8 p.m., 9 p.m.? ("In the south" (on the meridian) means also that a constellation has its highest altitude, and is therefore dominant in the sky.)
  • Now turn the star finder all the way around. As you turn it, notice that some constellations close to the North Star (Polaris), which is a star in the URSA MINOR, never set or rise. These constellations are visible throughout the year. Name them.

    •  
  • Clear skies:  Find the above stars and constellations in the night sky and confirm your results.

    • Lab         F3 V         Starfinder
     

  • Note: During Daylight's Savings Time, the time on the star finder trails by 1 hour.
  • Set the star finder to today's date at 8 p.m.
  • During the following exercises, turn the star finder slowly between 7 p.m. and 10 p.m., which is about our observation time.
  • Name three constellations that are setting in the West during this time.  Name 3 bright stars that are setting in the West.
  • Name 3 constellations which are rising in the East.  Name 3 bright stars which are rising in the East.
  • Redraw the constellations CASSIOPEIA, CEPHEUS, AURIGA, URSA MAJOR, ORION (online students don't need to submit their drawings). These constellations are easy to find in the sky. What do their names mean?
  • ORION is a winter constellation. At which dates would it be directly in the south at 7 p.m., 8 p.m., 9 p.m.? ("In the south" (on the meridian) means also that a constellation has its highest altitude, and is therefore dominant in the sky.)
  • Now turn the star finder all the way around. As you turn it, notice that some constellations close to the North Star (Polaris), which is a star in the URSA MINOR, never set or rise. These constellations are visible throughout the year. Name them.

    •  
  • Clear skies:  Find the above stars and constellations in the night sky and confirm your results.


    • Lab          F4 I    Coordinates

      1. Define:
      2. Estimate azimuth and altitude (note date and time of observation) of the following constellations on your starfinder.
      3. Find them in the sky.

        4.  

        		Azimuth (deg) Altitude (deg)
        Bootes

        Ursa Major

        Sagittarius

        Cassiopeia

        Delphinus


         
      4. Find these bright stars (and planet) in the sky.

        5.  

        		Azimuth
        (deg)        		 Altitude
        (deg)        		 Right Ascension
        (h m)        		 Declination
        (deg)
        Polaris



        Arcturus



        Altair



        Alpheratz



        Dubhe



        Fomalhaut



        Mars




    Lab          F4 V    Coordinates
     

    1. Define:
    2. Estimate azimuth and altitude (note date and time of observation) of the following constellations on your starfinder.
    3. Find them in the sky.
    4. Find these bright stars (and planet) in the sky.
        5.  

        		Azimuth
        (deg)        		 Altitude
        (deg)        		 Right Ascension
        (h m)        		 Declination
        (deg)
        Polaris



        Betelgeuse



        Sirius



        Algol



        Aldebaran



        Saturn




    Lab           F5        Spectra of gases

    Objective: Observe the spectra of several gases, compare them to supplied spectra from books and determine which gases they are. Notice that the spectrum of a gas is like a fingerprint identifying this gas.

    Procedure:

  • Before doing the following, go to the website of the Chemistry Department at the University of Wisconsin (under exercises in my "other websites"), respectively access their Spectroscope page (link doesn't work). Read through it (it's a short text) and do the self-check exercises.
  • The following spectra were taken in the physics lab at WNCC using an SLR camera with a 100mm objective, all photos had exposure times between 1/60 sec and 1/2 sec, photographed through a grating (600 lines per mm):

    •  

     

    The choices are Argon, Carbondioxid, Helium, Hydrogen, Krypton, Mercury, Neon, and Sodium.
     
    ... a ... e
    ... b ... f
    ... c ... g
    ... d ... h
    An example of a continuous spectrum from a light bulb: 
    		Spectrum of Regulus (a Leonis), (c) Martin Reble, Berlin.  Identify the absorption lines in this stellar spectrum (all from one element), then determine Regulus’ spectral type.  (I know that the red absorption line is missing, but you should be able to find the other three lines.)

     

  • The spectra of which gases have you seen?  Label them correctly.  Compare them to the spectra featured on John Talbot's Plasma Laser Astrophysics web site or the Portugese copy of the Virtual laboratory at the University of Oregon .

    •  
  • What kind of spectra are the laboratory ones? ...

    •  
  • Which properties of a star do the following tell us?  (With properties I mean temperature, luminosity, mass, radial velocity, and such.)

    •  

     

    spectral type - ...

    strength of lines - ... or ...

    Doppler shift - ...

    changing Doppler shift - ...

    present lines - ...

    split lines - ...

    skewed lines - ...
     
     

  • Examples of stellar absorption spectra (note that only the far purple is represented).  Check out the first three slides at this site at the University of Erlangen .

    •  

     


    Lab    F6    Stellar Spectra

    Part 1:  determine spectral lines in our Sun's spectrum.

    Access the Observatoire de Paris and follow my instructions.

    Which of these elements' absorption lines show up fairly STRONG in our Sun's spectrum?
     
     
    instructions:  make check marks for the settings "Plot dat", "Image data" 
    Element
    		 Wavelength(s)   color    weak or strong?   start wavelength   range 
    Calcium II Ca II 3934 & 3968   UV     _________ 3900 100
    Iron Fe 5227.2    green     _________ 5227 4
    Gold Au 5230.3    green     _________ ditto ditto
    Sodium Na 5890 & 5896  yellow     _________ 5860 40
    Helium He 5870  yellow     _________ ditto ditto
    Titaniumoxide  TiO 6159   red     _________ 6150 20
    Hydrogen H 6563   red     _________ 6560 10

    There are plenty more absorption lines for each element, but I only wanted to give you a sample.

    In the above table, you should have four "yes's" and three "no's".  After you've read through the lectures that I had recommended, you should be able to figure out why some lines show up and others don't.

    Answer:  _____________________________________________________________
     
     

    Part 2:  determine the spectral type of four stars.

    Find An Atlas of Stellar Spectra here.

    Note that the given part of each spectrum runs from 3800 to 4800 Å, i.e. in the far purple.

    Click on the image to see it enlarged.

    All stars are Main Sequence, luminosity class V "dwarfs" (this obviously is a misnomer for the O- and B-stars).

    You have to compare these spectra to the diagram in my lecture Measuring Stars which shows enough detail in the purple region.  Note that the spectral standards themselves represent only a middle portion of the spectra below.  Take the Calcium and Hydrogen lines as an orientation help.


    Click on the image to get a larger version.  The star names are from top to bottom HD 46223, a Leonis (Regulus), b Com, s Draconis .  Your choices for spectral type are O4, B7, G0, and K0.
     
     


     

    If you want to see the entire diagram from which I chose the above selection:

    The stars are from top to bottom:
    HD 46223, HD 46150
    u Orionis
    n Andromedae
    a Leonis (Regulus)
    a Lyrae (Vega)
    b Arietis, q Cassiopaiae, r Geminiorum
    45 Bootes, b Com
    b Camelopardalis, 16 Cygni A, 16 Cygni B, x Bootes A, s Draconis
    61 Cygni A, 61 Cygni B, HD 95735

    The spectral types to choose from are O4, O5, B0, B5, B7, A0, A5, A7, F0, F5, G0, G0, G2, G5, G8, K0, K5, K7, M2.  All of them are luminosity class V.


    Lab       F7      Optics

    Objective: Become familiar with basic optical principals.
     - Focal Point

     Put a lamp onto the front desk. With a convex lens, go the other end of the room and focus the lamp's filament onto the wall (it works everywhere along the wall). Measure the distance lens-wall, which in this case equals the focal length.

     - Magnifying Glass

     Lay your convex lens on top of a page in your book. Keep your eyes at a distance. Lift the convex lens slowly up. Describe what happens to its size and orientation (there will be about four different situations as the lens' distance to the book increases).
    Repeat the same for a concave lens.

     And now for concave and convex mirrors. Hold your face closely to the mirror and then remove it slowly. See what happens to the image.

     - Image formation / focal point

     a) usage of Fisher box: Put a 3- or 5-slit in front of the lamp, such that the extending rays are parallel. Take a convex lens and see where the focus is.
    Do the same for a concave lens and for concave and convex mirrors.
    Which of these four lenses/mirrors, do you think, are suitable for image formation?

     b) usage of optical bench: Assemble a convex lens, a lamp (semi-transparent screen with arrows) and a blank screen on the optical bench. Get an image of the arrows on the screen. See what happens to the image when you shift lens and screen.
    Do the same for a concave lens and for concave and convex mirrors.
    Which of these four lenses/mirrors are apparently suitable for image formation (you should be able to arrive at a definite answer, more so than on part a))?

     - Combination of lenses

     For a) above, put the convex and concave lenses together and see what happens.

     For b) above, put two lenses together (check your textbook and Lab F8 Telescopes) to get an astronomical telescope.

     - Questions:
    a) A telescope's objective is either a ____________ lens or a _____________ mirror.
    b) A telescope's eyepiece is always a ____________ lens.
    c) Apparently a concave lens does not produce a real image. Give a simple example of its use.

    Lab       F8      Telescopes

    Objective: Get to know how a telescope works.

    1. Name the two main groups of telescopes. Discuss their advantages and disadvantages.

      2.  
    2. Look at the telescopes that you use during the labs. What are their respective names?

      3.  
    3. Learn how to handle these telescopes.
    4. Name the important features (e.g. aperture) and parts (e.g. secondary mirror) of telescopes.

      5.  
    5. Build a telescope with the supplied lenses.

      6.  
    6. Demonstrate resolving power by putting two chalk points closely to each other on the board. First resolve them with the unaided eye and then with the telescope.
    7. Show how the telescope inverses a picture. How does this inversion affect observations?


    Objective: Get to know the powers of a telescope. (Write your answers on the back of this page)

       Definitions:
    1. Bring the 3 features of a telescope,
      1. a) resolving power (alpha = 11.6/D in seconds of arc),
      2. b) magnification (M = f objective/f eyepiece),
      3. c) light-gathering power (B ~ D squared)

        4. into the correct order starting with the most important.
    2. Construct a telescope on the optical bench.
    3. a) What lenses do you choose for greatest magnification?

      4. b) What objective lens do you choose for best resolution and brightness?
    4. Lightgathering power

      5. Assemble one faint (!, i.e. using the potentiometer) light bulb on the circuit board. Now you resembled a faint star.
      Go into the hallway (between trophies and library) with circuit board and telescope (you might have to lie on the ground to view through your telescope).
      Stand at a distance, where you can't see the faint bulb.
      Use your telescope. Can you see the bulb?
      If you happen to see the light creating several colors, what is this error called?
      (This is one disadvantage of refractors as compared to reflectors: it occurs only with lenses.)
       
    5. Resolving power

      6. Assemble two lamps in parallel, so that they have the same brightness. Stand at a distance, where you can barely distinguish between both lamps.
      = tan-1(dl/ds), (dl - distance lamp-lamp; ds - distance students-lamps) gives you the resolving power of your eyes.
      Go further away. Use your telescope to resolve both lamps.
      Using a telescope's equation for resolving power (top of page), how far away could these lamps be, while still being resolved?
       
    6. Magnification: Look at something far away. Estimate by how much it is magnified.

      7. How can the magnification of a telescope easily be changed?



    Lab        F9       Kepler's 3rd Law

    You need a scientific calculator.  I bet that the computer you're working one, has one when you click on "Start", "Programs", "Accessories", respectively check one of these online scientific calculators , another one , another one , and another .

    Objective: Kepler's 3rd law applies to the planets orbiting their central body, our Sun.  For these P^2 / a^3 is constant (P -Period; a-distance to central body, i.e. semimajor axis). Show that P^2 / a^3 is also constant for moons orbiting their respective central bodies, in this lab Jupiter, Saturn, Uranus, and Earth, i.e. every planet has its own constant.

    Then we will use Kepler 3 to determine at what height above Earth's surface we have to put a certain satellite.

    Help each other!
     

  • Check your textbook (e.g. Arny p.45), which shows P^2 / a^3 to be a constant (in this case the constant is 1.000, because Earth-years and A.U. are the chosen units, which are of course 1.000 for Earth).  Some tables don't show this constant: if you want, confirm that it is 1.000 by using the formula.
        •  
        Example:
         
        Planets

        		Period P
        [Earth-years]        		 Distance a
        [A.U.]        		 P^2 / a^3
        Mercury
        0.241
        		 0.387 1.002
        ..


        Earth 1.000 1.000
        1.000
        ..


        Jupiter
        11.86
        		 5.203
        0.999
        ..


        Uranus
        83.75
        19.19
        0.993
        ..


        ..


    Of course the numbers are not exactly 1.000 because of rounding as I was using 3 or 4 decimals.  Using all 6 decimals supplied in some textbooks makes the constant to be consistent to 6 decimals.
    What's the purpose of playing with these numbers?  THIS  IS  THE  RELATION  BETWEEN   DISTANCE  AND  PERIOD  FOR  ANY  ORBITING  BODY !  I.e. by knowing Kepler's 3rd law we can predict the orbits of everything: planets, moons, artificial satellites, Earth-threatening asteroids, binary stars, galactic rotations.  And the mass M of the central body is hidden in the constant ( P^2 / a^3 = constant = 4 p^2 / G M ).
     
  • Confirm Kepler's 3rd law for the moons of some planets. Note that you have to square   P  and divide by the cube of   a  .

    • On a graphing calculator it would look like this:
     
    The first line contains Mercury's period and distance, then there is Jupiter's moon Io, then Uranus' Miranda.  I used a graphing calculator's screen so I can show you which steps you have to do for these calculations.  Most of you own a simple calculator.  It certainly has a "x2 " key for squaring a number and a "xy" key (or yx, same thing) for the "^", so you'd type (for Mercury) ".241" .. "x2 " .. "/" .. ".387" .. "xy" .. "3" .. "=" .  On an even simpler calculator, multiply .241 twice, then divide by .387 three times.
    Repeat these sample computations on your calculator.  If you get my result, you know that you're doing it right. 

    Online scientific calculator , another one , another one , and another .

         
        Jupiter's moons

        		Period P
        [Earth days]        		 Distance a
        [planet radii]        		 P^2 / a^3
        Io 1.77 5.91 0.0152
        Europa 3.55 9.40
        Ganymede
        		15.0
        Callisto
        26.3
        For diagrams picturing the orbits of Jupiter's moons go to lab G1 Jupiter's moon and to the Kepler section in my VITs lecture .

        Saturn's moons

        		Period P
        [Earth days]        		 Distance a
        [planet radii]        		 P^2 / a^3
        Titan 16 20.3 0.0306
        Mimas 0.94 3.1
        Tethys
        1.93
        4.92
         
        Dione
        2.73
        6.26
         
        Iapetus
        79.2
        59.1
         
     Kepler's 3rd law is independent of the units used. So this time use kilometers.
        Uranus' moons

        		Period P
        [Earth days]        		 Distance a
        [km]        		 P^2 / a^3
        [10^-16]
        Miranda 1.41 130,000 9.049
        Umbriel
        		266,000
        Oberon


  • In the previous exercises you noticed that each planet has its own constant for Kepler's 3rd law. Now determine the Earth's constant. Take our Moon's distance in kilometers.
        •  
        Earth's satellites

        		Period P
        [Earth days]        		 Distance a
        [km]        		 P^2 / a^3
        [10^-14]
        Moon


        stationary
        satellite        		 1

    Now that you know the Earth's constant, work "backwards" and determine the distance   a   (in km) of a stationary communication satellite that hovers over the Atlantic to transmit television and radio programs as well as telephone links between Europe and North America. This satellite has a period of P = 1 day, so it stays always in the same place.  The "backwards" formula (invert the constant and take the cube root) : a = cube root (P^2 / const.)   or   a = (P^2 / const.)^(1/3)   .   What's the purpose?  There are currently 500 working satellites in orbit around Earth. All satellites obey Kepler's laws.  A company wants its satellite to orbit the Earth in 1 day (weather and communication satellites) - put it at the distance you just calculated.  Surveying and spy satellites need to orbit Earth at close distances: Kepler 3 (using Earth's constant) tells them that at 200 miles above the surface they need 1.5 hours for one orbit.
     
  • Each planet's constant includes this planet's mass. The masses of Mercury, Venus, and Pluto were not known accurately until the mid 1970's. Why not?
    • To my WNCC Astronomy home page .