This lab helps the students visualize Kepler’s laws of planetary motion using a computer program. The CDs with the Kepler software are stored in the server room (Rm 118), typically on the shelf with the other DVDs and tapes. Groups larger than 3 students are not good for this lab, since that leads to one or two people doing the work while the rest sit around getting bored.

Since this is a computer-based lab, you will have to use one of the computer labs on campus, and we typtically use Jacobs 129. Reserve the computer room way in advance of your lab using the ICT lab reservation request form, and make sure either you or the Head TA checks to ensure the software still works on the computers (sometimes we have issues when ICT does software updates). If you have a Windows laptop and want to play around with the software, you may need to put the threed32.ocx file in your C:Windowssystem folder. If the program doesn’t work at all, you can try using java applets as backups:

• First, Second, and Third laws Applet allows you to adjust the semi-major axis, the eccentricity, and the animation speed. Click each tab to demonstrate each law (sum of distances to foci, equal area in equal time, and period versus semi-major axis).
  • First law Applet allows you to pick the starting point and initial velocity of a planet orbiting our Sun
    First law Applet allows you to change the orbit size and eccentricity of a planet orbiting our Sun.
  • Second law “Continue” and “Pause” start and stop the simulation. Clicking “Start Sweeping” and then “Stop Sweeping” will show the area covered in a certain time, and then clicking “Start Sweeping” again at some other point in the orbit will show the area covered in that same time interval.
    Second law A simpler demo that shows areas at perihelion and aphelion
  • Third law Applet demonstrates how eccentricity doesn’t affect the period by showing two planets with the same semi-major axis but different eccentricities.
• Simple binay star orbit Applet allows you to adjust mass ratio, inclination, and eccentricity
• Chaotic planet orbits in a binary star system
  Various setups for Earth-Moon-Satellite 3body systems

You should go over the laws (and the law of gravity) in your intro lecture. This is a long lab to do and to grade. Stay on top of your students so they finish on time; if they goof off they’ll end up needing an extra half hour. Groups of five or larger are unwieldy for this lab, so have your students break into smaller groups if you need to.Explain exercises 1 and 2 but suggest doing them last. They can do them at home if they run out of time. Be warned, the students don’t visualize the sum of the distance to the foci staying constant, even with the imagery of the colored arrows. They’ll say something like ‘the blue arrows get shorter and then longer’ to describe what happens.

The instantaneous velocity equation, V=SQRT( (G(M+M) / (2/r – 1/a) ), really confuses the students. Remind them that they will set a and G(M+M) equal to 1 and then solve for V when r=0.5a for perihelion and when r=1.5a at aphelion. Some students just don’t know how to do this, but other students get it creatively wrong: they set a and G(M+M) equal to one, but then they stick in r=0.5a and don’t know what to do with a.

In the past, some machines only accepted mass-ratio values less than one, whereas others accepted anything. For the problem with m₁=4 and m₂=1, q=0.25 was a safe bet, as opposed to q=4. For finding the value of q “at which larger values cause the planet to ‘stay home,'” Give them a range to search in and suggest an increment to step through it, otherwise they have no clue where to start.

Alternately, you can use the non-computer Kepler’s Laws lab that Jillian wrote. You will need some supplies for the lab, though: string, tape, thumbtacks, and 8.5×11″ pieces of cardboard. Students completed this lab in 1.5 – 1.75 hours.

Useful websites:

• Mike’s Kepler’s Laws lecture
• Answer Sheets: .pdf
• Kepler’s laws almost the same as the program we use

Please go through this lab entirely before you teach it; you do not want to do this on the fly. This lab has students draw a fairly accurate representation of Mercury’s orbit using only a humble protractor. Why do we bother?

1. It’s awesome that they can get so close to the actual orbital parameters using only a protractor
2. We can show students how we know orbital shapes even when we can’t pan out of the solar system and see orbit tracks laid out in space
3. We can also show students that astronomy is tough but do-able
4. We’re evil (students usually only believe this one)

Demonstrate how to graph Mercury’s position either by using the document projector or by showing them Nikki’s awesome pre-lab lecture (9.3MB PPT also works moderately well in OpenOffice). Do this for a few positions, so they get the hang of it. Cat created an excellent cheat sheet for drawing the orbit. There is a copy of a blank orbit and extra copies of Cat’s cheat sheet in the Master Copy Binder in the Bx102 closet. Make extra copies if you need it. In fact, bring a few extra copies with you, just in case; you can always donate ’em to the next person to do the lab.

It helps the students if everyone draws their own orbit, rather than one person drawing it per group. No one is sitting around bored and they can pick the best orbit for their lab calculations. Students can confuse Earth and Mercury angles, and they get confused about flipping the protractor

for Eastern and Western elongations. It might help your students if they go through and draw all of their Earth positions first (and label each one with the elongation number), then draw all of the Eastern elongations, and then draw all of the Western elongations. Check each group’s first few Earth points to make sure they’re doing it correctly. One wrong point will send them into crazy orbit land.

Students don’t always make the connection between an elongation angle and the top-down view of the orbital setup. Candace created a wooden model which might help them grasp this. Students can put Mercury at various points in its orbit and see how far it would appear from the Sun from Earths’ point of view (example).

Also, the students won’t have had much practice using protractors. Explain that angles are measured with the vertex in the little circle of the protractor. Emphasize that the angle they will be measuring is from the normal (whatever number of degrees from 90^o), rather than going by the number written on the protractor (e.g. measuring 30^o to the left means making a mark at 60^o rather than 30^o).

Some students don’t understand why we convert from measuring the semi-major axis in millimeters to AU. They will continue to use their measurement in millimeters for the calculations, and consequently get really weird numbers.

Make sure you write on the board the accepted values for the orbit of Mercury:

Useful websites:

• Cat’s lecture: .pdf
• Helpful Handout
• Venus’s phases (also works for Mercury)
• Answer sheets: .pdf
• Venus orbit and apparent size and phase (also works for Mercury)
• Inferior planetary phases for the Copernican and Ptolemeic systems

Go through this lab on your own beforehand. You do not want to try teaching this blind This lab explains the only direct distance-measuring technique we have, which should be impressive; however, no matter what you do this lab involves a lot of math, which students usually don’t like. We normally project a ‘ruler’ on the front screen, measure the parallax of a stick with respect to the tick marks on the ruler, then convert the parallax angle to degrees and calculate a distance. The equipment for this lab should be set up at the back of the room. Two groups should be able to go at once and complete 8.1.1-8.1.2. While the other groups wait, they can answer questions in 8.1.3 – 8.2.

There should be a PDF file on the desktop of the computer labeled ‘parallax ruler’; if not, here is a copy. Open it in Acrobat and be sure to display it in full screen mode. You may also use the long paper ruler Nicole uses for her version of the parallax lab. It should be in the closet, but there is also a copy in the Master Copy binder.

There is a long piece of tape at the back of the room and three positions marked with Xs in the aisles between the tables. The students sit on chairs with their heads over the long piece of tape to do their parallax measurements. The object whose parallax they are studying is a coffee stirrer attached to a wooden base. When moving it to different distances, ensure that the coffee stirrer itself is right over the tape mark for that distance (as opposed to the front of the base being on the tape mark). The students should get within a meter or half a meter of the actual distances (except the third distance might be worse than that) but there will still be error in the student who does the measuring, as they move their heads slightly. Two protractors will be set up to measure the angular span of the tick mark ruler. The idea is that a student sits and sees how many degrees constitutes our 20 tick mark ruler, allowing them to convert their parallax angles from tick marks to degrees. They only use one eye for this measurement and make sure their head is over the long piece of tape in the back and the protractor is right up against the bridge of their nose. They will also need to measure the distance to each tape mark, and they can do this while the rest of the group measures parallax angles or angular span of the tick mark ruler.

To beat down your students’ errors it helps to have two people be “observers”, who hold their heads very still, blink their eyes, and measure the coffee stirrer’s parallax angle at the different distances. For each distance just average the parallax angle they report. Also average their baselines (distance between each pupil’s pupils). Just have one person measure the angular span of the tick mark ruler.

There are three parallax equations in the lab: tangent version, small-angle approximation version, and parsec version. Invariably, the students confuse them and end up not using the parsec version when calculating distances for stars. Make sure they understand what each equation requires in terms of units, what it spits out, and when to use them.

Jeff makes a recommendation to speed up the lab by making the actual parallax measurements a full-class activity. Break your lab into three groups. Have the parallax protractors set up at the back of the room. For your object use the green pointer stick (which might be next to the computer or bundled with the meter sticks) secured in one of the metal bases. Have 1/3 of the class do the parallax measurement for each distance (near, middle, far). Average the resulting measurements for each distance and have the whole class use these numbers. Pick a few students to measure the angle for the whole scale to get the ticks-to-degrees converstion factor and have the whole class use that.

The last question involves determining the distance to a star using two “pictures” taken 6 months apart. Teresa suggests explaining this to your students in 4 steps:

1. Find the scale
   
2. Measure how much star P shifts on the picture
   
3. Convert that shift to arcseconds using the scale you found in Step 1
4. Divide α by 2 to get θ and solve the parallax equation, d = 1/θ

Useful websites:

• Mike’s Parallax lecture
• Lauren’s Parallax Lecture: PDF
• Answer sheets: Version 1: .pdf, Version 2: .pdf
• Parallax applet, another parallax applet
• ESA’s Hipparcos mission

A lab involving lasers to teach students how light behaves with mirrors and lenses? Whoop-whoop! Each lab group should have an “optics bench” setup (bench with lenses and light; protractor and flat mirror with carpenter’s laser level), and Tom or the Head TA will help with setup. At the front of the room you will have the three-lasers-on-a-stick, the curved mirrors, and smoke machine. Since the lens light and laser light may be faint, you might want to turn most of the lights off. The fog machine takes a few minutes to warm up. If it is turned on before you begin your pre-lab lecture it will be warmed up in time for lab.

The equipment at the front of the room is meant to demo the behavior of curved mirrors. You can either do the demo once for the whole class at the beginning of lab, or do the demo as each group comes across that section of the lab. Use the smoke machine and lasers-on-a-stick to illustrate different light paths and demonstrate focal length. Tom made a rough curved mirror by attaching a series of flat mirrors to a curved piece of wood. This should help students transition from understanding how flat mirrors work and treating curved mirrors like finely faceted flat mirrors. Students are supposed to draw the light paths on a sheet at the end of the lab.

Students start out investigating a flat mirror with the laser level and are supposed to figure out that, when measured from normal, the angle of incidence equals the angle of reflection. Make sure they measure the number of degrees from perpendicular (90^o) instead of just reading off the number on the protractor; otherwise, you’ll get them saying that the angle of incidence was 70^o and reflection 110^o.

Students then investigate how lenses focus light. In the lab the lenses are referred to as “positive” (convex, magnifies image) and “negative” (concave, demagnifies image). Watch out, your students might amuse themselves by short circuiting the transformer, that is by clipping the black alligator leads to each other. This will eventually destroy the transformer. Please check at the end of the lab to make sure no one’s connected the leads together. Also, the alligator clips are soldered to the wires, but the connection isn’t strong enough to take a lot of metal fatigue. Remind the students not to play with them and the transformers will last a lot longer.

This lab is cool because after playing around with the individual lenses, the students get to build two telescopes, Galileo’s and Kepler’s. It’s like the telescope shown in picture below except without the brass cylinder body, Johnny Depp, or Orlando Bloom.

When students are building their telescopes, they might try to look through the telescope backwards. Remind them that the smaller lens is referred to as the eyepiece in the lab, so it should go next to their eyes, while the large lens is the primary that is imaged by the eyepiece and should be at the far end of the telescope.

Also, while the Galileo telescope works just fine the Kepler telescope seems to focus best when your eye is a little distance from the eyepiece rather than being smack up against it, as shown to the right.

It’s easy to calculate the magnification of Kepler’s telescope, since the students already calculated the focal length of both lenses. Galileo’s is trickier because one of the lenses is “negative” and has a negative focal length. To calculate the focal length of the “negative” lens, remind students of Figure 9.3 and the two paragraphs beneath it, which step them through the calculation.

The students may confuse the behavior of curved lenses and curved mirrors, but hopefully they’ll figure out that lenses refract while mirrors reflect and that concave mirrors focus but concave lenses defocus. Students may get confused between the shapes, but you can remind them that “concave” is like a “cave for the light”.

Bobby has an interesting way of explaining why the light refracts as from changing media, a physical model which gives them an intuitive feel for refraction. Imagine a car driving on a regular road. Imagine a sandy road crossing the regular road at an angle (not perpendicular). When the car reaches the sandy cross-road, the tire that hits the sand first will slow down, and the car will swerve in that direction.

Useful websites:

• Mike’s Optics Lab lecture
• Answer sheets: Version 1: .pdf, Version 2: .pdf.
• Behavior of lenses and mirrors
• Refraction of a straw
• Refraction by different materials

This is a quick lab to do but a lot of ideas for the students to digest. Students get to look at spectra from different elements and from blackbodies of different temperatures, which should give them an idea of how we can know an object’s temperature and composition just from the light it emits. Some of the guys may be color blind. That doesn’t mean they can’t do the lab; in fact, this is the one lab where it won’t matter. You might want to turn out the lights for this lab.

In class your teacher might not have covered the Bohr model of the atom and the idea of quantization; if this is the case, you will have to explain it. Good luck. Since students get confused about emission, absorption, blackbodies, and the different ways we display spectra, Jillian created a reference sheet to give to your students. There are extra copies in the Master Copy Binder, so please give them to your students. If you explain about the Doppler effect and radial velocity determinations, make sure they don’t mistakenly think that all red stars are receding and all blue stars are approaching.

Typically you will have several ‘spark tubes’ set up around the room. These are black boxes — ha ha ha. No, really: the power supplies are 1′ tall black boxes that plug into the wall and send current through glass gas tubes. Well, except for two setups that look like they are from Dr. Frankenstein’s lab with bare metal prongs to grasp either end of the gas tube. What elements do you show? A few suggestions are hydrogen, helium, neon, and mercury. You will need to set up one ‘mystery element’ with the table-top spectrographs pointed at it, and we suggest you use hydrogen. The idea is that the students measure the wavelength of the lines they see and determine which element it is by comparing their lines to a table in the lab. The gas tubes are in the Bx closet, in the back in the farthest metal cabinet, usually on the top shelf in three large plastic boxes. Warning: some tubes might be mislabeled! We go through and add labels to each tube, but they come off after a while, or fall off and are mistakenly attached to the wrong tubes.

You will also need to set up a blackbody source, which is just a tungsten bulb attached to a variable power supply (with an awesome retro dial on it!). Students have had trouble seeing how the continuum source varies with temperature: they might see that it gets dimmer as it gets cooler, but you will have to point out to them that they only see the blue/purple light (or see it the strongest) when the most current is running through the bulb.

Section 10.6 refers to a web applet which shows blackbody curves for different temperatures. You can either use the projector and go through this section as a class or have individual groups go up and use the computer during lab. Students are asked for peak wavelengths for different temperature blackbodies. The applet doesn’t list peak wavelength explicitly, so they have to figure it out from the graph. You could alternately use another applet which does list the peak wavelength (when you click on the graph). Students don’t get question 10.6.6, so you might end up having to point out the inverse relationship between temperature and peak wavelength and pointing out that room temperature is around 300 K (makes the math easier, anyway).

The hand-held spectrographs are not the most precise instruments in the world, so they are just to give the students an idea of how spectra appear and vary. The hand-held spectrographs cost $30 each to replace, so warn your students that they are not toys. If any spectrographs don’t work, put them aside and let either Tom or the Head TA know. The table-top spectrographs are more accurate, however you need to shine a flashlight on the white reflector tabs to illuminate the scale in the eyepiece.

Students can get confused about light and energy and think that photons have a temperature, making gamma ray photons hotter than radio photons. If they don’t understand that light travels at a constant speed in a vacuum, they will also think that gamma rays travel faster than radio waves.

Useful websites:

• Mike’s Spectroscopy Lab lecture
• Answer sheets: Version 1: .pdf, Version 2: .pdf
• Blackbody applet
• Exciting an electron in a Bohr atom
• Spectral lines of neutral atoms, and David’s Whizzy version
• Kirchoff’s Laws applet

This is mostly a binder lab. Make sure you have answers on hand, for students find the most interesting ways to make mistakes. There is no way to avoid it: students get confused when subtracting times. Just … be patient. As you know and love from the intro lab, there are image scale questions in this lab. Some of your students will still be confused by the fact that the image scale changes for each image. Keep reminding them that they need to use the size of the Sun to figure out the scale of each image (they conveniently contains either the whole Sun or half of the Sun). A backup of the images is kept here.

Please explain how images of the Sun are taken with a coronograph. We’ve noticed that when asked to measure the extent of the corona students measure the black disk of the coronograph instead of the light around the Sun.

If your lab is during the day, you can use the solar telescopes to show the students the Sun. These telescopes filter out some 99.9% of the light and have an H-alpha filter. To point the telescope at the Sun, it’s easiest to look at the shadow of the frame. The frame is longer than it is thick, so when you minimize the size of the shadow it must be pointed close to the Sun. A small white dot will appear on the circular finder scope, which you can center to get the Sun in the eyepiece. You can tune the wavelength a little around H-alpha by turning the barrel clockwise and counter-clockwise. The focus is changed using the silver knob underneath the eyepiece. Check SpaceWeather to see if the Sun has any sunspots the day of your lab.

If your lab is at night, or it’s cloudy, you can use the electromagnet to demonstrate the shape of a dipole magnetic field. Students can experiment by pouring iron filing in the white trays and placing a magnet under the tray. If they put it in the tray, they have to clean the damned filings off it themselves.

The Sun rotates every 25 days at the equator and takes progressively longer to rotate at higher latitudes:
25 days @ equator
27 days @ 35^o
33 days @ 75^o
35 days @ 90^o

Useful websites:

• Mike’s Sun Lab lecture
• Cat’s lecture: .ppt
• Answer sheets: Version 1: .pdf, Version 2: .pdf.
• SpaceWeather
• SOHO satellite has excellent movies of the Sun and also where we got the MDI intensitygram images
• The solar spectrum in visible
• Integrated Space Weather Analysis System (ISWA). Select events to show effect of flares on the solar system

In theory this lab teaches students about stellar evolution and familiarizes them with the different sections of the HR diagram. Your lecture should cover the basics of how stars change over their lifetime and the different sections of the HR diagram. Emphasize that the diagram is just a plot of temperature and brightness, and that in practice we use the proxies of color and magnitude. Oh, and that we really like star clusters because the stars all formed at roughly the same time and are at rougly the same distance (nixing that pesky reddening/distance problem). If you are printing the HR diagram lab, please print from the PS file and not from the web page. The images are scaled differently on the web and it will screw up your numbers. Have the students use the first line of the table to learn to use the dynameter properly, calibrate how far in the star has to be to be properly measured. Please ensure the students use Eqn. #2 to calculate the (B-V) color, rather than just subtracting the numbers. Watch out, they might get confused and try to put the equation number in the equation. When the students graph their points, make sure they label each point; that way they can go back and remeasure the correct star.

It helps to force every student to make their own HR diagram, especially if they have to hand it in with their summary. That way no one sits around bored while one person in the group does all the graphing, and in theory they might understand it better if they do it themselves. If you want to save time, you can use these pre-made HR Diagram graphs, which have the 53 given points plotted:

There is a copy of the TA graph, as well as extra copies of the pre-made student graph and the B and V filter images, in the Master Copy Binder.If you are using the two week long version of the HR diagram lab, you will use this version of the lab. Additional help can be found here.

Useful websites:

• Mike’s HR Diagram Lab lecture
• Answer sheets: .pdf, 2 week version
• HR diagram simulator does not include HB, RGB, AGB
• More complicated simulator shows path of star on diagram for different masses
• More complicated simulator animation shows path and size and color of star
• Life of the Sun its size at different point in its life.

This is an arts-and-crafts style of lab intended to help students visualize how objects look depending on one’s viewpoint. Students consider how different distributions of objects appear depending on whether they are viewed from the center or from the outside. Students then plot locations of four types of objects (nebulae, open clusters, globular clusters, and galaxies) on a map of the sky. They make a globe out of this map and figure out what idealized distributions best describe what objects and from that generalize about our galaxy. On the bright side the lab should explain why we know the shape of our own galaxy even though we’re stuck inside it. On the down side this lab requires good spatial visualization skills that not all of your students may have.

This lab refers to two basic distributions: flattened disk (duh), and “uniform” (objects distributed uniformly inside a sphere).

You might find it useful if you do the first part of the lab, the distributions of the classroom, with the class as a whole. Students have trouble visualizing how the distributions would look from different viewpoints. You can have each group member make a globe per object type, or have them do all of the objects on the same globe. At the end of the lab students are asked to draw our galaxy as it would appear from the outside, showing where the nebulae, open clusters, and globular clusters are located. Please check this drawing to ensure it looks something like this and not this.

There are extra copies of the map in the Master Copy Binder.

Useful websites:

• Mike’s Mapping the Galaxy lecture
• Answer sheets: .pdf
• Pulsar distribution on the sky
• Globular cluster distribution on the sky
• Gamma ray bursts on the sky map of 2,704 from BATSE, redder dots indicate higher energy events
• The Milky Way from gamma to radio
• Better resolution map

This binder lab familiarizes your students with galaxies by having them look at pictures of spirals, ellipticals, interacting galaxies, and dwarf irregulars. Students will examine shape and color differences and (hopefully) glean an understanding of the various stellar populations in different galaxies.

In your intro lecture you should cover types of galaxies and the Hubble tuning fork diagram. If your students haven’t done HR Diagram lab, or maybe even the Spectroscopy lab, and if they haven’t covered the whole color-temperature-age thing about stars, they will be confused. You might want to take a minute to cover stellar evolution. Regardless, they still might confuse the age of red supergiants and red dwarfs, so please emphasize that or they will think that every kind of red star means a really old stellar population.

This is a long lab, so if students take longer than 2 minutes to classify/discuss a galaxy, they are taking too long. Have them give an explanation for their choices and move to the next one.

After we go through the difficulty of teaching the students about star colors and population ages, we then describe pink/red HII regions. Immediately, the students want to say that HII regions are red and so must indicate an old stellar population. Explain how the young stars pump out a lot of high energy light that make the surrounding gas glow pink. The fact that the gas hasn’t been blown away by their stellar wind, and the fact that there are still such massive blue stars, are both signs that these stars just formed. Use the analogy of rain the Summer: it’s so dry and hot that water should evaporate quickly — if you see raindrops on the sidewalk, that must mean it just rained.

Color blind students suffer until they hit the multiwavelength images, which are thankfully black and white. Students in general sometimes have trouble with the multi-wavelength section because they aren’t used to seeing images with narrow filters. Remind them which colors of light correspond to what kinds of stars.

Useful websites:

• Mike’s Galaxy Morphology Lab lecture
• Answer sheets: .pdf
• The Milky Way from gamma to radio
• Andromeda galaxy in optical and IR
• Sombrero galaxy in X-ray, optical, IR
• Cartwheel galaxy in X-ray, UV, optical, and IR
• Carina nebula in visible and IR
• A person in visible and IR

This is like a mini-binder lab, since there is only one binder and the students only look at one picture for the lab. This lab has students start by examining the Hubble Deep Field North image (actually, they count galaxies) and finish by calculating the average density of the universe. Hopefully the students will get three things from this lab:

1. The power of estimation (and understanding errors in estimation)
2. The reason astronomers cannot study “the whole universe” and do small surveys instead
3. That there’s a lot of stuff out there but that there’s even more space

Like Orbit of Mercury, it’s best to work through this lab ahead of time. Also, count the chairs in the room before your students get there. The students may not understand the parallel between the chairs example and the galaxies, insisting that a survey can still be done to count every single chair … try to explain it in terms of University budgets, and what it would be like to replace all of the uncomfortable chairs on campus. Instead of using the black and white HDF image in the lab, have the students use the color print outs in the How Many Galaxies binder in the closet (but don’t forget to collect the images after lab, otherwise we have to print more out).

This lab is full of unit conversions, which gives the students a lot of trouble. Check their work often before they wander off on some weird garden path of mathematics. It’s a given that when they have to divide by a number in scientific notation, they’ll type in their calculators 2 / 3 x 10⁸ rather than 2 / (3 x 10⁸). When their numbers get too large or too small, look for a mistake like that.

At the very end of the lab, the students are asked about the density they calculate for the universe and whether this is large or small. It seems students don’t always have a good grasp of what density means, or they confuse it with mass. The students are asked to compare the universe’s density to that of a single atom of hydrogen in a cubic cm (1.67 x 10^-24 g/cm³). For fun you can compare it to the density of gold (19.32 g/cm³), water (1 g/cm³), Earth’s atmosphere (1.29 x 10^-3 g/cm³), Mars’ atmosphere (2.0 x 10^-5 g/cm³), etc..

You can also project a high resolution version of the HDF grid image or you could point out the HDF poster on the left side of the front of the room.

Useful websites:

• Answer sheets: .pdf
• Hubble Deep Field
• Hubble Ultra Deep Field
• Zoom-in gif of HDF

This lab does the impossible task of relating the concepts of the Doppler effect, redshifting of light, and age of the universe. The students measure the redshift of the calcium doublet in galaxy spectra, calculate the recession velocity of those galaxies, determine the Hubble constant, and then play around with the Hubble constant to get a rough age of expansion of the universe. Yeah, they do all of that. In your intro lecture you should go over the Doppler Effect for sound and then transition to how it works for light. As a demo, there is a tuning fork on a string in the closet, hanging from some magnets on the side of the metal shelves.

Try to stress that the Hubble constant is a relation, the slope of the plot of distance and recession velocity. The students then play around with their value for the Hubble constant, wherein there is manipulation of scientific notation numbers by unit conversion, etc.. Just as in How Many Galaxies, they will mess up this math and forget order of operations when manipulating the numbers. When doing unit conversion, the students may make the mistake of cross-multiplying instead (they figure it’s a good trick, so it works everywhere).

Students can have trouble with the measurements and calculations. This lab is no exception. Consider the spectra they are given. The spectrum at the top of the image is the visible part for our Sun, showing some absorption lines. Those lines are schematically represented in the images below that as black lines. Note the nice calcium doublet in the purple. The students are supposed to measure in millimeters the shift between the rest frame doublet and the galaxy cluster doublet by measuring the distance between the leftmost of the doublet lines (393.3 nm). Frustratingly, students in the past have measured from the rest frame leftmost to the galaxy cluster rightmost. It might or might not help for the students to see the spectra in color, but just in cast you want to print some out, here is a color image of the spectra. There are also extra copies of the color image in the Master Copy Binder.

Try to make them understand that redshifting is a perspective effect: a receeding galaxy appears red to us but it’s not actually emitting more red light because of its motion, just as we would appear red to them but aren’t actually emitting more red light. Watch out, for the students may think that all red stars are receeding and all blue stars are approaching, forgetting about intrinsic star color.

Kurt created a neat little demo gadget: a Doppler Ball (shown to the right). There’s a speaker inside the ball and a 9V battery inside the medicine capsule. When you press the switch at the base of the capsule, the speaker emits a single tone. If you swing it over your head like a lasso, students should hear the tone Doppler shift. The Doppler Ball should be stored in the Bx102 closet.

Also, students have gotten confused about the ‘How do we measure distances to galaxies’ section … you might want to work that out on the board, perhaps at the end of your lab lecture. If you go on to get them to understand how the universe can not have a center, all the better.

Useful websites:

• Mike’s Hubble’s Law Lab lecture
• Answer sheet: .pdf
• Doppler applet demonstrates sound speed and moving objects
• Hubble and his first version of the graph
• Hubble’s Law diagram showing Virgo cluster deviations
• Hubble’s Law diagram using SNe, galaxies, etc.
• Expansion of the universe why clusters aren’t ripped apart
• Expanding bread with raisins
• Expanding universe red-shifting light

This lab is totally optional and is in the form of a webpage. This page has links to a series of astronomy sites such as APOD and Hubble Space Telescope. Ideally, students visit a site, learn about something, and write about what they learned in the text box provided on the WWW Extra Credit webpage. After they visit all of the pages we list, they fill in their name, their professor’s name, their TA’s name and click the “submit” button. This emails the text to the webmaster, who sends to the appropriate TA

Some TAs use this as a make-up lab, and some don’t use it at all. However, don’t tell your students about the make-up until the very last lab, otherwise you’ll have students skipping a lab knowing they’ll be able to make it up.

If the WWW Extra Credit webpage doesn’t work, or any of the sites are down, let either Jon or the webmaster know. Make sure your students hit the “submit” button so it emails the form rather than trying to print out the page, otherwise the text they wrote might get cut off in the printout.

The last lab of the semester is often a review lab. This serves two purposes: a last chance for the students to turn in/pick up work and to review the astrophysics covered in lab. The usefulness of the first purpose is pretty clear. But since there is no lab exam like many Biology and Chemistry labs have (one more reason to take Astronomy courses), why do you need to review the material? For one, it’s part of being a good TA to ensure your class actually learned something. For another, many professors like to put questions about the labs on the final exams, so it’s useful to cover the material again.

The actual “review” part of the Review lab has no formal structure, so you are open to doing whatever you want. This can range from just asking if anyone has any questions to giving a full-blown lecture. Most take the form of a question and answer period where you try to clear up anything they don’t understand (astro related topics only). The trick is how to provoke them into asking questions. Just asking if they have any questions almost always leaves to no one having questions. They want to get out of the lab as fast as they can and don’t want to look stupid in front of their classmates by asking stupid questions.

The most effective way to get them to ask questions is to pass out notecards at the beginning of class. Have them write down their name and a question. Tell them this is how they get their points for the day, even though most professors do not assign any points to the Review lab. The students don’t need to know that. Give a brief rundown of all the labs you did over the course of the semester to remind them of everything they did. Then gather the cards and run through them. By forcing them to write down a question and by keeping them anonymous as you go through them, the students are much more likely to actually ask about things they don’t understand. You can usually fill the entire lab time with questions this way and actually get interesting discussions.