Comment on how the pencil appears to move with respect to a background object. Now, repeat this but with the pencil at a different distance from your face. How does the apparent shift of the pencil change?
Send a screen shot or copy of this plot to Chris. Comment on your plot. Do you see a relationship? Compare it with a published HR diagram: for example, see Wikipedia, Hertzsprung-Russell Diagram
Sort the data by B-V. (Remember, this is a measure of temperature.) How does B-V compare with the spectral types in the table? Make a table to express the relation. Make a third column for temperature. How does your table compare with the axes in the published HR diagram from Wikipedia?
Using the distance modulus equation, what distance do you derive?
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The pencil moves as you close left eye then right eye. For me its moves when I close my right eye which means that my right eye is dominant. The closer the pencil is to the eye the more it moves. This is the result of simple trigonometry
ReplyDeleteThe M-V(brightness or luminosity) to BV(temperature) matches very well to the HR diagram. There is the diagonal stripe of the main sequence stars running upper left to lower right. While a few red giants are in the top right corner.
ReplyDeleteI plot the HR diagram with my students. It is very challenging. The temperature is on a log scale while luminosity run from +13(dim) to -6(bright) which is not very logical.
My spectral types matched very well with the published HR diagram on Wikipedia.
I analyzed HD332087
It had a temperature of 6000-7500 and a luminosity of 1.5-5.0 and a spectral class of F0. It had a V= 9.18 and MV = 1.7
Plugging this into the equation the distabnce came out as 313 parsecsor 1021 light years. I do not know if this is correct.
Darn, my eyes are too far apart to see a single image, it keeps moving on me. Binocular vision helps form a single image, but in 3-Dimensions. Yes, when I close one eye, compare the near object to distant background I see a shift in position. The closer the near object, the more the shift.
ReplyDeleteMy HR plot looks a LOT like the book copy. I like plotting with Excel, never have before. I like that the kids in class can do this and make sense of what the HR diagram really MEANS.
The rest of the assignment will have to follow later when I am on my school computer.....
When I close the left eye and open the right, the shift of the pencil's position is to the right. And if I close the right eye and open the left, the shift of the pencil's position is to the left. The relative shift is greater for a closer object than the farther object
ReplyDeleteBased from my table, Class B stars have a temperature range from 11600K – 12500K, Class A stars have a temperature range from 7800K – 9360K, Class F tars have 5840K – 7030K, Class G stars have 4140K – 5280K, Class K stars have 3420K – 4330K and Class M stars have 3000K – 3130K. I used the simulator to get the temperature of these stars . After correlating all the data, I notice that the more negative is the B-V the greater is the temperature.
My plot is similar to the HR diagram from wikipedia . Hot stars are found at the upper left hand end of the Main Sequence (band across the middle part of the graph) while cooler stars are found to the lower right.
The distance of the star HD331085 is 6.31 parsecs or 20.58 lightyears.
I sorted the data by B-V (Temperature) and as temperature goes up, the spectral classification goes in this order (BAFGKM) with increasing #’s following the letters. As I correlate this information to known temperatures for these classifications I get the Hertzsprung-Russell Diagram that compares temperature with absolute magnitude. It also correlates with color and luminosity (a 4 axes graph).
ReplyDeleteHD 331061 classified as an A5 has Absolute Magnitude of Mv = 1.3 (from my chart of nearby stars) and an apparent magnitude of V = 10.9 (from SIMBAD). When plugged into the distance modulus equation it comes out to 109.9 parsecs – or about 358 Light Years.
I love that I can show my advanced math students how logarithms are actually used – by real people – earning real money!
The shift in position of the depends in the distance to the eye. The closer the object to the eye the farther is the shift. The shift is towards right when I closed my left eye then closed the right eye and the shift is towards left when I closed my right eye then closed the left eye.
ReplyDeleteThe Mv vs B-V graph of the stars provided matches the HR diagram. The main sequence stars are represented showing a decrease in absolute brightness as the temperature(B-V) decreases.
Using excel data and calculating the temperatures of the stars using the B-V values, I derived the following temperature ranges and spectral class of the stars.
Type B stars has a temperature from 11000K to 15000K
Type A stars has a temperature from 7300K to 11000K
Type F stars has a temperature range from 5500 K to 7300 K.
Type G stars has a temperature range from 4700 K to 5500 K.
Type K stars has temperature range from 3500 K to 4700 K.
Type M stars would vary in temperature from 2900 K to 3500 K.
Star HD 331066 is classified as A6 with a temperature of 7400K. Its distance is 17.14 parsecs (56.7850873 lightyear)
Closing my left eye then the right eye will give me a right shift and closing the right eye then the left will give me a left shift of position. The closer the pencil to the obeserver the greater is the shift.
ReplyDeleteThese are the classes and corresponding temperature range. these are base from the excel data
B 10,000 - 15000K
A 7,500 - 10,000 K
F 6,000 - 7,500 K
G 5,000 - 6,000 K
K 3,500 - 5,000K
M < 3,500 K
For HD331054 its distance using the modulus equation is 8.87156012037961 parsecs ( 28.9358022 lightyear)
If I close my left eye then open the right, the pencil moves to the right. If I close my right eye then the left, the pencil moves to the left. The closer the pencil to the eye the greater is the shift in position
ReplyDeleteThese are my temperatures for the stars and their spectral Class:
Temp Spectral Class
9760 A1
9630 A2
8260 A3
8260 A4
8160 A5
7550 A6
7800 A7
12500 B0
14800 B1
13200 B2
14800 B2
13500 B2.5
13200 B3
12500 B3
13200 B3
12000 B5
12000 B7
11200 B8
11600 B9p
6830 F0
6640 F2
6130 F2mF5
6030 F6
5840 F6
4670 G1
4960 G5
4920 G8
4790 G8
4140 G9
3930 K0
3770 K0
4440 K2
3290 K3
4000 K5
3210 K5
3420 K7
3130 M0
3340 M1
3070 M3
3000 M4
These stars are arranged from hottest to coolest (OBAFGKM). The more negative is the
B-V the higher the temperature.
The scattered graph I plotted was similar to the HR diagram.
For my star HD 332087, using the distance modulus equation, I got a distance of 17.06parsecs (55.6462018 light years)
The pencil closer to your eyes has an apparent shift which is larger than the pencil held at arms length. So stars that have a large apparent parallax will be closer than stars with a small parallax. Loved the parallax applet. Definitely using that with my class.
ReplyDeleteIn general, the hotter the star, the brighter the star. One exception is the red giant branch which has stars that are really bright, but cool. The main sequence is clearly visible, but what is unusual is the number of really hot, really bright stars. I think less than 5% of stars are type O and A, but these stars dominate in the HR Diagram. This is probably because the fainter stars are less likely to be measured. It also looks like there are a few stars on the red giant branch. One difference between my HR Diagram and the one on Wikipedia is the lack of white dwarfs.
My table listing the B-V magnitudes as they correlate with spectral type and temperature match up pretty well with the HR Diagram on Wikipedia.
To calculate the distance to my M star, HD 331072, I found B-V to be 1.53 which correlates to an absolute magnitude of around 11. Using the distance modulus with V = 10.17 and Mv = 11, the star is 6.82 pc away! Although I don’t think this distance is too far to use the parallax method with. I think the farthest star you can calculate the distance to with the parallax method using ground based observations is around 40 pc. And much farther with a space based observation.
I held a pencil about six inches from my face and then at arm’s length: When I alternate closing one eye at a time, the pencil appears to shift position to a greater extent when it is closer to my face. When it is at arm’s length, it only appears to change position about 25% of how far it changes when held closer.
ReplyDeleteWhen I made a graph of B-V data vs. Mv data I saw a clear relationship: The more luminous the stars (smaller Mv) have lower B-V differences (higher temperatures). The published chart that I looked at showed the same trends. (But I didn’t see any White dwarfs represented by data points in the lower left corner of the chart).
The published HR chart has four different values: spectral class (temp) on the top X axis, B-V on the bottom X axis, Mv on the right Y axis, and luminosity on the left Y axis. The table that I made has all of this data accept luminosity.
I chose to calculate the distance of HD 332087. (Temp = 7210 K, Spectral type: F0 D). An FO spectral class corresponds to a B-V of around 0.3. From the graph, I found that the Mv is roughly 2. Solving for distance, the equation becomes distance = 10 to the power of {(V-Mv + 5)/5}. I got 15.8 parsecs. That seemed really close before I realized it meant about 51.5 light years. But it still seems relatively close … I would like the check the actual data but I can’t find where it lists distance on Simbad.
Parallax mini-experiment: When focusing on the distant chair, the pen showed greater apparent movement when it was closer to my eye than when it was farther away.
ReplyDeleteNow THAT is a scatter plot! Compared to a typical plot of values in a classical physics experiment, it shows more scatter than it does pattern, but comparing this to a more complete HRD, I can see some of the patterns emerging that aren’t initially obvious. The graph includes mostly the main sequence stars and a few of the Giants. I don’t see any representatives of the white dwarf stars in this data set, but there are a very few that could be classified among the Bright Giants or Supergiants. So stars in general show a lot more variation than, say, balls rolling down an incline!
My table has B-V values ranging from -.23 to 1.74, which is similar to the HRD in Wikipedia (theirs goes as high as 2.3, but I don’t see any starts in that part of the graph, beyond about 2!)
HD 331078 – B 10.39; V 10.05, so B-V = 0.34, which corresponds to a Mv of 2 (F2 type star)
V − Mv = 5log10(d ) -5
10.05 – 2 =5log(d) -5
Gives a distance of 407 parsecs
The pencil seems to shift more as it gets closer to my face. So, if a star has a greater parallax (more of a shift), it will be closer to Earth.
ReplyDeleteThe relationship in my plot is that as the color difference (B-V) goes up, the magnitude also increases by becoming a more negative number. My plot and table looked very similar to those on Wiki, except that the range of values was different.
According to SIMBAD, HD331059 is a K5 star. Using the data for a K5 star on the Excel sheet, I found the distance to be 21.9 parsec.
I use the edge of my cabinet as my point of reference to the position of the pencil. As I open and close my eyes I started moving the pencil closer and farther my face. The closer the pencil to my face the longer the distance of its movement from the point of reference.
ReplyDeleteThe scatter plot chart shows that the B-V goes up forming a diagonal line.
Based on SIMBAD
HD331059 is a K5 star with B=10.83; and V=9.73
B-V = 1.09 which corresponds to Mv 0.7 K0 star
V-Mv=5log10(d)-5
9.73-.7=.6990(d)-5
9.03=.6990(d)-5
The distance I got is
d= 17.9185 par secs
Nice work, but always remember significant figures when giving the final answer. You could round to 3 significant figures for the distance.
ReplyDeleteFrom John Webster
ReplyDeleteWhen looking at the pencil with my left eye the object was inline with the pencil. When I shifted to my
right eye, the pencil appeared to move to the left of the object. When the pencil was held closer to my
face, the shift appeared greater to the left. This is the same principle that optical rangefinders use to
calculate the distance to objects.
My plot of the B-V and Mv data was very similar to the H-R diagram I saw on Wikipedia. The stars with
the higher (greater negative values ) Absolute magnitudes plotted on the upper left of the plot with the
smaller values on the bottom right.
When the B-V data was arranged in a table with the spectral types, the stars ranged from the hotter
B0-B1 to the cooler M4 spectral types. The Hotter(smaller) B-V values corresponded with the hotter
spectral types stars with the greater Mv values, which also correspond with the star placements on the
H-R diagram.
I choose the star HD 331085. From the previous module I found that it is a Spectral Type KO with a V
value of 9.12. I looked up the Mv value for this spectral type and got a value of 6.0 for Mv. Using the
formula I got a value for d of 42.15 Parsec or 137 LY.
1. Parallax exercise with pencil
ReplyDeleteIf I close one eye and line up a pencil with a background object and then close that eye and open the other, the background object is no longer aligned with the pencil. The pencil appears to move.
The close the pencil is to my face, the farther the pencil appears to move with relation to the background object.
I think it would be fun to do this in the classroom using a student as a background object. Once the closed eye is changed a second person can be advised where to stand so they are in line with the pencil. Tape measures would be used to measure distances from face to pencil, face to student1 and student1 from student2. Students can use this information to perform/confirm calculations/measurements.
2. My plot of the nearby stars data generated with EXCEL resembles the shape of the H-R Diagram shown in Wikipedia. The shape of the main sequence stars was apparent.
BV Spect. Types Temp.(K)
-0.23 to -0.09 B 10,500 to 15,000
0 to 0.21 A 7,400 to 10,500
0.28 to 0.49 F 6,000 to 7,400
0.62 to 0.8 G 4,700 to 6,000
0.79 to 1.36 K 3,500 to 4,700
1.41 to 1.74 M <3,500
3. I calculated the distance for HD331246. From SIMBAD it said that the star was classified as a B3. Looking at our table of data of nearby stars, I took the V and Mv for a star that was also listed as a B3. Plugging that data in to the distance modulus equation, I calculated 143 parsecs.
I've done the parallax experiment with my students many, many, many a time. The initial result is simple, close your right eye and the pencil moves to the right. Close your left eye and the pencil moves to the left.
ReplyDeleteI always have my students take two meter sticks and perform the experiment with further meter stick as the background object. I do this so that they can explore which objects move faster or slower and develop a technique for moving the closer meter stick such that the two meter sticks are on top of each other. This is a useful activity for practicing for finding virtual images. I always try to dovetail optics with astronomy, I find that they synergize extremely well.
Anyway...moving on. I only have the generic google apps spreadsheet so the HR diagram I generated is upside down, since I haven't been able to figure out how to make the Y axis go from positive values to negative values in an upwards direction in Google Docs. Still if I look at it upside down it looks like a man sequence HR diagram.
Sorting the table by B-V helps to reinforce the somewhat silly memmonic of ``Oh Be A Fine Girl and Kiss Me.'' as clearly the hotter the star the closer it is to the start of the sentence.
I choose HD331078 as my star of interest and I believe that it's absolute magnitude is about a 2 and it's apparent magnitude is a .034. Stepping through the calculation that gives a distance of 4.04 parsecs.
Hmmm....that was very bad and very incorrect, evdently. I should have used a B-V value of about 10 which, reading from the graph, would haev given me an apparent magnitude of approximately 1.5. Soooo.....let's redo that calculation and perhaps not end up with egg on my face.
ReplyDeleteV - MV = 5 log(d) - 5
(V - MV + 5)/5 = log(d)
d = 10^((V-MV+5)/5)
d = 10^((2-1.5+5)/5)
d = 13 parsecs
Sorry about that, and I'm particularly sorry about that if I did it wrong -again-!
Did I say -again-? Here's again: The MV value is 10.05 and the B-V value is .35 which gives me a V value in the neighborhood of 3 from my HR plot. Plugging through those numbers I get 251 parsecs as the distance.
ReplyDelete