Assignment #7 – Transits of Venus & Mercury - Faculty Web Pages

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Figure 1 (from GSFC/NASA) If the Earth is 1.00 AU from the Sun, and Venus is 0.72 AU from the Sun, then during transit, when all three are in a straight line, Venus must be 0.28 AU from Earth (1.00 AU - 0.72 AU = 0.28 AU). Two observers on Earth (Observers A and B in Figure 1) take pictures of the transit. They see two different things, thanks to the idea of parallax. Because the two observers are at different points of the Earth, they each see Venus take a slightly different path across the Sun. Observer A will see Venus transiting a bit lower on the Sun than Observer B (the difference between the two paths of Venus across the Sun are greatly exaggerated in the diagram). The larger the separation between Observer A and Observer B, the larger the difference in what they see. If we carefully measure the difference between the position of Venus against the Sun during the transit as observed by Observer A and the transit as observed by Observer B, we can use that difference to calculate the diameter of the Sun. Let's do this with Stellarium. Everything we do with Venus, is, of course, the same as what we will do later with Mercury. Let's look at the transit of Venus from the North Pole. Start Stellarium. Change the Date & Time to June 7, 2004, at 10:00 PM. Change your location to the North Pole by clicking as close to the top edge of the map in the Location window, or, more accurately, by setting the Latitude to be 90° in the Location window, if you didn't click exactly on the North Pole. Close the Location window. Notice that it is still light out, even though it's 9 PM! Find and center the Sun, and then zoom in until it fills the screen. The Field of View (FOV) should be about 0.7°. If you don't see the Sun, it probably means you haven't displayed the Planets - do this by checking the Show Planets box in the Planets and Satellites section of the Sky sub-menu in the View window. Turn off the Atmosphere (if it is on) by pressing the A key. Finally, press the Switch Between Equatorial and Azimuthal Mount button in the bottom toolbar until the little telescope icon I slit up, to make the plane of the Ecliptic horizontal. This last step is very important! The Switch Between Equatorial and Azimuthal Mount button should be lit up. Press L a few times to speed up the passage of time and watch for a few moments. At about 10:15 PM, you should see the tiny black circle appear on the lower left side of the Sun, blocking the light of the Sun. That's Venus! Watch as Venus starts to transit across the Sun. This is what you would have seen if you had looked at the Sun (with heavy sunglasses, of course!), on June 7 of 2004, from the North Pole! You can see that a transit is really another word for an eclipse, except that now the object passing between us and the Sun is not the Moon, but Venus. Stop the motion of Venus when it gets about halfway across the Sun. Now carefully mark the position of the center of Venus (as best you can) on the screen with a piece of tape or a Post-It note. 2
Now, while Venus is sitting there in the middle of the Sun, open the Location window and change your location to the South Pole by clicking as close as you can to the South Pole on the map, or by adjusting the Latitude to 90° South. Close the Location Window. Notice that you will have to turn off the Ground (by pressing the G key) to be able to see the Sun. Did you see that Venus hopped to a slightly different position? The hop is small, but noticeable. The hop is caused by parallax, which is due to the different latitudes of the two observing locations! We looked at the Sun at the same moment from the North Pole, and then the South Pole. This, of course is impossible in real life. • Why is it impossible to see Venus from both the North Pole and the South Pole at the same time? (Hint: look at the date and remember our “Seasons” assignment) ____________________________ _________________________________________________________________________________ Get a ruler (marked in centimeters and millimeters, not inches!), and measure the size of the entire Sun, in millimeters, on screen, from the left to the right edge. Enter this in Table 1 below as Total Sun Size. Now measure the amount that Venus shifted when we moved from the North to the South Pole. Measure from the point you marked with your Post-It note to the center of Venus' new position. Measure carefully - Venus will have only shifted by a few millimeters! Enter this as Venus' position change in Table 1. Table 1 Total Sun size (mm) Venus' position change (mm) Now let's use this information to calculate the diameter of the Sun. First let's figure out how far Venus moved from Observer A to Observer B, expressed as a fraction of the whole size of the Sun. To do this, divide Venus' position change by the Total Sun size from Table 1. The result is the fraction of the entire Sun that Venus moved. Call it p . p= Venus' position change Total Sun size 3 = ________________ This should be a pretty small number, since the difference between the two positions of Venus is pretty small. The fraction of a Sun diameter that Venus moved between our two views is a small fraction of the Sun's total diameter. Now, if you look at Figure 1, you might notice (if you remember your geometry) that the triangles formed by the two bases SO and ST and their common apex at Venus are similar triangles. This means that that the ratio of any two “similar” parts (sides or angles) of the two triangles are the same. Ratio, of course, just means “divided by.” Let's choose the two bases (SO and ST) and the two heights (0.28 AU and 0.72 AU) as our two similar parts of the two triangles. So we can write: S O 0 .28AU = S T 0.72AU
Page 1: 1 Name: ___________________________
Page 5 and 6: As you did with Venus, change your

Assignment #7 – Transits of Venus & Mercury - Faculty Web Pages

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