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

More documents

Recommendations

Info

or S T = 2 . 571× S O Equation 1 Now we know what SO is – it's the distance between our two observers, which in this case is just the diameter of the Earth, since one observer is at the North Pole, and the other is at the South Pole! Look at Figure 1 if you're confused about why this is. Look up the diameter of the Earth in your textbook (there's a table of Planetary Data in one of the appendices in the back of the book). Remember, astronomers have known this number since Eratosthenes first calculated it 2200 years ago! S O = diameter of the Earth = ______________________________________ km Now plug this value into Equation 1 to find S T - the separation of the two transit locations. S T = ________________________________________ S T is the separation of the transit positions at the distance of the Sun – in other words, it's how far apart the two images of Venus would be if we projected them in straight lines onto the surface of the Sun. But we've already shown that the size of the change in Venus' position on the Sun is only a small fraction of the whole Sun's diameter. So ST is only a correspondingly small fraction of the whole Sun diameter. To find the whole Sun diameter, Ds, we must divide ST by the fraction s . units! D S = S T p Equation 2 Plug in your values of p and S T into Equation 2 and calculate D S . Don't forget to list the correct D S = _________________________________ Congratulations! You've just calculated the diameter of the Sun, merely by watching Venus pass in front of it and using some clever geometry! Pretty amazing! We could also, if we wanted, use these same measurements to calculate the exact length of the Astronomical Unit, or AU, in kilometers, but that would require a tiny bit of slightly advanced math (trigonometry), so we'll leave that for another exercise! Now let's do the same thing, only this time with the November 8, 2006 transit of Mercury. Change the Date & Time to November 8, 2006, at 11:00 AM. Change your Location back to the North Pole. Mercury is about to begin crossing the face of the Sun. Press L to speed up time and watch as Mercury transits across the face of the Sun. Stop time when Mercury is halfway across the Sun. Notice that since Mercury is much smaller than Venus, and is farther away than Venus, it shows up as a much smaller dot on the face of the Sun. Again, make sure the Ecliptic plane is horizontal by checking to make sure the Switch Between Equatorial and Azimuthal Mount button is lit-up in the toolbar. 4
As you did with Venus, change your observing site between the North Pole and the South Pole and measure the change in Mercury's position. It's much harder this time, because Mercury, being much closer to the Sun than Venus, hops a much smaller amount when you switch observing locations. Do your best to use the ruler to measure the small change in Mercury's position between the two observing locations and record it and the Sun's total size in Table 2 below. Table 2 Total Sun size (mm) Mercury's position change (mm) Now we just do the same calculations for Mercury that we did for Venus. The only change is that Mercury's distance from the Sun is 0.39 AU, not 0.72 AU (Mercury is, of course, closer to the Sun than Venus!). So now, instead of Equation 1, we have S O 0.61AU = or 5 S T 0.39AU S T = 0 .639× S O Equation 3 Do this calculation, using the same value for S O - the diameter of the Earth - that you used before. S T = ________________________________________ Now calculate p the same way you calculated it before: by dividing Mercury's position change by the Total Sun size. p= Mercury's position change Total Sun size = _____________________________ And finally, calculate D S (the diameter of the Sun), just like you did with Equation 2, only this time using Mercury instead of Venus: D S = S T p Equation 4 D S = _________________________________ Now we have two measurements of the diameter of the Sun. Hopefully they're the same – or at least near each other! Take the average of your two values of DS by adding the two values and dividing by two. Call this average value
Page 1 and 2: 1 Name: ___________________________
Page 3: Now, while Venus is sitting there i

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?