CLEA: Transits of Venus and Mercury

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Transits of Venus and Mercury 414) The points you have measured should appear to be connected by straight lines, whichgives a jagged appearance to the tracks. Next we need to fit a single line to each track,smoothing out experimental imprecisions. Choose the Data---Curve Fit---Quadraticmenu option, and you will see single slightly curved lines fit to the data.15) The shift, or parallax of Venus, π m , between any two tracks is what we use todetermine the length of the Astronomical Unit. It can be measured at any time during thetransit, but we will want to measure all three shifts between the three combinations of thethree sites (Udaipur vs El Teide, Udaipur vs Learmonth, and Learmonth vs El Teide), sowe need to choose a time when the transit is visible from all three sites. To do this,choose Data----Select Observation Time and a slider will appear below the plot. If youslide it back and forth, you will see three circles appear on the tracks that represent thepositions of Venus as seen from the three sites at the time set on the slider. Find a timewhen the transit is visible from all three sites. Click OK to set that time into thecomputer. A small window opens at the top of the page recording the time and theparallaxes as seen between the three pairs of sites the units of parallax will be in fractionsof a solar radius, and will later have to be converted into arc seconds. Record that data onthe table below:OBSERVATION TIME (UT):SiteParallax (Solar Radii)Parallax of El Teide-Udaipur (solar radii)Parallax of El Teide-Learmonth (solar radii)Parallax of Udaipur-Learmonth (solar radii)16) We need additional information to use in the formula on page 12 for the length of theAstronomical Unit: the “projected baseline” between any two sites, the distance to thesun and Venus in Astronomical Units, and the angular size of the sun (to convert theparallaxes to arc seconds.The computer calculates this information once the observing time is selected.Simply choose Data---Sun, Planet, Baseline Data from the plot display window, andanother window will open up with all this data. Choose List---Print on this window toprint out the data. You should now be able to use the data from that table (not all thedata it prints out is needed), to fill in the table on the next page, which is what you willneed to calculate the Astronomical Unit using the formula from page 12A= B • (D es - D ev ) • 206265π m • D ev • D esCAUTION: Be sure your units are correct before you plug into this formula. B is in km,D ev and D es are both in AU, and π m is in seconds of arc!DATA TABLE FOR CALCULATING THE LENGTH OF THEASTRONOMICAL UNITDATE AND TIME OF OBSERVATION (UT)DISTANCE OF SUN, D es (A.U.)
Transits of Venus and Mercury 5DISTANCE OF VENUS, D ev (A.U.)Apparent Diameter ofSun (arc seconds)Apparent Radius of Sun(arc seconds)=Diameter/2El Teide-Udaipur El Teide-Learmonth Udaipur-LearmonthProjected Baseline (km) Projected Baseline (km) Projected Baseline (km)Measured Parallax π m(arcseconds)Measured Parallax π m(arcseconds)Measured Parallax π m(arcseconds)17) Now use the data from the table above to calculate the length of the AstronomicalUnit using the parallax from each of the three pairs of observing sites and the formulafrom page 12. Also calculate the average value and enter it in the table below.THE LENGTH OF THE ASTRONOMICAL UNIT DETERMINED FROMTRANSIT OBSERVATIONS (km)El Teide-UdaipurEl Teide-LearmonthUdaipur-LearmonthAVERAGE FROM THREE SITESQUESTIONS TO CONSIDER:1) What is the percentage difference between your answer and the currently acceptedvalue of the Astronomical Unit?2) Transits of Mercury occur more frequently than Transits of Venus. How do you thinka transit of Mercury might appear different? Why weren’t transits of Mercury used todetermine the length of the AU? Why might it be harder to get a good value fromobservations of the Transits of Mercury?Format for writing up report:The report should describe what you did, what you recorded, how you analyzed the data,and what you concluded. Be brief---you don’t need to write down every mouse click youmade. But be clear, so that if someone unfamiliar with the experiment were to read it, thatperson could understand just what you did and why. Include the following sections:• Introduction describing the background and motivation for the work.• Data and basic measurements, including, if applicableo A sample image.o Printout of data tables
Page 1 and 2: Using the Transit of Venus to Deter
Page 3: Transits of Venus and Mercury 38) W

CLEA: Transits of Venus and Mercury

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