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Extra Transit of Venus Cover Sheet: Activity: Extra Transit of Venus Name:________________________________________________________________ Date Submitted:____________________________________________________ Returned for Revision:____________________________________________ Resubmitted:________________________________________________________ Date Recorded as Satisfactory:___________________________________ By :_____________________________________________________________ PHYS 1000 /AST 1040 Self Paced Activity: June 5, 2012 Transit of Venus Objective: To make measurements of the Solar System from observations of the June 5, 2012 transit of Venus. Background: When an inferior planet (Venus or Mercury) is at a place in the solar system called inferior conjunction, it is passing the Earth on the way around the Sun. Another point in the orbit (relative to the Earth) is superior conjunction, where the planet is aligned with the Sun but farther than it. These points are in contrast to opposition, which occurs when a superior planet is opposite the Sun in the sky. For the inferior planets, the vast majority of the passes in front of the sun do not transit the sun, but traverse north or south of it. Occasionally one does: the tables below show the transits for Mercury and Venus. Source: http://eclipse.gsfc.nasa.gov/transit/transit.html Transits of Mercury: 1901-2050 Date Universal Time 1907 Nov 14 12:06 1914 Nov 07 12:02 1924 May 08 01:41 1927 Nov 10 05:44 1937 May 11 09:00 1940 Nov 11 23:20 1953 Nov 14 16:54 1957 May 06 01:14 1960 Nov 07 16:53 1970 May 09 08:16 1973 Nov 10 10:32 1986 Nov 13 04:07 1993 Nov 06 03:57 1999 Nov 15 21:41 2003 May 07 07:52 2006 Nov 08 21:41 2016 May 09 14:57 2019 Nov 11 15:20 2032 Nov 13 08:54 2039 Nov 07 08:46 2049 May 07 14:24 Transits of Venus: 1601-2400 Date Universal Time 1631 Dec 07 05:19 1639 Dec 04 18:25 1761 Jun 06 05:19 1769 Jun 03 22:25 1874 Dec 09 04:05 1882 Dec 06 17:06 2004 Jun 08 08:19 2012 Jun 06 01:28 2117 Dec 11 02:48 2125 Dec 08 16:01 2247 Jun 11 11:30 2255 Jun 09 04:36 2360 Dec 13 01:40 2368 Dec 10 14:43 Equipment and Supplies: Ruler, calculator. Data: 6 Sun’s diameter: DSun= 1.39 x 10 km 8 Distance from the Sun to Earth: dSun-Earth= 1.496 x 10 km 8 Distance from the Sun to Venus: dSun-Venus= 1.082 x 10 km Section I: Find the diameter of Venus. 1) Measure the diameter of the solar disk with a millimeter ruler. Take several measurements and find the average. LSun = _____________ mm. 2) Measure the diameter of Venus with the ruler. (It is the large black dot on the face of the Sun.) Take several measurements and find the average. LVenus = ______________mm 3) If Venus were crossing the Sun at the distance to the Sun, then the diameter of Venus would be equal to the product: DVenus =(LVenus/LSun) x DSun. BUT, Venus is closer to the Earth than the Sun is, so the occultation disk appears larger than that. How many times farther away is the Sun from the Earth compared to Venus (from the Earth)? Let’s call this number M = _______________. 4) This factor needs to be introduced into the previous calculation since Venus is actually smaller by this amount. DVenus = (LVenus/LSun) x (DSun/M) = _______________ km. 5) Compare your measurements to the standard value of the diameter of Venus: 12100 km. Find your percent error via the equation | Standard - Observed| %error = ×100. Standard %error = ________________________. 6) Compare the diameter you calculate to the diameter of the Earth: 12800 km. Do your measurements support the claim that Venus is Earth’s sister planet (due to them having similar sizes?) 7) What are sources of error? How could this experiment be improved? Section II: Estimate the orbital speed of Venus. Here we will attempt to estimate how fast Venus is moving in its orbit by the formula distance speed = time . Even though we know that the planets move in curved trajectories called ellipses, for short periods of time we can approximate the path of a planet as a straight line. From http://eclipse.gsfc.nasa.gov/OH/transit12.html : The principal events occurring during a transit are conveniently characterized by contacts, analogous to the contacts of an annular solar eclipse. The transit begins with contact I, the instant the planet's disk is externally tangent to the Sun. Shortly after contact I, the planet can be seen as a small notch along the solar limb. The entire disk of the planet is first seen at contact II when the planet is internally tangent to the Sun. Over the course of several hours, the silhouetted planet slowly traverses the solar disk. At contact III, the planet reaches the opposite limb and once again is internally tangent to the Sun. Finally, the transit ends at contact IV when the planet's limb is externally tangent to the Sun. Contacts I and II define the phase called ingress while contacts III and IV are known as egress. Position angles for Venus at each contact are measured counterclockwise from the north point on the Sun's disk. 1) How long does it take Venus to go from Contact I to Contact III? Convert the answer to seconds: ΔtIIII− = _____________ s. 2) Over this short amount of time, it is fair to approximate the path of Venus as a straight line. Using similar triangles, estimate how far Venus has traveled in this time (see the figure below.) The similar triangles share the Earth at one vertex. ΔxVenus-estimate =_____________________________ km. 3) This estimation is wrong. The Earth has also moved during the transit. We can approximate the extra distance the Earth has covered by knowing that the Earth moves at vEarth = 30 km/s.Calculate how far the Earth moved during that time using ΔxvtEarth= Earth IIII− . ΔxEarth =____________________________ km. 4) Since both Earth and Venus moved over the transit, some extra distance has to be added to the estimate of Venus’s motion. The amount to add is dSun-Venus approximately Δxxextra=Δ Earth = ___________________km. dSun-Earth 5) Sum these two values to get the total distance Venus has moved in this time. Δxxtotal=Δ Venus-estimate+Δ x extra =________________ km. 6) This estimate is still wrong- why? Because it was assumed that Venus transited across the diameter of the sun. However, it didn’t go that far, it went across from one point to another. Use a ruler to measure the diagram ‘2004 and 2012 Transits of Venus’ (above). Measure the distance (in mm) of the track of Venus, and also across the diameter of the Sun. Call the ratio of the length of Venus’s track to the length of the diameter p, where p should be a number less than 1. p = _________________________. 7) The final estimate of the distance that Venus has traveled is obtained by multiplying the result in part (5) by the multiplicative factor in part (6). Δxpxfinal=Δ total =________________ km. 8) The speed of Venus is therefore Δx v final Venus == ______________________ km/s. ΔtIIII− 9) Compare your answer to the standard value of the orbital speed of Venus: vstandard = 35.0 km/s. Find the percent error as you did in Section I %error = ___________________________________. Section III: Discussion 1) Look at the tables that give the calendar for the transits of Mercury and Venus. Do you notice any trends amongst the dates? What kind of transits occur more often, those of Venus or those of Mercury? What is a plausible explanation for this? 2) The Kepler space mission (kepler.nasa.gov) is designed to discover planets around other stars by studying the brightness of those stars during planetary transits. Kepler is sensitive to brightness changes of 1/10000 which occur when a planet blocks out a tiny fraction of the light being emitted by the star it orbits. Given the area of Venus and the Sun, do you think that Kepler would be able to detect a transit of Venus? Why or why not? .
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