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--------- #1480 - Venus passed in front of the Sun on June 5, 2012.
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- Venus has not crossed the face of the Sun since 1882. It transited the Sun again in 2012, June 5th. We are fortunate in the U.S. to be on the sun-facing side when this happens. The Venus transit will not happen again until 2117, someone needs to take notes for me. I will miss this one.
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- (See footnote 1 for the years of Venus’ transits). On Tuesday, June 5, Venus crossed from one edge of the Sun to the other. It takes 6.7 hours. You need a welder’s mask or eclipse glasses to witness it.
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- There is a lot of interesting math involved. One equation is used to learn the distance from the Earth to Venus. We use the “ small angle formula” to do these calculations.
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------------------------------------ angle arc seconds = 206,265 Diameter / Distance
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------------------------------------ angle in radians = 57.2958 Diameter / Distance
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- This equation works because for very small angles the cosine = 1 The sine and tangent = the angle. And, one complete circle is 2*pi radians = 360 degrees. 1 radian = 57.3 degrees. An example of how small an angle one arc second is the angular diameter of a tennis ball 8 miles away.
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- The Moon is about ½ angular degree. The Sun is about the same size in the sky as evidenced by a total eclipse. The angular degree of the Sun is 0.5244 degrees. The diameter of the Sun is 139,000 kilometers.
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------------------ 0.5244 angular degrees * 3600 = 1,888 arc seconds.
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- The diameter of Venus as it transit’s the Sun is 58.6 arc seconds , which about 3% of the total transit distance. The diameter of Venus is 12,600 kilometers. Using the equation above to calculate the distance to Venus:
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------------------------- Distance = 206,265 / 58.6 * 12,600 kilometers.
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------------------------ Venus Distance = 44.3 million kilometers
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------------------------ Venus Distance = 27.6 million miles.
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--------------------- Earth is 149.6 million kilometers from the Sun
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-------------------- Venus is 108.2 million kilometers from the Sun
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-------------------- Distance from Earth to Venus when they are lined up with the Sun = 149.6 - 108.2 = 41.4 kilometers.
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- How long does it take Venus to transit completely across the face of the Sun as viewed from the Earth? How fast is Venus and Earth traveling?
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- If we assume the planets orbit in perfect circles the travel distance is 2 * pi * radius. The time for the Earth is one year to complete one orbit.
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--------------- Earth travels = 2 * pi * 149.6 million km = 940 million km, or 584 million miles.
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--------------- Earth year = 365.24 days * 24 * 3600 = 31.6 million seconds.
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---------------- Earth speed = distance / time = 940 / 31.6 = 29.7 km / sec, or 66,543 miles per hour.
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--------------- Venus travels = 2* pi * 108.2 million km = 680 million km
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--------------- Venus year = 224.7 days * 24 * 3600 = 19.4 million seconds.
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----------------- Venus speed = 680 / 19.4 = 35 km / sec, or, 78,410 miles per hour.
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- The difference in the speed of Venus to the speed of the Earth = 35 - 29.7 = 5.3 km/sec.
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- Traveling at 5.3 km / sec how long does it take to cross the diameter of the Sun, 139,000 km?
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---------------- Time = Distance / time = 139,000 / 5.3 = 26,264 seconds
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---------------- Time to travel diameter = 7.3 hours.
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- The transit on June 5, 2012 does not cross a perfect diameter. The transit time crossing the cord of the circle is 24,000 seconds or 6.7 hours. Did you miss it? It will not happen again until 2117.
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- (1) Years Venus transit across the Sun occurs: 1631, 1629, 1761, 1769, 1874, 1882, 2012, 2117, 2125, 2247, 2255, 2360, 2368. Occurring in the months of June and December.
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