24 April 2013

Days of No shadows at Noon

We have all heard the story on how Eratosthenes measured the circumference of the earth. Eratosthenes observed that during high noon when sun was at Zenith a well at a place called Syene did not cast any shadow on June 21st; we call this day as summer Solstice. On same day, Solstice, during high noon a shadow was cast when a vertical stick was kept in Alexandria. Based on the angle of shadow cast by the sun he calculated the circumference of the earth, he gave a value of 40233km.
Sun rises in the east and sets in the west, this we notice easily as the duration is very small. The Sun does move in north-south direction too, this we normally notice as seasonal changes more than position of the sun, as the movement of the Sun in north-south direction takes months together.
Sun will be directly overhead at equator on march21/22; the shadow will be at its minimum on that day during high noon. This day is called Equinox and Sun’s angle is taken as Zero degree declination.
As days pass, due to earth’s axis inclination of 23.5degrees, Sun starts moving towards north from March 21st to June 21st. On June 21st Sun would have reached maximum angle of 23.5degrees, this day is called summer Solstice, and after reaching north most angle Sun starts moving back towards equator. The Sun reaches back to zero declination, on September 22nd and this position is called autumn equinox. From this day Sun will move towards south reaching southernmost angle of -23.5 on December 21st, again after reaching this declination sun starts moving towards equator and cycle continues.
Now coming back to shadows, we have seen that there will be minimum or no shadow on equinox day on equator regions like Congo, Uganda and Kenya etc. All other regions not on equator or zero latitude will have shadows on that day. So when will other regions can have minimum or no shadow?
Here is good and easy way to know when the Sun will be directly overhead and there will no shadows in area we live. All we need to know is the declination of the sun and latitude of the place we live, on the day these two match; the Sun will be directly overhead at noon, with minimum or no shadow cast. That means we should live in a region which is less than or equal to 23.5degrees on either side of the equator.
Here is list of declination of the Sun; find out where and when there will be no shadow day based on latitude of your place….Make sure the reference is a vertical  pole or stick and time you check is at exact noon.
Bangalore will have minimum shadow on April 24/25th and again on Aug 19th.
Declination(Dec) is given in Degrees, Minutes and Seconds




  RA  Dec  
YearMonthDatehmso'"
2013Apr104120.3542649.6
2013Apr20445944957.3
2013Apr304837.851259.9
2013Apr405216.7753557.1
2013Apr505555.9155848.5
         
2013Apr605935.2562133.8
2013Apr71314.864412.6
2013Apr81654.587644.6
2013Apr911034.617299.3
2013Apr1011414.8975126.4
         
2013Apr1111755.4481335.6
2013Apr1212136.2783536.5
2013Apr1312517.485728.7
2013Apr1412858.8491912
2013Apr1513240.694045.9
         
2013Apr1613622.710210.1
2013Apr171405.14102324.3
2013Apr1814347.95104428.1
2013Apr1914731.1311521.2
2013Apr2015114.7111263.3
         
2013Apr2115458.68114634.1
2013Apr2215843.0812653.1
2013Apr232227.912270.2
2013Apr242613.17124655
2013Apr252958.913637.1
         
2013Apr2621345.113266.3
2013Apr2721731.8134522.2
2013Apr2822119.0114424.7
2013Apr292256.73142313.2
2013Apr3022854.99144147.6
         
2013May123243.791507.5
2013May223633.15151812.6
2013May324023.0815362.5
2013May424413.57155337.1
2013May52484.63161055.9
         
2013May625156.27162758.6
2013May725548.49164444.9
2013May825941.2917114.5
2013May93334.66171727
2013May103728.61173322.3
         
2013May1131123.13174859.8
2013May1231518.2218419.5
2013May1331913.87181920.9
2013May1432310.0918343.7
2013May153276.87184827.8
         
2013May163314.219232.7
2013May173352.08191618.3
2013May183390.5192944.2
2013May1934259.45194250.3
2013May2034658.94195536.1
         
2013May2135058.942081.5
2013May2235459.4720206.3
2013May233590.51203150.2
2013May24432.05204312.9
2013May25474.09205414.2
         
2013May264116.6321454
2013May274159.66211512
2013May2841913.1821257.9
2013May2942317.17213441.6
2013May3042721.63214352.9
         
2013May3143126.54215241.6
2013Jun143531.892217.4
2013Jun243937.6622910.3
2013Jun344343.83221650
2013Jun444750.422246.3
         
2013Jun545157.33223059.2
2013Jun64564.6223728.3
2013Jun75012.19224333.7
2013Jun85420.08224915.2
2013Jun95828.25225432.6
         
2013Jun1051236.67225925.8
2013Jun1151645.3123354.7
2013Jun1252054.1623759.3
2013Jun135253.18231139.4
2013Jun1452912.35231455
         
2013Jun1553321.64231746
2013Jun1653731.04232012.4
2013Jun1754140.52232214
2013Jun1854550.04232351
2013Jun1954959.623253.1
         
2013Jun205549.16232550.5
2013Jun2155818.7232613.1
2013Jun226228.21232610.9
2013Jun236637.66232544
2013Jun2461047.05232452.2
         
2013Jun2561456.34232335.7
2013Jun266195.52232154.5
2013Jun2762314.58231948.6
2013Jun2862723.5231718
2013Jun2963132.25231422.9
         
2013Jun3063540.8123113.4
2013Jul163949.1723719.4
2013Jul264357.2923311.1
2013Jul36485.15225838.7
2013Jul465212.74225342.1
         
2013Jul565620.03224821.7
2013Jul67026.99224237.4
2013Jul77433.61223629.4
2013Jul87839.86222958
2013Jul971245.7222233.2
         
2013Jul1071651.16221545.2
2013Jul1172056.182284.3
2013Jul127250.752200.6
2013Jul137294.84215134.2
2013Jul147338.45214245.5
         
2013Jul1573711.55213334.6
2013Jul1674114.1321241.7
2013Jul1774516.1821147
2013Jul1874917.6921350.8
2013Jul1975318.64205313.3
         
2013Jul2075719.02204214.7
2013Jul218118.84203055.3
2013Jul228518.08201915.2
2013Jul238916.7420714.6
2013Jul2481314.83195453.9
         
2013Jul2581712.34194213.3
2013Jul268219.27192913
2013Jul278255.61191553.2
2013Jul288291.3819214.2
2013Jul2983256.56184816.4
         
2013Jul3083651.15183359.9
2013Jul3184045.16181925.1
2013Aug184438.5718432.2
2013Aug284831.4174921.6
2013Aug385223.63173353.5
         
2013Aug485615.2617188.3
2013Aug5906.311726.1
2013Aug69356.75164547.5
2013Aug79746.61162912.6
2013Aug891135.87161221.8
         
2013Aug991524.55155515.5
2013Aug1091912.63153753.8
2013Aug119230.13152017.2
2013Aug1292647.0415225.9
2013Aug1393033.38144420.4
         
2013Aug1493419.1514260.8
2013Aug159384.3614727.6
2013Aug1694149.01134841
2013Aug1794533.12132941.3
2013Aug1894916.69131028.9
         
2013Aug1995259.7512514
2013Aug2095642.31123126.9
2013Aug2110024.38121138
2013Aug221045.98115137.5
2013Aug2310747.14113125.6
         
2013Aug24101127.8611112.8
2013Aug2510158.17105029.3
2013Aug26101848.08102945.4
2013Aug27102227.610851.4
2013Aug2810266.7794747.7
         
2013Aug29102945.5892634.6
2013Aug30103324.059512.3
2013Aug3110372.2184341.3
2013Sep1104040.068221.9
2013Sep2104417.638014.3
         
2013Sep3104754.9273819
2013Sep4105131.9571616.2
2013Sep510558.736546.4
2013Sep6105845.2963149.7
2013Sep711221.626926.7
         
2013Sep811557.7654657.7
2013Sep911933.7152422.9
2013Sep1011139.495142.7
2013Sep11111645.1143857.5
2013Sep12112020.64167.6
         
2013Sep13112355.9635313.3
2013Sep14112731.2333015
2013Sep1511316.413713
2013Sep16113441.532447.5
2013Sep17113816.6122059
         
2013Sep18114151.6815747.7
2013Sep19114526.7613433.9
2013Sep2011491.8711118
2013Sep21115237.040480.2
2013Sep22115612.302440.9
         
2013Sep23115947.670120.4
2013Sep2412323.160221
2013Sep2512658.8104523
2013Sep26121034.64-1845.1
2013Sep27121410.66-1327.1
         
2013Sep28121746.9-15528.6
2013Sep29122123.38-21849.3
2013Sep3012250.11-2428.7
2013Oct1122837.13-3526.6
2013Oct2123214.43-32842.6
         
2013Oct3123552.06-35156.4
2013Oct4123930.01-4157.4
2013Oct512438.31-43815.4
2013Oct6124646.98-5120
2013Oct7125026.03-52420.9
         
2013Oct812545.47-54717.5
2013Oct9125745.32-6109.6
2013Oct1013125.6-63256.7
2013Oct111356.32-65538.6
2013Oct1213847.5-71814.7
         
2013Oct13131229.16-74044.8
2013Oct14131611.32-838.4
2013Oct15131954-82525.3
2013Oct16132337.21-84735
2013Oct17132720.99-9937.2
         
2013Oct1813315.34-93131.5
2013Oct19133450.3-95317.5
2013Oct20133835.87-101454.9
2013Oct21134222.1-103623.3
2013Oct2213468.98-105742.3
         
2013Oct23134956.54-111851.6
2013Oct24135344.8-113950.7
2013Oct25135733.78-12039.3
2013Oct2614123.48-122117
2013Oct2714513.93-124143.3
         
2013Oct281495.14-13157.8
2013Oct29141257.12-13220.3
2013Oct30141649.88-134150.1
2013Oct31142043.43-14127.1
2013Nov1142437.78-142050.6
         
2013Nov2142832.93-14400.4
2013Nov3143228.9-145855.9
2013Nov4143625.69-151736.8
2013Nov5144023.29-15362.7
2013Nov6144421.72-155413.1
         
2013Nov7144820.96-16127.5
2013Nov8145221.03-162945.7
2013Nov9145621.92-16477.2
2013Nov1015023.63-17411.6
2013Nov1115426.17-172058.4
         
2013Nov1215829.54-173727.3
2013Nov13151233.74-175338
2013Nov14151638.77-18929.9
2013Nov15152044.63-18252.8
2013Nov16152451.33-184016.2
         
2013Nov17152858.86-18559.8
2013Nov1815337.23-19943.2
2013Nov19153716.42-192356.1
2013Nov20154126.45-193748
2013Nov21154537.29-195118.6
         
2013Nov22154948.96-20427.5
2013Nov2315541.43-201714.4
2013Nov24155814.71-202939
2013Nov2516228.77-204140.8
2013Nov2616643.61-205319.6
         
2013Nov27161059.21-21434.9
2013Nov28161515.56-211526.6
2013Nov29161932.64-212554.2
2013Nov30162350.42-213557.5
2013Dec116288.9-214536.2
         
2013Dec2163228.03-215449.8
2013Dec3163647.8-22338.3
2013Dec416418.18-22121.3
2013Dec5164529.14-221958.4
2013Dec6164950.64-222729.6
         
2013Dec7165412.67-223434.5
2013Dec8165835.18-224113
2013Dec917258.15-224724.7
2013Dec1017721.54-22539.6
2013Dec11171145.34-225827.3
         
2013Dec1217169.51-23317.8
2013Dec13172034.02-23740.9
2013Dec14172458.85-231136.5
2013Dec15172923.97-23154.3
2013Dec16173349.34-23184.4
         
2013Dec17173814.95-232036.5
2013Dec18174240.75-232240.6
2013Dec1917476.73-232416.6
2013Dec20175132.84-232524.5
2013Dec21175559.06-23264.1
         
2013Dec2218025.36-232615.5
2013Dec2318451.71-232558.7
2013Dec2418918.07-232513.5
2013Dec25181344.42-23240.2
2013Dec26181810.71-232218.6
         
2013Dec27182236.92-23208.8
2013Dec2818273.01-231730.8
2013Dec29183128.94-231424.8
2013Dec30183554.69-231050.8
2013Dec31184020.21-23649

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