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    Mathematical prediction of "Manhattanhedge" ??
    From: Joe Wong
    Date: 2022 Jun 29, 06:58 -0700

    Manhattanhenge (also called “Manhattan Solstice”) is a rare phenomenon during which the setting sun aligns perfectly with Manhattan’s street grid, allowing the sunlight to beam through the East-West streets. The spectacle can be witnessed twice a year. 

          I was having a thought about whether one could predict the exact date and time of 'Manhanttanhendge' by refering to the almanac and doing several steps of astronomical calculations. I was a bit rusty with trigonometry since it has been almost a decade after I graduated from college,and I'm not quite sure whether my calculation method is sound, despite the fact that the result somehow checks out. 

         The general idea is to obtain the GHA and declination value by solving the astronomical triangle with these known parameters(sun's azimuth/observer's lat & long/sun's altitude)

         1.sun's azimuth: 299°(aligns with east,westward street of manhattan)

          2.observer's coor: 40.747°N 73.982°W (East 34th Street and Park Avenue, one of the perfect observing locations as decribed by tourism websites )

         3.sun's altitude: almost 0°(by pre-computing,it is known that the sun's elevation never exceeds 0°40′ during Manhattanhedge, although atm.refraction do seem to "lift" the sun up quite a bit)

         Fig 3 worksheet shows how I obtained the GHA and Dec. value, which are 183°52.3′ and 21°32′55″ respectively. I then used the Dec.value as a first guide to locate the approx.date in the NA(any certain dec. value only appear twice at most in the almanac) and 21°32′55″ has poped up in the column of "UTC19:00 28th May" , then the fine GHA value of 183°52.3′ would bring us to “UTC 00:00 29th May GHA 180°39.5′ Dec N 21°34.9′”, the relatively accurate culumn to predict "Manhanttanhedge". By substracting the two GHAs(Almanac GHA and my calculated GHA) ,you can get the GHA inc. to determine the minutes and seconds of the lineup.(In my case, GHA inc. is 3°12′48″,therefore the exact UTC is 12mins51secs past 00:00, just a dozen seconds off from the recorded event time of Manhattanhedge"20:13 EDT May 29 2022") 

          Above are the entire precedures that I took, any idea about whether the method is sound is quite welcomed.






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