|MadSci Network: Astronomy|
Therese, 1/ What I think you are detecting is a factor known as the equation of time, or ET. Over 12 months the Sun's position in the sky , recorded at exactly the same time of day as measured by a watch, traces a distorted figure of eight, or analemma, in the sky; the dates when the Sun's position corresponds exactly to the position expected from your watch are 16 April, 14 June, 2 Sep, and Dec 25. In other words midday on your watch sees the Sun exactly on the meridian (allowing for artificial Summer Time, if any) ie ET = 0 extreme values are -14.3 mins 11 Feb Sun appears to be running slow +3.7 mins 14 May Sun appears to be running fast -6.4 mins 26 July Sun appears to be running slow +16.4 mins 3 Nov Sun appears to be running fast This phenomenon reflects the fact that the Earth travels at a slightly different speed around the sun at different times of the year - ie the day of 24.2422 hours is only an average, with a small range of error. This in turn is due to the fact that the Earth's orbit is not a precise circle - it is a an ellipse, of VERY small eccentricity. You have actually demonstrated that our orbit is an ellipse. If you were to record this ET factor each week over a year, and also the Sun's elevation above the horizon at the same time, and then plot a graph of time the Sun crosses the meridian against elevation above the horizon, you would draw out the "figure of eight" analemma It would be very neat with a sundial- most people would find this small variation easier to plot with a telescope/setting circles- but a good sundial at least shows the general idea. >Would it be possilbe If I did that no >shadow would occur due to the sun being exactly perpendicular to the Earth where >I live in Michigan? I Yes- at noon local Michigan time the Sun would be approximately on the Meridian - but your Mid Standard time factor is different from mine (0) because we are on different longitudes. The Sun crosses your meridian and reaches its highest point in the sky at due South, at a time determined by your longitude, with the Standard Time determined by longitude ( Eastern Standard Time for example runs 5 hours later than my own Greenwich Mean Time- or Universal UT time). Your exact midday is a little more complicated since the Standard Time zones cover 15 degrees longitude in each band. If your longitude for instance is 95 degrees west, your midday would be 6 hours 20 minutes after mine; thus, assuming the standard time factor of 6 hours is your official time zone, the true midday- meridian crossing would still be delayed 20 minutes each day. You should, for ease, start your experiment on June 14 when the ET is zero see above; you will then get your true longitude factor- ie difference between true local time, and GMT plus the standard time zone factor( 6 hours in Michigan?). A good school project might be to find your true longitude by observing at what clock time the sun's shadow is truly zero, and working back including your standard time zone factor on June 14- having done that, you could propose doing a weekly measurement to see at what time meridian occurred and so demonstrate the first paragraph above?? I note that Ann Arbor, Michigan has a Time Zone of 5 hours, ie that Ann Arbor and Michigan officially runs 5 hours behind Universal or Greenwich Mean Time. More simply, I have afternoon tea when you have lunch - (approximately!) Thus, Ann Arbor, and much of Michigan is assumed to be 75 dgegrees west in longitude. As I said before, your own locale may well not be exactly at 75 degrees W - your task on June 14 could be to find your longitude as determined by the sun. It will be 75 degrees +/- up to 7.5 degrees( 67.5 to 82.5degrees West), since that is how the Time Zones are organized.
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