MadSci Network: Astronomy

Re: I created a sundial in which I record its shadow everyday @ the same time

Date: Fri Jun 5 14:44:54 1998
Posted By: Michael Martin-Smith, Other (pls. specify below), Family Physician, Fellow,BIS, amateur astronomer( BAA), British Interplanetary Society
Area of science: Astronomy
ID: 896800643.As


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
>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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