MadSci Network: Astronomy

Re: Re: will a shadow be in the same place at the same time\date a year later?

Date: Fri Jul 2 08:36:05 2004
Posted By: Kenneth Beck,
Area of science: Astronomy
ID: 1088594116.As

Dear Anne,

 As a research scientist, I will directly answer your artistic question 
with a short, practical answer and a long, subtle answer.

The short answer is YES.  For all practical, artistic purposes a shadow 
cast today by an immobile object (e.g., a statue) will occur with the 
same length, same position, and at the same time of day one year hence.  
The shadow’s perspective will not change in a practical, artistic way 
from this year to the next vis-à-vis other immobile objects within its 
local neighborhood. 

The long answer is NO. A shadow’s position will change from year-to-year, 
decade-to-decade, and century-to-century.  This is due to a number of 
subtle processes with causes both known and unknown, including: Luni-
Solar precession, planetary precession, nutation, Chandler Wobble, Annual 
Wobble, Long Wobble, and linear drift. The shadow cast by an immobile 
object will be unique in history within periodic variation.   

Let's first consider that a calendar year made up of 24-hour solar days 
(solar day: the time it takes the Earth to rotate once on its axis so 
that the Sun is observed in the same longitudinal position in the sky) is 
approximately 365.25 solar days long.  This is what gives rise to 
our “Leap Year” every fourth, even year.  We add in one whole solar day 
every four years to keep our daily calendar more or less accurate.  

In the event, what this means positionally is that we have actually 
lagged behind a quarter of a day in terms of our revolution around the 
Sun compared to 365 complete days (a calendar year) of rotation around 
the Earth’s axis.

Ok, so what? Well, remember the reason we have four seasons. The Earth’s 
axis of rotation is tilted with respect to our revolution around the Sun 
by ~23.5 degrees.  During a complete year, the apparent position of the 
Sun moves alternatively north 23.5 degrees (Summer Solstice in London) 
then south 23.5 degrees in latitude (Winter Solstice in London), then 
back for Summer in London. A change of 94 degrees latitude per year…per 
365 days.

So, on average 94 degrees/365 days = 0.258 degrees latitude change/day.  
Or, 0.064 degrees latitude change in a quarter day.  Thus, considering 
the quarter day lag in a calendar year, observationally the Sun has 
changed it altitude in the sky by 0.064 degrees from one year to the next 
starting at the leap year (this year, for example).  After three years, 
this will amount to 3 X 0.064 degrees = 0.192 degrees difference.  But 
then - leap year - we begin again.

A change in altitude of the Sun in the sky is equivalent to a change in 
shadow length and position on the ground.  It will be a maximum after 
three years and a minimum in the fourth, leap year.  I’ll leave it to 
you – being an artist who understands perspective – to do the 
triangulation/trigonometry and see that the change in shadow position and 
length may not amount to much for an object the size of a woman or 
giraffe.  But it could be somewhat noticeable for an object the size of 
Everest or Kilimanjaro.

Hope this helps and good luck on the project!

---* Dr. Ken Beck

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