|MadSci Network: Astronomy|
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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