Noah Kalendar

Noah Kalendar arrives in Washington, D.C. and is uncertain of the date.  He does note that the Washington Monument casts a shadow tip path that is a straight line during the course of the day of his arrival.  About what day of the year is it?

a.     June 21

b.     December 21

c.     March 21

d.     March 21 or September 21

The Answer is:

Noah arrived in Washington, D.C. on the equinox.  During the course of the year, any prominence on the Earth will cast a unique daily shadow tip path as a function of the time of the year.  On the equinox (vernal or autumnal), the Earth’s axis is not tilted toward the Sun (its axis is in a plane perpendicular to the plane containing the Earth and Sun), thus the shadow tip path of the Washington Monument is flattened to a straight line.  The rest of the year the Earth’s axis has a varying tilt toward or away from the Sun that results in a prominence casting a shadow tip family of curves (resulting from conic intersections—circles, ellipses, parabolas or hyperbolas).  These curves become concave upward after the autumnal equinox through the winter and then flatten to a straight line on the vernal equinox and then become concave downward through the summer flattening to a straight line with the return of autumn in the northern hemisphere.  The seasonal effect on the shadow tip path is illustrated in Figure 43 .

Figure 43.  Shadow Tip Path Seasonal Effect