The red curve is the shortest route between them.
The Moon comes to its Last Quarter place again on March 1, at 23 Universal Time (which is 6 PM in eastern North America). We’ve been talking about how this Moon phase shows the way we’re traveling, since it is crossing sunward in front of us, so I thought I’d try to make a picture.
The Moon is beyond Earth at a distance, just now, of about 58 Earth-radii (somewhat nearer than its average of about 60). Our viewpoint is an average Moon-distance back in the opposite direction. The arrow through the Moon shows its travel from two hours earlier to two hours later. And an arrow on Earth’s equator shows how much it rotates in one hour.
A person (out of sight) around on the front of the Earth is experiencing sunrise and seeing the Moon overhead – if he’s standing up on his ship, he is a living arrow of the Earth’s motion. On the back of the Earth, the Sun is setting for, among other places, Guantánamo in Cuba.
Yes, that does happen about 23 UT on this date.
While plotting how to include the Moon in this kind of globe picture (which I’ve used mainly for showing the tracks of eclipses), I didn’t bother yet to delete a red line left from some other thinking; it represented a great-circle route from, maybe, New York to Paris. I would have deleted it, but happened to read an item (in a Guardian article of Feb. 16) that made me think of giving this illustration a second purpose. The 91 prisoners remaining at Guantánamo Bay are allowed to pray for twenty minutes five times each day, and there are painted arrows showing them the direction to Mecca.
I wondered which way, exactly, these arrows point. Guantánamo and Mecca are at almost the same latitude (20 and 21 degrees north) but at longitudes very far apart (75 west and 40 east). You might think that the direction from Guantánamo to Mecca is the straight line you would draw between them on a familiar map of the Earth, such as a rectangular map with the Mercator projection. In that case the direction from Guantánamo to Mecca would be just about due east. But in reality the shortest distance between them, as between any two places on a globe, is a great circle arc, such as would be made by a string stretched tightly between two pins planted in a model globe. Because Guantánamo and Mecca are so far apart, the great-circle route curves well to the north in latitude before dropping back south.
If a Muslim prisoner at Guantánamo sees a “to Mecca” arrow and it points not east but about 30 degrees to the north of east, will he suspect: “That arrow doesn’t point to Mecca, it points to Europe. Are the infidels trying to get me to bow down to Rome?”
Prayer is one of the five pillars of Islam, and the five times for prayer are dawn, noon, afternoon, sunset, and darkfall.