Which way is up? An observation and a few computations.

While listening to some music and meditating tonight, my head did not feel upright. By moving my head from side to side, I figured my neck was straight because it felt as if it were at maximal extension. Still, there was something tugging my head back and to the left. Then I realized my head was pulled, more or less, toward the current position of the moon. I wanted to know if this was completely crazy (my guess: yes, crazy), so I tried a second experiment and then ran some numbers.

I turned to face the opposite direction, and tried to undo my mental moon bias. After several minutes of relaxation, my head felt pulled right and forward -- still toward the moon. The sensation wasn't strong in absolute terms, but I definitely felt like the world had gone slightly sideways and my head was not balanced. Even now, facing a new direction, I still feel a tug (back and right, this time, still toward the moon).

After looking up Newton's law of gravity, as well as a few masses and distances, here are some relative forces that might help us gain some perspective.

Mass 1	Mass 2	Distance	Gravitational attraction
Human head, 5 kg	Earth's Moon, 7.36 E+22 kg	385,000 km	0.16 micronewtons (uN)
Head	Another head	1 m	0.0017 uN
Head	Earth's Sun, 1.99 E+30 kg	1.5 E+8 km	29,480 uN
Head	Earth	3,175 km	49 N

So my head's attraction to the sun should swamp the attraction to the moon. However, it was about 11:30pm when I did this experiment, which (I think) means the sun should be just about directly "underneath" me, pulling my head almost straight through the Earth's center. Since Earth's attraction on my head is about 1690 times stronger than the sun's, I'm unlikely to notice the sun's force in this configuration. So much for the sun, and even accounting for the not-perfect alignment at this hour I think the sun would also be pulling my head to the left in the first experiment.

I don't think I should conclude anything from my numbers. That said, I know my head felt pulled in an odd direction, toward the moon, even after turning around. The sensation is better described as gravity going somewhat sideways, and my head did not feel balanced until I moved it back and left. I am willing to believe that a very aware human can sense small differences in force. Consider that human fingers can sense about one-thousandth of an inch discrepancy between two surfaces (a woodworking estimate I read once), and human ears can detect pressure variations down to one-billionth of an Earth atmosphere.

An ear drum is about 55 square millimeters. One atmosphere is about 0.0103 kg per square millimeter. So one atmosphere of pressure variation on an ear drum exerts a force differential of about 0.57 kg times 9.8 m/s^2, or 5.57 newtons (can I really make that calculation? Help would be appreciated!) One billionth of that is 0.00557 micronewtons, which is roughly 28 times weaker than the force of attraction between my head and the moon. And human hearing is weak compared to other animals.

In Mysore-style Ashtanga Vinyasa yoga practice, the day of a full moon or new moon is observed by resting. One explanation for this tradition is that on these days the moon's gravitational attraction is most opposed to the Earth's attraction (full moon), or most aligned with it (new moon), resulting in undesirable lightness or heaviness. These days are called "moon days". I have not yet accepted this explanation, since the moon's attraction on the preceding or subsequent day would be very similar to the attraction on the moon day. However, I am entirely willing to believe we can detect the gravitational attraction of the moon, which seems reasonable given the calculations I just made. There are other explanations for my particular symptoms tonight, but I won't ignore the moon's attraction in the future.

Besides, I've always been attracted to the moon.