Monday, March 9, 2015

Geometry

Our bedroom has a large skylight facing west. You can see out of it while lying in bed, and a couple of times I've tried stargazing with binoculars in bed when I wake up in the middle of the night (which I often do, since I rarely sleep continuously for more than four-hour stretches). In the winter I am able to see the Pleiades setting. Sometimes on a clear winter night the moon shines in through the skylight like a giant floodlight and wakes us up. Fortunately the window has a shade for such occasions. I was thinking about why the moon only shines through the skylight during the winter and realized that it's just a simple problem in geometry and astronomy.

As the solar system was forming 4.6 billion years ago, it took the shape of a rotating disk. All of the planets and the moon still orbit around the sun in approximately the same disk shape, which is the plane formed by the orbit of the earth known by astronomers as the ecliptic. Another important fact is that the axis on which the earth spins is not perpendicular to the ecliptic but is off by about 23.4°. That angle is responsible for our seasons. When the axis is tilted toward the sun in the northern hemisphere, more photons of light from the sun strike the surface of the northern hemisphere than when it is tilted away from the sun, and this causes summer. It is easy to notice the change of the seasons by observing where the sun rises and sets on the horizon every day. At the summer solstice the sun rises and sets at its northernmost points on the horizon; it is the longest day, and the north gets its greatest daily sun exposure then.

At the winter solstice, the northern hemisphere is angled the farthest away from the sun, and the least amount of sunlight strikes its surface. However, at that place in the orbit the situation with the moon is different. The sun, moon and earth are all on about the same plane year-round. At the winter solstice, while the earth is tilted away from the sun in the north, during the night, when the moon is visible in the opposite direction from the sun, the northern hemisphere reaches its maximum tilt toward the moon at a visible time of day. Therefore, the moon reaches its maximum visible distance above the horizon in the north around the time of winter solstice, the opposite of the situation with the sun. In the short term there is no change in the northern hemisphere's relationship to the moon; this difference is caused simply by the change in the time of day when the moon is visible. Our skylight is situated such that the moon only rises high enough to shine through it during the period near winter solstice. The moon reaches its lowest visible point above the horizon around summer solstice in the north.

I find it interesting that simple geometrical facts like these can have such a large impact on our lives. If the tilt of the earth's axis were 0°, like that of Mercury, we would have no seasons. The evolution of life on the planet might have been completely different from what occurred. If the tilt were 97.8°, like that of Uranus, the seasons would be far more extreme. We would have six months of light followed by six months of darkness. Give or take a few degrees from our current angle, we might not exist at all.

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