Years, Months, and Days: Different Measures of Time in Astronomy

Author: 丛雨
Reviewed by: 毫秒

  When we think about the lengths of a year, month, or day, the first figures that probably come to mind are the familiar 365 days, 30 days, and 24 hours. In astronomy, however, years, months, and days come in several different kinds and lengths. Here is a brief introduction to a few of them.

Sidereal and Solar Days

  The Sun, Moon, and stars appear to rise in the east and set in the west because Earth rotates. Earth’s rotation period is 23 h 56 m 4 s, known as one sidereal day. Clearly, this is not the 24-hour day of everyday life, which is one mean solar day. Why are they different? Because Earth rotates on its axis while also orbiting the Sun. Imagine that Earth stopped rotating: during the time it took to complete one orbit around the Sun, people on Earth would still experience one cycle of day and night—although, because Earth orbits counterclockwise, the Sun would then rise in the west and set in the east. A solar day is the length of a full day–night cycle. Once Earth’s orbital motion is taken into account, the sidereal day and solar day cannot be equal, as shown below.

  As the diagram shows, after Earth completes one sidereal rotation, point A must turn through a small additional angle before it returns to the same position relative to the Sun. A mean solar day is therefore longer than Earth’s rotation period. In fact, because Earth’s orbital speed is not uniform, the actual length of a solar day varies. This true interval from one apparent solar noon to the next is called an apparent solar day.

Sidereal and Synodic Months

  The Moon is Earth’s only natural satellite and a striking feature of the sky. Its changing phases are closely connected to the lunar months used in the traditional Chinese calendar. The phases change because the Moon orbits Earth, altering its position relative to the Sun as seen by observers on Earth and, in turn, changing how much of its sunlit side they can see. One cycle of lunar phases lasts 29 d 12 h 44 m 3 s (29.53 days) and is called a synodic month. The Moon’s orbital period around Earth, meanwhile, is 27 d 7 h 43 m 11.5 s (27.32 days), known as a sidereal month.

  Why does the cycle of lunar phases differ from the Moon’s orbital period? The reason is the same as the one behind the difference between a sidereal and solar day: Earth orbits the Sun, carrying the Moon with it. Place the Moon’s orbit around Earth into the diagram from the previous section. By the time the Moon has completed one orbit around Earth, it has also traveled through an angle around the Sun. It must therefore continue for a while before the Sun, Earth, and Moon return to the same relative positions and a full cycle of lunar phases is complete. The accompanying figure combines a diagram showing that one mean solar day is longer than one sidereal day with another showing the cause of lunar phases; these correspond to Sections I, “Sidereal and Solar Days,” and II, “Sidereal and Synodic Months.”

  At this point, consider another question: how long is a day and night on the Moon? Combining the two issues just discussed gives the answer: a solar day on the Moon lasts exactly one synodic month. Earth has tidally locked the Moon, so the same side always faces Earth and its rotation and orbital periods are equal. Starting from that orbital—or rotational—period and applying the same reasoning, we find that one synodic month is the length of a complete day–night cycle on the Moon.

Sidereal and Tropical Years

  If you simply assume that one orbit of Earth around the Sun defines the length of a year, you are badly mistaken. Astronomy recognizes many kinds of “year.” Here we will introduce only two: the sidereal year and the tropical year.

  A sidereal year is Earth’s orbital period: 365 d 6 h 9 m 10 s (365.256 days). A tropical year can be regarded as the cycle of the seasons: 365 d 5 h 48 m 46 s (365.242 days). Why can we not simply use Earth’s orbital period as the cycle of the seasons? The main reason is that the gravity of the Sun and Moon affects Earth’s rotation axis. Earth is not a perfect sphere, and its axis is tilted by 23°26′. Solar and lunar gravity make that axis trace a clockwise wobble around the direction perpendicular to the ecliptic plane—Earth’s orbital plane—with a period of 26,000 years. This phenomenon is called precession. The resulting shift in Earth’s rotation axis makes the interval between two consecutive passages of the Sun directly over either tropic shorter than Earth’s orbital period.

  If you are familiar with the celestial coordinate system, you may have heard of two effects of precession: the changing north celestial pole and the motion of the vernal equinox. On the celestial sphere, the wobble of Earth’s rotation axis appears as the north celestial pole circling the north ecliptic pole. Polaris—Alpha Ursae Minoris—is our current pole star, but around 3,000 years ago, Thuban—Alpha Draconis—lay close to the north celestial pole. Precession also makes the vernal equinox, one of the intersections of the ecliptic and celestial equator, drift slowly westward along the ecliptic. A tropical year can therefore be defined more precisely as the interval between two successive passages of the Sun through the vernal equinox.

  In reality, the varieties of astronomical time and period are far more complicated than this article can cover. This has been only a concise introduction to part of the subject, with every effort made to keep it accurate. Astronomers have also devoted considerable effort to reconciling these measures with the conventions of everyday life. Leap seconds, leap months, and leap years are all devices people have adopted to minimize discrepancies between physical time and civil time.

References

1.Fundamentals of Astronomy, Liu Xuefu, Higher Education Press
2.Astronomy, Time, and Calendars, Li Zhiping and Jia Huange, China Meteorological Press