General Astronomy/Yearly Motions

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General Astronomy
Daily Motions Yearly Motions Phases of the Moon


Why do we have seasons? A little thought will suggest that it can't have much to do with the Earth's distance from the sun, as that would affect the Southern and Northern Hemispheres at the same time. (In fact, the Earth is marginally closer to the sun around December than at other times of the year.) Why, then are there seasons?

Every year, the Earth completes one orbit of the Sun. We see this observe the effect as the change of the seasons and the movement of the constellations. Over the course of a year, the Sun moves through a great circle on the celestial sphere, tracing out the same path year after year. This path is called the ecliptic. The ecliptic is not only the path of the Sun in the sky; it also marks the plane of the Earth's orbit of the Sun. The planets orbit the Sun in different planes but near to the ecliptic.

The Earth is tilted with respect to the ecliptic plane by 23.5°

The axis of the Earth's rotation is tilted by 23½° with respect to the plane of the ecliptic. Globes are typically built with an inclined rotation axis. The 23½° North latitude is marked as the Tropic of Cancer and the 23½° South latitude is marked as the Tropic of Capricorn. In the Northern Hemisphere, the Sun will pass directly over head only between June 20th and 22th along the Tropic of Cancer. That day is called the day of the summer maximum or Solstice in the Northern Hemisphere. In the Southern Hemisphere, the Sun will pass directly over head only once between December 20th and 23rd along the Tropic of Capricorn. Anywhere between the Tropic of Cancer and the Tropic of Capricorn, the Sun will pass directly overhead at least twice during the year, but the Sun will never pass overhead for people living outside the tropics. Within the Tropics, over the course of a year, the Sun's position in the sky changes, beginning in the southern sky about December 21, moving to the northern sky in mid-year, and ending the year back in the southern sky.

The tilt of Earth's rotation axis causes a 23½° tilt of the great circle of the ecliptic with respect to the Earth's equator. The ecliptic and the equator intersect at two points, but are otherwise separated by up to 23½°. When the sun lies at one of the intersections, it is directly overhead somewhere on the equator. This occurs at the equinox, and the points on the sky where the equinox intersects the equator are also called equinoxes. Once every year, the Sun passes through the equator going north. This happens in late March — the "vernal" or "spring" equinox. The "autumnal" equinox occurs when the Sun passes through the equator in late September.

On the equinox days, the day and night are equally long. This is the origin of the name equinox, which is from Latin for "equal night." On the day of the equinox, the Sun rises due east and sets due west. It doesn't rise to directly overhead, though, except for observers on the Equator. The equinoxes are the only days of the year that have 12 hours of daylight and 12 hours of dark. After the vernal equinox, moving into Northern summertime, the Sun begins rising in the northeast and sets in the northwest. Days in the Northern Hemisphere become longer, while days in the Southern Hemisphere become shorter.

The points at which the Sun is at its greatest distance from the equator are called the solstices. The solstices mark the longest and shortest day of the year. The longest day of the year is the summer solstice, and the shortest day is the winter solstice. In the Northern Hemisphere, the summer solstice occurs when the Sun is farthest north, while the winter solstice occurs at the Sun's southernmost point. In the Southern Hemisphere, the solstices are reversed.

Viewed from space, we see that the Earth's tilt changes the exposure of different parts of the Earth to the Sun. Observers in the Northern Hemisphere will see the Sun at its lowest position in the southern sky, about December 21. They see it this way because the Southern Hemisphere is tilted towards the Sun and the Northern Hemisphere is tilted away. About June 22, the situation is reversed, with the Northern Hemisphere pointed toward the Sun, and the Sun will be in its extreme high point in the sky at solar noon. For an observer in the Southern Hemisphere, the Sun will appear at its lowest point in the sky in the north, about June 22, while the Sun will appear at its high point in the sky about December 21. One effect of this phenomenon is that during the months of Northern Hemisphere summer, the North Pole will be able to receive sunlight twenty-four hours a day. The Sun will remain visible through much of the autumn, passing below the horizon at the autumnal equinox. As winter sets in at the North Pole, the Sun will not be seen for six months, while that portion of the Earth is tilted away from the Sun.

As one moves toward the Earth's equator from either pole, this effect becomes less severe. At the Arctic or Antarctic Circles, one will only see a 24-hour sunlit day on the summer solstice. Further toward the equator, days will get longer during the summer and shorter during the winter; the nearer to the equator, however, the less difference there will be between the number of hours of illumination and night hours. At the equator, there's practically no difference between the length of day all through the year.

Clearly, the annual motion of the Earth around the Sun is the cause of Earth's seasons. What effect gives rise to this seasonal change is less obvious. At first glance, one might think that winter occurs when the Earth is farther from the Sun. If we realize the Northern and Southern Hemispheres have winter at different times of year, we see that this can't be right. Also, the Earth's orbit is very nearly circular. The change in the Earth's orbital distance is much too small to have a noticeable effect on Earth's climate.

Certainly the length of time each day during which sunlight falls on a particular location has a great deal to do with the seasonal changes in temperature. However, another effect less obvious, but more influential is the angle at which the sunlight hits a region. At the equator, there is little difference throughout the year as the Sun varies by 23.5 degrees on either side of the vertical. The length of the ray's path on Dec 21 at solar noon is increased by a factor of only 1.1 from a direct vertical path and the reduction of the sunlight is small. The more direct radiation gives the maximum amount of heat and energy to the earth where it falls, and therefore these areas will receive the most warmth. Away from the equator, however, the Earth's tilt means that sunlight is not received so directly and a greater amount of the Sun's energy is blocked by the longer path it takes through the atmosphere. At 50 degrees north latitude, the path the Sun's rays travel through the atmosphere on Dec 21, at solar noon, will be increased by a factor of 3.5 from a direct vertical path. In general, the rays will come at an angle that depends on the time of day, the latitude of the region from the equator, and the position of Earth in its orbit.

The constellations in the ecliptic, the zodiac, have a long history in the tradition of astrology. In most newspapers, you can read a (completely unscientific) prediction of your future or some personal advice, specific to your birthday. Each entry is associated with one of the constellations of the zodiac and a range of birth dates. In the tradition of astrology, the constellation the Sun occupied on your birthday, your "sign," reveals information about your personality and your future.

Interestingly, the dates given for each constellation in the newspaper don't match the Sun's position in the sky for those dates. There is a mismatch between the date in the newspaper and the real position of the Sun of a little more than a month. The mismatch appears because the dates corresponding to each sign were set thousands of years ago. Over the course of thousands of years, the Earth "wobbles" on its axis, causing the calendar and the positions of the stars in the sky to shift. This wobble is caused by the pull on the equator by the sun and moon, and is called precession. It affects the positions of all the constellations with respect to the equinoxes and the pole.

The precession of the Earth is like the movement of a top. If you spin a top with the axis tilted, the axis will slowly rotate as the top spins. Likewise, the Earth's axis remains tilted at 23½°, but the orientation of this tilt changes over the course of thousands of years.

Since precession changes the direction in which Earth's pole points, it also changes which star is the North Star, if any. Earlier, we quoted Shakespeare, who referenced Polaris in Julius Caesar, describing it as the northern star. Strictly, this would be incorrect. Polaris was not "fixed" in the sky in Julius Caesar's time because Earth's axis was pointed differently, toward the Big Dipper.

Precession is a slow drift, and a difficult motion to detect. The motion of the stars from precession only becomes noticeable to the unaided eye after many, many years of careful observation, although it becomes very quickly noticeable through a telescope. The Greek astronomer Hipparchus was the first to measure the precession by comparing his own observations to observations collected a century and a half before.

Precession changes the position of the Earth in its orbit for the solstices and the equinoxes. As the Earth's axis turns over, the moment when it points most closely towards the Sun changes, and so the seasons change. If a calendar didn't account for this, the seasons would drift as the axis precessed. Eventually, the Northern Hemisphere would be cold in July and warm in January, and the Southern Hemisphere would have warm July weather and cold January weather. The calendar takes the extra motion of precession into account by using the tropical year as its basis. The year as we usually define it is a sidereal year, the time it takes for the Earth to make one orbit around the Sun. In one year, as we usually measure it, the Earth really completes a little more than a full orbit around the Sun. During a sidereal year, the Sun moves fully around the sky and back into the same position with respect to the stars. In a tropical year, the Sun goes from the Vernal Equinox, around the sky, and back to the Vernal Equinox again. During this time, the equinox has shifted slightly in its position, so that a tropical year is a bit shorter than a sidereal year.

It's easy to identify the progression of the calendar if you take careful notice of the sky. Next time you see sunrise or sunset, take notice of whether the Sun is setting due west or just north or south of west. Many ancient cultures watched the motion of the Sun carefully and over long periods of time. Using simple techniques and tools, they were able to measure periods like the length of a year very accurately. Ancient people who took notice of celestial motion would have found that the summer solstice occurred every 365 days. They would also notice that the solstice was delayed an extra day every four years. This is the reason for the leap year in the modern calendar. The delay occurs because the length of the year is a little more than 365 days — closer to 365¼ days long. By taking some simple observations over a period of a few years, it is possible to measure the length of a year to surprising accuracy using this technique.

Solar calendars have been used throughout history. The ancient Babylonians thought the year had only 360 days, and made their calendar accordingly. The Islamic calendar is lunar, and is 11 (1/2) days different than the solar calendar. The Hebrew calendar is lunisolar.

Our modern calendar is handed down to us from the Ancient Roman civilization. The calendar took its first mature form as the Julian calendar, almost exactly the same as the one used today. It had 365 days in a year, with a 366-day leap year every four years. In the Julian calendar, years divisible by 4 — such as 1992, 1996, and 2008 — are leap years. This gave the Julian calendar an average of 365¼ days per year, which is very close to the true 365.2422 day length for a tropical year.

Although the drift of the Julian calendar is slow, the error in the calendar had accumulated enough by the sixteenth century that the Catholic Church became concerned about the drift's effect on the date of the celebration of Easter. The Italian chronologer Aloisius Lilius invented modifications to the Julian calendar to correct the difference. Pope Gregory XI instituted the new calendar, now named the Gregorian calendar, in the year 1582.

The Gregorian calendar was identical to the Julian calendar except that the leap year was skipped on years not divisible by 400. In the years 1600, 2000, and 2400, there would be a leap year in the Gregorian calendar, but not 1800, 1900, or 2100. This produced a year of average length 365.2425 days, much closer to the correct value than the Julian calendar. The Gregorian calendar accumulates only 3 days of error over 10,000 years.

General Astronomy
Daily Motions Yearly Motions Phases of the Moon

Discussion questions[edit]

1) On the date of the summer solstice, the sun is overhead on the Tropic of Cancer, and on the date of the winter solstice the sun is overhead on the Tropic of Capricorn. Draw a quick sketch that shows the relative positions of the sun and the earth on those dates.

2) On the date when the sun is overhead on the Tropic of Capricorn, the sun is actually located in the constellation of Sagittarius. So why did the Greeks name Tropic of Capricorn the Tropic of Capricorn instead of the Tropic of Sagittarius?