2.4: The Sun

The Path of the Sun

We define the day by the presence of the Sun in the sky, and the night by its absence. But, how often do we consider its path through the sky? Before people had portable ways to tell the time, the Sun was used to separate the day into morning, noon, and evening. The Sun's path subtly changes in declination, or how high it is in the sky, every day throughout the year, unless you live at the equator. Let's explore the path of the Sun in the sky, how it changes, and how it affects the Earth.

Rising and Setting of the Sun

We described the movement of stars in the night sky, but what about during the daytime? The stars continue to circle during the day, but the brilliance of the Sun makes them difficult to see. On any given day, we can think of the Sun as being located at some position on the hypothetical celestial sphere. For thousands of years, astronomers have been aware that the Sun does more than just rise and set. It changes position gradually on the celestial sphere, moving each day about 1° to the east relative to the stars. The path the Sun appears to take around the celestial sphere each year is called the ecliptic. Every day the Sun rises about 4 minutes later relative to the stars, the same time difference between the sidereal and solar day.

As the months go by and we look at the Sun from different places in our orbit, we see it projected against different places in our orbit. If we could see the stars during the day, we would see the Sun in front of different stars in the background in Figure \(\PageIndex{1}\). In practice, we must determine which stars lie behind and beyond the Sun by observing the stars visible in the opposite direction at night. For example, in June, the highest constellation in the sky at midnight would be either Ophiucus or Scorpius, which would mean that the Sun was in front of Taurus. In August, we would see part of Sagittarius, indicating that the Sun was in between us and Cancer. After a year, when Earth has completed one trip around the Sun, the Sun will appear to have completed one circuit of the sky along the ecliptic. The belt of constellations that the Sun passes through over the year is called the zodiac. Table \(\PageIndex{1}\) has a list of the constellations in the zodiac and the dates when the Sun passes in front of them. Note that these dates are different than astrological tables because the orientation of Earth's spin axis has shifted a bit, changing the timing of the zodiac since the original tables were made thousands of years ago.

Figure \(\PageIndex{1}\) : Constellations on the Ecliptic. As Earth orbits the Sun each year, the Sun appears to move along the ecliptic through the zodiac constellations, sitting in front of a different constellation each month, such as Taurus in June and Cancer in August. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{1}\).

Table \(\PageIndex{1}\): Constellations on the Ecliptic

Constellation on the Ecliptic	Dates When the Sun Crosses It
Capricornus	January 21-February 16
Aquarius	February 16-March 11
Pisces	March 11-April 18
Aries	April 18-May 13
Taurus	May 13-June 22
Gemini	June 22-July 21
Cancer	July 21-August 10
Leo	August 10-September 16
Virgo	September 16-October 31
Libra	October 31-November 23
Scorpius	November 23-November 29
Ophiuchus	November 29-December 18
Sagittarius	December 18-January 21

The ecliptic does not lie along the celestial equator but is inclined to it at an angle of about 23.5°. In other words, the Sun's annual path in the sky is not linked with Earth's equator. This is because our planet's axis of rotation is tilted by about 23.5° from a vertical line sticking out of the plane of the ecliptic Figure \(\PageIndex{2}\). The inclination of the ecliptic is the reason the Sun moves north and south in the sky as the seasons change. As a result, people in the Northern Hemisphere see the Sun north of the celestial equator and high in our sky in June, and south of the celestial equator and low in the sky in December.

Figure \(\PageIndex{2}\) : The Celestial Tilt. Earth's rotation axis is tilted 23.5° from the line perpendicular to the ecliptic, which tilts the celestial equator by the same amount relative to the ecliptic and causes the Sun to appear north or south of the celestial equator at different times of year. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{2}\).

The Seasons

Except for those living at the equator, people experience changes in temperature throughout the year. The difference between seasons gets more pronounced the farther north or south from the equator we travel, and the seasons in the Southern Hemisphere are the opposite of what we find on the northern half of Earth. With these observed facts in mind, let us ask what causes the seasons.

Many people have believed that the seasons were the result of the changing distance between Earth and the Sun. If true, it should be colder when Earth is farther from the Sun, and hotter when the Earth is closer. Although Earth's orbit around the Sun is an ellipse, its distance from the Sun varies by only about 3%. That's not enough to cause significant variations in the Sun's heating. Also, Earth is actually closest to the Sun in January, when the Northern Hemisphere is in the middle of winter. Also, the two hemispheres have opposite seasons. If distance was the primary cause of the seasons then the entire Earth would experience the same season at the same time. The seasons are actually caused by the 23.5° tilt of Earth's axis.

The Seasons and Sunshine

Figure \(\PageIndex{3}\) is Earth's annual path around the Sun, with Earth's axis tilted by 23.5°. Note that our axis continues to point the same direction in the sky throughout the year. In June, the Northern Hemisphere is pointed towards the Sun and is more directly illuminated. In December, the situation is reversed: the Southern Hemisphere is pointed at the Sun, and the Northern Hemisphere is tipped away from the Sun. In September and March, the two hemispheres receive equal amounts of sunshine.

Figure \(\PageIndex{3}\) : Seasons. As Earth orbits the Sun with its axis tilted 23.5° and pointing in a fixed direction in space, the Northern Hemisphere tips toward the Sun at the summer solstice and away from it at the winter solstice, producing the seasons. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{3}\).

How does the Sun's pointing at one hemisphere translate into making it warmer for us down on the surface of Earth? There are two effects we need to consider. When we point at the Sun, sunlight hits us at a more direct angle and is more effective at heating Earth's surface (Figure \(\PageIndex{4}\)). You can get a similar effect by shining a flashlight onto a wall. If you shine the flashlight straight on, you get an intense spot of light on the wall. But if you hold the flashlight at an angle, then the spot of light is more spread out. In the Northern Hemisphere, sunlight in June is more direct and intense and more effective at heating.

Figure \(\PageIndex{4}\) : Direct Sunlight. Sunlight strikes the ground more directly in summer (a), concentrating the same amount of light over a smaller area, while in winter (b) the same sunlight spreads over a much larger area and heats the ground less effectively. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{4}\).

The second effect has to do with the length of time the Sun spends above the horizon (Figure \(\PageIndex{5}\)). Even if you've never thought about astronomy before, we're sure you have observed that the hours of daylight increase in summer and decrease in winter. Let's see why this happens.

An equivalent way to look at our path around the Sun each year is to pretend that the Sun moves around Earth, on a circle called the ecliptic. Because Earth's axis is tilted, the ecliptic is tilted by about 23.5° relative to the celestial equator. As a result, where we see the Sun in the sky changes as the year passes. Figure \(\PageIndex{5}\) demonstrates the path of the Sun at different times of the year as seen from the Northern Hemisphere. On June 21, the Sun rises north of east and sets north of west. For observers in the Northern Hemisphere of Earth, the Sun spends about 15 hours above the horizon in the United States, meaning more hours of daylight. On December 21, the Sun rises south of east and sets south of west. It spends 9 hours above the horizon in the United States, which means fewer hours of daylight and more hours of night in northern lands. On March 21 and September 21, the Sun spends equal amounts of time above and below the horizon in both hemispheres.

Figure \(\PageIndex{5}\) : Seasonal Paths of the Sun. The Sun's daily path lies north of the celestial equator around the June solstice, on the celestial equator at the equinoxes, and south of the celestial equator around the December solstice, changing how many hours it spends above the horizon each day. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{5}\).

Let's look at what the Sun's illumination on Earth looks like at some specific dates of the year, when these effects are at their maximum. In the Northern Hemisphere the summer solstice is on, or close to, June 21. During the summer solstice, the Sun shines down directly upon the Northern Hemisphere of Earth. It appears about 23° north of the equator, and passes through the zenith of places on Earth that are at 23° N latitude. The situation is shown in detail in Figure \(\PageIndex{6}\). To a person at 23° N, the Sun is directly overhead at noon. This latitude, where the Sun can appear at the zenith at noon on the summer solstice, is called the Tropic of Cancer.

We also see in Figure \(\PageIndex{6}\) that the Sun's rays shine down all around the North Pole at the solstice. As Earth turns on its axis, the North Pole is continuously illuminated by the Sun. All places within 23° of the pole have sunshine for 24 hours. The Sun is as far north on this date as it can get; thus, 67° N is the southernmost latitude where the Sun can be seen for a full 24-hour period. This region is sometimes called the land of the midnight Sun. That circle of latitude is called the Arctic Circle. Note that as Earth turns on its axis the North Pole is in constant sunlight while the South Pole is veiled in 24 hours of darkness. Everywhere within 23° of the South Pole is called the Antarctic Circle. The Sun is at the zenith for observers on the Tropic of Cancer.

Figure \(\PageIndex{6}\) : Earth on June 21. At the June solstice, sunlight illuminates the Northern Hemisphere most directly, keeping the region within 23° of the North Pole in continuous daylight while the same area around the South Pole remains dark. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{6}\).

The situation is reversed 6 months later, around December 21. The winter solstice in the Northern Hemisphere is in Figure \(\PageIndex{7}\). Now it is the Arctic Circle that has the 24-hour night and the Antarctic Circle that has the midnight Sun. At latitude 23° S, called the Tropic of Capricorn, the Sun passes through the zenith at noon. Days are longer in the Southern Hemisphere summer and shorter in the north. In the Northern Hemisphere, it is winter and at higher latitudes, there may be only 9 or 10 hours of sunshine during the day.

Figure \(\PageIndex{7}\) : Earth on December 21. At the December solstice, sunlight illuminates the Southern Hemisphere most directly, keeping the region within 23° of the South Pole in continuous daylight while the same area around the North Pole remains dark. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{7}\).

Halfway between the solstices, near March 21 and September 21, the Sun is on the celestial equator. From Earth, it appears above our planet's equator and shines equally on both hemispheres. Every place on Earth then receives roughly 12 hours of sunshine and 12 hours of night. The points where the Sun crosses the celestial equator are called the vernal, for spring, and autumnal, for fall equinoxes. The dates indicated for the solstices and equinoxes are approximate. Depending on the year, they may occur a day or two earlier or later.

The Seasons at Different Latitudes

The seasonal effects are different at different latitudes on Earth. Near the equator, the temperature variation throughout the year is not as extreme as it is at higher latitudes. Every day of the year, the Sun is up half the time, so there are approximately 12 hours of sunshine and 12 hours of night. Local residents define the seasons by weather patterns, such as wet and dry seasons, rather than by the amount of sunlight. As we travel north or south, the seasons become more pronounced, until we reach extreme cases in the Arctic and Antarctic.

At the North Pole, all celestial objects that are north of the celestial equator are always above the horizon and, as Earth turns, circle around parallel to it. The Sun is north of the celestial equator from about March 21 to September 21, so at the North Pole, the Sun rises when it reaches the vernal equinox and sets when it reaches the autumnal equinox. Each year there are 6 months of sunshine at each pole, followed by 6 months of darkness.

Clarifications about the Real World

In our discussions so far, we have been describing the rising and setting of the Sun and stars as they would appear if Earth had little or no atmosphere. In reality, the atmosphere allows us to see a little way “over the horizon.” This effect is a result of refraction, the bending of light passing through air or water. Because of this atmospheric refraction, the Sun appears to rise earlier and to set later than it would if no atmosphere were present. Also, the atmosphere scatters light and provides some twilight illumination even when the Sun is below the horizon. Astronomers define morning twilight as beginning when the Sun is 18° below the horizon, and evening twilight extends until the Sun sinks more than 18° below the horizon.

These atmospheric effects require small corrections in many of our statements about the seasons. At the equinoxes, for example, the Sun appears to be above the horizon for a few minutes longer than 12 hours, and below the horizon for fewer than 12 hours. These effects are most dramatic at Earth's poles, where the Sun actually can be seen more than a week before it reaches the celestial equator.

The summer solstice is not the warmest day of the year, even if it is the longest. The hottest months are the months after the summer solstice. This is because weather involves the air and water covering Earth's surface, and these large reservoirs do not heat up instantaneously. You have probably observed this effect for yourself. For example, a pond does not get warm the moment the Sun rises but is warmest late in the afternoon, after it has had time to absorb the Sun's heat. In the same way, Earth gets warmer after it has had a chance to absorb the extra sunlight that is the Sun's summer gift to us. The coldest times of winter are a month or more after the winter solstice.

Examples and Exercises

Example: Rising Stars

The Sun makes a complete circle in the sky approximately every 24 hours, while the stars make a complete circle in the sky in 4 minutes less time, or 23 hours and 56 minutes. This causes the positions of the stars at a given time of day or night to change slightly each day. Since stars rise 4 minutes earlier each day, that works out to about 2 hours per month \((4 \text{ minutes} \times 30 = 120 \text{ minutes or } 2 \text{ hours})\). So, if a particular constellation rises at sunset during the winter, you can be sure that by the summer, it will rise about 12 hours earlier, with the sunrise, and it will not be so easily visible in the night sky. Let's say that tonight the bright star Sirius rises at 7:00 p.m. from a given location so that by midnight, it is very high in the sky. At what time will Sirius rise in three months?

Solution

In three months' time, Sirius will be rising earlier by:

\[90 \text{ days} \times \frac{4 \text{ minutes}}{\text{day}} = \text{360 minutes or 6 hours} \nonumber\]

It will rise at about 1:00 p.m. and be high in the sky at around sunset instead of midnight. Sirius is the brightest star in the constellation of Canis Major (the big dog). So, some other constellation will be prominently visible high in the sky at this later date.

Exercise: Rising Stars

If a star rises at 8:30 p.m. tonight, approximately what time will it rise two months from now?

Answer

 

In two months, the star will rise: \(60 \text{ days} \times \frac{4 \text{ minutes}}{\text{day}} = \text{240 minutes or 4 hours earlier.}\) This means it will rise at 4:30 p.m.

Example: Axial Tilt

In Figure \(\PageIndex{7}\), the Tropic of Cancer is the latitude for which the Sun is directly overhead on the summer solstice. At this time, the Sun is at a declination of 23° N of the celestial equator, and the corresponding latitude on Earth is 23° N of the equator. If Earth were tilted a bit less, then the Tropic of Cancer would be at a lower latitude, closer to the equator.

The Arctic Circle marks the southernmost latitude for which the day length is 24 hours on the day of the summer solstice. This is located at 90° - 23° = 67° N of Earth's equator. If Earth were tilted a bit less, then the Arctic Circle would move farther North. In the limit at which Earth is not tilted at all, its spin axis is perpendicular to the ecliptic, the Tropic of Cancer would be right on Earth's equator, and the Arctic Circle would simply be the North Pole. Suppose the tilt of Earth's axis were tilted only 5°. What would be the effect on the seasons and the locations of the Tropic of Cancer and Arctic Circle?

Solution

If Earth were tilted less, the seasons would be less extreme. The variation in day length and direct sunlight would be very small over the course of a year, and the Sun's daily path in the sky would not vary much. If Earth were tilted by 5°, the Sun's position on the day of the summer solstice would be 5° N of the celestial equator, so the Tropic of Cancer would be at the corresponding latitude on Earth of 5° N of the Equator. The Arctic Circle would be located at 90° - 5° = 85° N of the equator.

Exercise: Axial Tilt

Suppose the tilt of Earth's axis were 16°. What, then, would be the difference in latitude between the Arctic Circle and the Tropic of Cancer? What would be the effect on the seasons compared with that produced by the actual tilt of 23°?

Answer

 

The Tropic of Cancer is at a latitude equal to Earth's tilt, so in this case, it would be at 16° N latitude. The Arctic Circle is at a latitude equal to 90° minus Earth's tilt, or 90° - 16° = 74°. The difference between these two latitudes is 74° - 16° = 58°. Since the tilt of Earth is less, there would be less variation in the tilt of Earth and less variation in the Sun's paths throughout the year, so there would be milder seasonal changes.

Example: The Position of the Sun in the Sky

The Sun's coordinates on the celestial sphere range from a declination of 23° N of the celestial equator, or +23°, to a declination 23° S of the celestial equator, or -23°. So, the Sun's altitude at noon, when it crosses the meridian, varies by a total of 46°. What is the altitude of the Sun at noon on March 21, as seen from a place on Earth's equator? What is its altitude on June 21, as seen from a place on Earth's equator?

Solution

On Earth's equator, the celestial equator passes through the zenith. On March 21, the Sun is crossing the celestial equator, so it should be found at the zenith (90°) at noon. On June 21, the Sun is 23° N of the celestial equator, so it will be 23° away from the zenith at noon. The altitude above the horizon will be 23° less than the altitude of the zenith (90°), so it is 90° - 23° = 67° above the horizon.

Exercise: The Position of the Sun in the Sky

What is the altitude of the Sun at noon on December 21, as seen from a place on the Tropic of Cancer?

Answer

 

On the day of the winter solstice, the Sun is located about 23° S of the celestial equator. From the Tropic of Cancer, a latitude of 23° N, the zenith would be a declination of 23° N. The difference in declination between zenith and the position of the Sun is 46°, so the Sun would be 46° away from the zenith. That means it would be at an altitude of 90° - 46° = 44°.

Further Exploration

• The Motions of the Sun Simulator from Columbia University's Center for Teaching and Learning provides a demonstration of the Sun's apparent motion in the sky as the Earth rotates each day, and its changing altitude with latitude and time of year.