2.3: Earth

Mapping Earth and Sky

In order to create an accurate map, a mapmaker needs a way to uniquely and simply identify the location of all the major features on the map, such as cities or natural landmarks. Similarly, astronomical mapmakers need a way to uniquely and simply identify the location of stars, galaxies, and other celestial objects. On Earth maps, we divide the surface of Earth into a grid, and each location on that grid can easily be found using its latitude and longitude coordinate. Astronomers have a similar system for objects on the sky.

Locating Places on Earth

Let's begin by fixing our position on the surface of planet Earth. Earth's axis of rotation defines the locations of its North and South Poles and of its equator, halfway between. Two other directions are also defined by Earth's motions: east is the direction toward which Earth rotates, and west is its opposite. At almost any point on Earth, the four directions, north, south, east, and west, are well defined, despite the fact that our planet is round rather than flat. The only exceptions are at the North and South Poles, where the directions east and west are ambiguous because points exactly at the poles do not turn.

We can use these ideas to define a system of coordinates attached to our planet. Such a system, like the layout of streets and avenues in a city, helps us find where we are or want to go. Coordinates on a sphere, however, are a little more complicated than those on a flat surface. We must define circles on the sphere that play the same role as the rectangular grid that you see on city maps.

A great circle is any circle on the surface of a sphere whose center is at the center of the sphere. For example, Earth's equator is a great circle on Earth's surface, halfway between the North and South Poles. We can also imagine a series of great circles that pass through both the North and South Poles. Each of the circles is called a meridian. All meridians are perpendicular to the equator, crossing it at right angles. Any point on the surface of Earth will have a meridian passing through it. The meridian specifies the east-west location, or longitude, of the place. Longitude is defined as the number of degrees of arc along the equator between your meridian and the one passing through Greenwich, England, which has been designated as the Prime Meridian, defined as 0°.

Your latitude is the number of degrees of arc you are away from the equator along your meridian. Latitudes are measured either north or south of the equator from 0° to 90°. The latitude of the equator is 0°. As an example, the latitude of San Francisco is 38° N. The latitude of the South Pole is 90° S, and the latitude of the North Pole is 90° N. Figure \(\PageIndex{1}\) is a map of Earth with lines of latitude and longitude traced in white, including the equator and Prime Meridian. As an example, we can find the latitude and longitude of Washington, DC. To do so, we measure the distance west from the Prime Meridian, and north from the equator. Washington, DC's coordinates are 38° N and 77° W. If we wanted to find the capital of Madagascar, Antananarivo, we would measure east from the Prime Meridian and south from the equator to find it near 19° S and 47° E.

Figure \(\PageIndex{1}\) : Latitude and Longitude. This globe shows the grid of latitude and longitude lines used to pinpoint any location on Earth, such as Washington, DC, at 38° N and 77° W. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{1}\).

The Length of the Day

The length of the day is measured in terms of the rotation of Earth, but there is more than one way to define it. Usually, we think of it as the rotation period of Earth with respect to the Sun, called the solar day. After all, for most people sunrise is more important than the rising time of Arcturus or some other star, so we set our clocks to some version of Sun-time. However, astronomers also use a sidereal day, which is defined in terms of the rotation period of Earth with respect to the stars.

A solar day is slightly longer than a sidereal day because as demonstrated in Figure \(\PageIndex{2}\), Earth not only turns but also moves along its path around the Sun in a day. Suppose we start when Earth's orbital position is at day 1, with both the Sun and some distant star, located in the direction indicated by the long white arrow pointing left, directly in line with the zenith for the observer on Earth. When Earth has completed one rotation with respect to the distant star and is at day 2, the long arrow again points to the same distant star. However, notice that because of the movement of Earth along its orbit from day 1 to 2, the Sun has not yet reached a position above the observer. To complete a solar day, Earth must rotate an additional amount, equal to 1/365 of a full turn. The time required for this extra rotation is 1/365 of a day, or about 4 minutes, so the solar day is about 4 minutes longer than the sidereal day. Because our clocks are set to solar time, stars rise 4 minutes earlier each day. Astronomers prefer sidereal time for planning their observations because in that system, a star rises at the same time every day.

Figure \(\PageIndex{2}\) : Sidereal Day and Solar Day. This top-down view of Earth orbiting the Sun compares Earth's rotation relative to a distant star with its rotation relative to the Sun, showing why the solar day runs about four minutes longer than the sidereal day. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{2}\).

Locating Places in the Sky

Positions in the sky are measured in a way that is very similar to the way we measure positions on the surface of Earth. Instead of latitude and longitude, however, astronomers use coordinates called declination and right ascension. To denote positions of objects in the sky, it is often convenient to make use of the celestial sphere, the North and South celestial poles, and celestial equator, as points of reference. Declination on the celestial sphere is measured the same way that latitude is measured on the surface of Earth, from the celestial equator toward the north, in positive degrees, or south, in negative degrees. So Polaris, the star near the north celestial pole, has a declination of almost +90°.

Right ascension (RA) is like longitude, except that instead of Greenwich, the arbitrarily chosen point where we start counting is the vernal equinox, a point in the sky where the ecliptic, the Sun's path, crosses the celestial equator. RA can be expressed either in units of angle, or degrees, or in units of time. This is because the celestial sphere appears to turn around Earth once a day as our planet turns on its axis. Thus the 360° of RA that it takes to go once around the celestial sphere can just as well be set equal to 24 hours. Each 15° of arc is equal to 1 hour of time. For example, the approximate celestial coordinates of the bright star Capella are RA 5h or 75° and declination +50°.

The Turning Earth

Since the seventeenth century, it has been generally accepted that Earth turns on its axis, causing the rising and setting of Sun, Moon, and stars. In 1851 the French physicist Jean Foucault suspended a 60-meter pendulum, in Figure \(\PageIndex{3}\), with a mass of about 25 kilograms from the dome of the Pantheon in Paris and started the pendulum swinging evenly. If Earth had not been turning, there would have been no alteration of the pendulum's plane of oscillation, and so it would have continued tracing the same path. Yet after a few minutes Foucault could see that the pendulum's plane of motion was turning. Foucault explained that it was not the pendulum that was shifting, but rather Earth that was turning beneath it. You can now find such pendulums in many science centers and planetariums around the world.

Figure \(\PageIndex{3}\) : Foucault's Pendulum. As Earth rotates beneath this swinging pendulum, its plane of motion gradually shifts, knocking down the ring of targets around the platform in sequence over about 12 hours. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{3}\).