4.1 Earth and Sky

Earth's coordinate system and celestial coordinates are the tools we use to pinpoint locations on our planet and in the night sky. On Earth, we rely on latitude and longitude. In the sky, we use right ascension and declination. Both systems work on the same basic principle: two numbers that specify a unique position.

These coordinate systems also help explain what you actually see when you look up. Because Earth is constantly spinning, stars appear to drift across the sky, some objects never set below the horizon, and different parts of the sky become visible at different times of night and year.

Earth's Coordinate System

Latitude and Longitude on Earth

Think of Earth wrapped in a grid. Latitude tells you how far north or south you are from the equator, while longitude tells you how far east or west you are from a reference line called the prime meridian.

• Latitude measures angular distance north or south of the equator
  • Ranges from 0° at the equator to 90° at the poles
  • Northern Hemisphere: 0° to 90° N
  • Southern Hemisphere: 0° to 90° S
• Longitude measures angular distance east or west of the prime meridian
  • Ranges from 0° to 180° E or 0° to 180° W
  • The prime meridian (0° longitude) passes through Greenwich, England
  • 180° longitude roughly corresponds to the International Date Line

Combining the two gives you a unique coordinate pair for any spot on Earth's surface. New York City, for example, sits at about 40° N, 74° W. This is the same principle behind GPS navigation.

Celestial Coordinate System

Right Ascension and Declination in the Sky

To map the sky, astronomers imagine a giant celestial sphere surrounding Earth, with all the stars and other objects projected onto its inner surface. This sphere has its own equator and poles, which are just Earth's equator and poles extended outward into space.

• The celestial equator is the projection of Earth's equator onto the celestial sphere
• The celestial poles are the projections of Earth's North and South Poles (Polaris, the North Star, sits very close to the celestial north pole)

The two coordinates that locate objects on this sphere mirror how latitude and longitude work on Earth:

• Declination ($\delta$) measures angular distance north or south of the celestial equator
  • Ranges from +90° (celestial north pole) to -90° (celestial south pole)
  • Polaris has a declination of about +89°, since it's nearly at the north celestial pole
  • The stars of the Southern Cross sit around $\delta$ ≈ -60°
• Right ascension ($\alpha$) measures angular distance eastward along the celestial equator from a reference point called the vernal equinox
  • Instead of degrees, right ascension uses hours, ranging from 0h to 24h (since the sky completes a full circle in about 24 hours)
  • The vernal equinox (0h) is the point where the Sun crosses the celestial equator heading northward in March
  • For reference: Orion is near $\alpha$ ≈ 5h, and Ursa Major is near $\alpha$ ≈ 11h

Together, these two values pinpoint any object on the celestial sphere. Sirius, the brightest star in the night sky, is located at $\alpha$ = 6h 45m, $\delta$ = -16° 43'.

Celestial Motion vs. Earth's Rotation

Earth rotates from west to east around its axis once every 24 hours. This rotation is why celestial objects appear to rise in the east, arc across the sky, and set in the west. The objects aren't actually moving that way; it's Earth spinning underneath them.

A few key concepts follow from this:

• Circumpolar objects are stars close enough to a celestial pole that they never dip below the horizon from your location. They appear to trace circles around the pole all night long. Ursa Minor (the Little Dipper) is circumpolar for most Northern Hemisphere observers. How many stars are circumpolar for you depends on your latitude: observers closer to the poles see more circumpolar stars, while observers near the equator see almost none.
• The zenith is the point on the celestial sphere directly above you. It changes depending on where you are on Earth and what time it is.
• The meridian is an imaginary line arching from the north celestial pole through your zenith to the south celestial pole. When an object crosses the meridian, it reaches its highest point in the sky, called culmination. The meridian also divides the sky into eastern and western halves.

Horizon Coordinate System

The horizon system describes where objects appear relative to your local sky, rather than on the celestial sphere as a whole.

• Azimuth measures angular distance along the horizon starting from due north and increasing clockwise (north = 0°, east = 90°, south = 180°, west = 270°)
• Altitude measures angular distance above the horizon (0° at the horizon, 90° at the zenith)

This system is intuitive for pointing out objects in real time, but the coordinates change constantly as Earth rotates and as you move to a different location.

Earth's Motions and Time

Earth's rotation gives us two slightly different definitions of a "day":

• A sidereal day is the time for Earth to complete one full rotation relative to the distant stars: approximately 23 hours and 56 minutes. After one sidereal day, the same stars return to the same positions in your sky.
• A solar day is the time between two consecutive solar noons (when the Sun is highest): 24 hours. It's about 4 minutes longer than a sidereal day because Earth has also moved a little along its orbit, so it needs to rotate slightly extra for the Sun to return to the same position.

One more slow motion to know: precession. Earth's rotational axis doesn't point in a fixed direction forever. Instead, it traces out a slow circle in space, like a wobbling top. One full cycle takes about 26,000 years. This means the "North Star" gradually changes over millennia. Right now it's Polaris, but thousands of years ago it was a different star, and thousands of years from now it will be again.

Historical Models of the Universe

• Ptolemy (2nd century CE) proposed a geocentric model with Earth at the center. Planets and the Sun orbited Earth, and the model used complex circular motions called epicycles to account for observed planetary movements.
• Copernicus (16th century) introduced a heliocentric model placing the Sun at the center of the solar system. This simpler arrangement better explained planetary motions and marked a major turning point in astronomy.