Natural Science - Year I

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Science Web Assignment for Unit 5

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# Unit 5: Naked-Eye Astronomical Observations of the Planets

##### For Class
• Topic area: Astronomy: Naked eye observations
• Terms and concepts to know: Planets, stars, constellations, coordinate systems, conjunction, opposition
• See historical period(s): Babylon and Egypt

## Naked Eye Astronomy: Daily Motions

#### Coordinate systems

The earliest coordinate system is the natural one bounded by the horizon. We count around from the north pole (blue curve, azimuth) and up from the horizon (red curve, altitude). We can share these coordinates with anyone near us, but someone observing at a later time, or from a different position on the Earth's surface, won't be able to use our coordinates to find the same star.

In order to keep track of the positions of stars, we use a coordinate system similar to the latitude-longitude system used for earth. Imagine all the stars in the sky on a sphere--for tracking position purposes, we don't need to know the distance to the object. Now take the earth's equator and extended it out to the sphere; extend the earth's poles out to the sphere. Because of the earth's rotation on its axis, the celestial sphere appears to rotate on the same axis.

Think of yourself as an observer on the earth's surface. Your position has a specific latitude--that is the measure of your position north or south of earth's equator--let's say north, to make this simpler. The point on the celestial sphere directly overhead is your zenith. It is as far north of the celestial equator as you are north of the earth's equator. If you are at the equator, your latitude is zero and directly above you is the celestial equator (0 degrees) and the north celestial pole is on your horizon. If you are at the north pole, the celestial equator is on your horizon, and the pole star (90 degrees north) is directly overhead at your zenith.

Most of the time, though, you are in between the equator and the north pole. You can figure out where from the pole height, the angle between the north pole star and your north horizon. The angle between the celestial north pole and the north horizon is the same as the angle between the zenith and the celestial equator (your latitude). So your latitude and pole height are the same.

A star on the sky has an angle called the declination of the star above or below the celestial equator. The units of declination are degrees, and there is ninety degrees between the equator and the north celestial pole, just as there are ninety degrees between the earth's equator and its north pole. A star halfway between the celestial equator and the north pole thus has a 45 degree north declination.

It also has a position along the celestial equator like the longitude on earth. We measure the longitude by counting east or west from Greenwich, England. We need a starting point in the sky, though, and the one that astronomers use is the point where the sun's path (the ecliptic) crosses the celesital equator with the sun moving into the northern hemisphere.

This is the vernal (spring) equinox point. We count eastward, the direction the sun moves against the background stars along the equator to get the Right Ascension of the star. Right Ascension units are in hours; there are 24 hours going all the way around the celestial equator counting left from the vernal equinox. In the diagram, the star is about 1/3 of the way around the sphere, so its RA should be about 8 hours. Using Right Ascension and declination, we can identify the location of all the stars in the sky as seen from earth, and the changing position of the planets.

#### Planetary Motion

All of the planets lie in a flat disk around the sun, so from earth, they also appear to move along the ecliptic, although they are sometimes above or below it. But the planets do not move continuously eastward. Instead, all the planets show periodic retrograde motion, where they stop, move backwards (west and to the right when facing south), and then stop again before moving eastward. This loop-the-loop motion is caused by the combination of the planet's own motion and the earth's motion.

For example, as the earth moves around the sun, it overtakes the slower moving outer planet Mars. As it passes Mars, that planet appears to move backwards. Then as earth gets further from Mars, Mars appears to resume its normal motion. In fact, Mars is always moving in the same direction—it is earth's changing perspective that makes it look like Mars goes backwards.

The ancient astronomers of Egypt and Mesopotamia were able to note this odd behavior. The points when the planets appear to stop and change direction are the stationary points of their orbits. As we see in the history section, these were worth noting as ways to date events.

The key points then of a planet's motion were:

• Prograde motion: the normal motion of the planet eastward against the background of the Zodiac constellations.
• Stations: the periods when the planet appeared to stop moving altogether, as it changed direction from prograde to retrograde motion (or from retrograde to prograde).
• Retrograde motion: the temporary westward motion of the planet
• Solar Conjunction: the point at which the planet was in the same part of the sky as the sun, and rose and set with the sun (and was thus very hard to observe). At solar conjunction, a planet is overhead at noon, just like the sun. Planets could also be in conjunction with each other.
• Opposition: the period when the planet was on the opposite side of the sky from the sun, and was overhead at midnight.

The movie below shows predicted positions of Mars every 6 hours between April 1 and December 16, 2018 as seen from Earth against the background sky. The yellow line marks the plane of the ecliptic. What do you notice about the "path" of Mars in the sky?

Another easily observed phenomena is the limited motion of Mercury and Venus, which never get very far from the sun's position in the sky. According to our heliocentric model, this is because they go around the sun, so as seen from earth, they just go back and forth as the sun moves across the sky (think of a pendulum in a moving platform). Mercury and Venus can be on the far side of the sun, and they can be between the sun and us. Both of these points are solar conjunction (Copernicus will distinguish between superior or far side of the sun, and inferior or near side of the sun conjuntions). However, Venus and Mercury can never be in opposition on the far side of earth from the sun.

The other planets go around the sun but further out than the earth, so sometimes they are behind the sun, and sometimes on the far side of the earth from the sun (at "opposition"), but they can never be between the earth and the sun.

You may begin to see why the early astronomers, assuming that the earth stood still in space, had a great problem in explaining this irregular motion of the planets.

### Study/Discussion Questions

• Why do the planets appear to change direction when observed from earth over long periods of time?
• How do the rates of planetary motion depend on the distance from the sun?

### Further Study On your Own (Optional)

• Nick Strobel has published a very thorough discussion of many aspects of naked-eye astronomy at the Astronomy Notes site.