# Math Tutorials and Moreby George

## Math Tutorials and Moreby George

### Movement of the Sun, Moon, Stars, and Planets

From early times man has had an interest in the objects he saw in the heavens. Great significance was often attached to the ways these objects seemed to move. In this section we will look at how the stars and planets appear to move as viewed from the earth. We have mentioned that each star follows a circular path across the sky that repeats about every 24 hours. However, the stars move together so that their relative positions remain unchanged. For this reason they are often referred to as the fixed stars. The star Polaris appears to be fixed to viewers in the northern hemisphere and there are polar stars that appear to be fixed to viewers in the Southern hemisphere Thus, the movement of the stars is exactly what would be expected if all the stars were located on a giant rotating sphere whose axis passes through Polaris and the southern polar stars and which makes a complete rotation every 24 hours. The fixed stars do not appear to change in brightness.

The Sun appears to follow a circular path each day, rising in the east and setting in the west. However, the sun's position relative to the fixed stars changes slightly each day (about 1° per day). This daily movement is in an eastward direction relative to the fixed stars and the sun completes a cycle through the stars in a year. The path of the sun through the fixed stars lies in a plane that is inclined about 23.5° to the plane of the equator. The sun passes through different constellations at different times of the year, and this is what gave rise to the signs of the zodiac. Of course, the position of the sun relative to the fixed stars can only be observed for a short time before sunrise and after sunset.

The moon, like the sun, moves daily relative to the fixed stars, but its motion is faster. Its path is inclined about 5° to that of the sun and it completes a cycle in about 27.3 days. However, since the sun has moved during the moon's cycle, it takes a short time for the moon to realign itself with the sun. Thus, the time between full moons is about 29.5 days. The phases of the moon are due to the fact that different portions of the illuminated half of the moon are visible to an observer on the earth when the moon is in different parts of its orbit.

There were five planets (not counting the sun and moon) that were known to ancient astronomers — Mercury, Venus, Mars, Jupiter, and Saturn. On any given night a planet (when it is visible) moves just like one of the fixed stars. You may have heard that stars flicker and planets don't. There is some truth in this, but it is difficult to identify planets on this basis alone. The main thing that distinguishes planets from stars is that on successive nights they, like the sun and moon, move slowly eastward relative to the fixed stars. The paths of the planets lie within 8° of the path of the sun; so they pass through the same constellations. Each of the planets at certain times exhibits retrograde motion in which it stops and moves for a while in the reverse direction before stopping again and then resuming its eastward motion. The planets Mercury and Venus never appear very far from the sun. Mercury is always within 28° of the sun and Venus is always within 46° of the sun. Thus, Mercury and Venus are only visible in the hours just before sunrise and the hours just after sunset. As the sun makes its yearly journey, Mercury and Venus move back and forth across the sun. Unlike the stars, the planets do change brightness. They are brightest during their retrograde motion. This complicated movement of the planets is what makes modeling their movement versus time difficult.