Motion of Celestial Bodies

All the celestial bodies have two types of motion: absolute and apparent. Apparent motion is important to navigators. Apparent motion is the motion of one celestial body as perceived by an observer on another moving celestial body. Since apparent motion is relative, it is essential to establish the reference point for that motion. For example, the apparent motion of Venus would be different if observed from the earth or the sun.

 

Apparent Motion

The earth’s rotation and revolution causes the apparent motion of the celestial bodies. Rotation causes celestial bodies to appear to rise in the east, climb to a maximum height, then set in the west. All bodies appear to move along a diurnal circle, approximately parallel to the plane of the equator.

The apparent effect of rotation varies with the observer’s latitude. At the equator, the bodies appear to rise and set perpendicular to the horizon. Each body is above the horizon for approximately 12 hours each day. At the North and South Poles, a different phenomenon occurs. The same group of stars is continually above the horizon; they neither rise nor set, but move on a plane parallel to the equator. This characteristic explains the periods of extended daylight, twilight, and darkness at higher latitudes. The remainder of the earth is a combination of these two extremes; some bodies rise and set, while others continually remain above the horizon.

The greater the northerly declination (Dec) of a body, the higher it appears in the sky to an observer at the North Pole. Polaris, with a Dec of almost 90°, appears overhead. Bodies with southern Dec are not visible from the North Pole.

A circumpolar body appears to revolve about the pole and never set. If the angular distance of the body from the elevated pole is less than the observer’s latitude, the body is circumpolar. For example, the Dec of Dubhe is 62° N. Therefore, it is located at an angle of 90°– 62° from the North Pole, or 28°. So, an observer located above 28° N views Dubhe as circumpolar. Although Figure 8-3 uses the North Pole, the same characteristics can be observed from the South Pole.

Figure 8-3. Some bodies are circumpolar.

Figure 8-3. Some bodies are circumpolar.

If the earth stopped rotating, the effect of the earth’s revolution on the apparent motion of celestial bodies would be obvious. The sun would appear to circle around the earth once each year. It would cover 360° in 365 days or move eastward at slightly less than 1 degree per day. The stars would move at the same rate. That is why different constellations are visible at different times of the year. Every evening, the same star appears to rise 4 minutes earlier.

 

After half a year, when the earth reached the opposite extreme of its orbit, its dark side would be turned in the opposite direction in space, facing a new field of stars. Hence, an observer at the equator would see an entirely different sky at midnight in June, than the one that appeared at midnight in December. In fact, the stars seen at midnight in June are those that were above the horizon at midday in December.

Figure 8-4. Seasonal changes of earth’s position.

Figure 8-4. Seasonal changes of earth’s position. [click image to enlarge]

Seasons

The annual variation of the sun’s declination and the consequent change of the seasons are caused by the revolution of the earth. [Figure 8-4] If the celestial equator coincided with the ecliptic, the sun would always be overhead at the equator, and its Dec would always be zero. However, the earth’s axis is inclined about 66.5° to the plane of the earth’s orbit, and the plane of the equator is inclined about 23.5°. Throughout the year, the axis points in the same direction. That is, the axis of the earth in one part of the orbit is parallel to the axis of the earth in any other part of the orbit. [Figure 8-5]

Figure 8-5. Ecliptic with solstices and equinoxes.

Figure 8-5. Ecliptic with solstices and equinoxes.

In June, the North Pole is inclined toward the sun so that the sun is at a maximum distance from the plane of the equator. About June 22, at the solstice, the sun has its greatest northern Dec.

The solstice brings the long days of summer, while in the Southern Hemisphere, the days are shortest. This is the beginning of summer for the Northern Hemisphere and of winter for the Southern Hemisphere. Six months later, the axis is still pointing in the same direction; but, since the earth is at the opposite side of its orbit and the sun, the North Pole is inclined away from the Sun. At the winter solstice, about December 21, the sun has its greatest southern Dec. Days are shortest in the Northern Hemisphere, and winter is beginning. Halfway between the two solstices, the axis of the earth is inclined neither toward nor away from the sun, and the sun is on the plane of the equator. These positions correspond to the beginning spring and fall.