Planetary Phases and Retrograde Motion

The planets Mercury and Venus, closer to the Sun than the Earth, are called the inferior planets while planets farther from the Sun than the Earth are termed the superior planets (Mars, Jupiter, and so on). Viewed from the Earth, all planets go through phases as they revolve about the Sun. However, the inferior planets exhibit phases different from the superior planets. Inferior planets go through the same phases as the Moon (Figure 8.1), but the superior planets show only two phases (Figures 8.2), namely, full and gibbous.

Figure 8.1 Inferior Planet Phases

The labeled positions are called Aspects.

When an inferior planet is between the Earth and the Sun, its phase is new and it is said to be at inferior conjunction. The planet isn’t visible at this time because of its new phase. Usually an inferior planet will pass above or below the Sun because its orbital plane is inclined to the ecliptic plane. But Mercury and Venus sometimes pass directly between the Earth and Sun at inferior conjunction. With a telescope one can see the dark disk of the planet silhouetted against the Sun. This is not an eclipse but an event called a transit. When an inferior planet is on the other side of the Sun, it is at superior conjunction and has a full phase. However the planet won’t be visible at this time because it is near or even behind the Sun.

As a planet orbits the Sun, the angle between it and the Sun changes. The angle between the Sun and planet is called the angle of elongation. This angle is greatest when an inferior planet is at either maximum western elongation (first quarter) or at maximum eastern elongation (third quarter). The maximum angles of elongation are about 28 degrees for Mercury and 48 degrees for Venus. So these planets are never seen very far from the Sun.

Figure 8.2 Superior Planet Phases

Looking south, a planet at eastern elongation would be to the left of the Sun while at western elongation it would appear to the right of the Sun. An inferior planet east (left) of the Sun rises after the Sun and sets after the Sun. Because it is visible in the evening sky around sunset, it is sometimes referred to as an evening "star." If the planet is west (right) of the Sun, it rises before the Sun and being visible in the morning is often called a morning "star."

Usually planets move eastward through the Zodiac, but from time to time they change their direction of motion and move westward. This westward motion is known as retrograde motion. Inferior planets retrograde near inferior conjunction.

At opposition, the phase of a superior planet such as Mars is full. It is on the opposite side of the Earth from the Sun. This means that wherever the Sun is in the sky, the planet will be 180 degrees away. For example, if the Sun is setting, the planet will be rising. A superior planet retrogrades when it is near opposition. This happens for Mars every 2.1 years and for the other outer planets about every year. Because the planet is closest to the Earth, at opposition, it is at its brightest. So at opposition superior planets rise about sunset, are at their brightest, and are retrograding.

At western quadrature and eastern quadrature, a superior planet is 90 degree west or east of the Sun, respectively, and exhibits a gibbous phase. The phase at conjunction is full, but the planet isn’t visible because it is close to or behind the Sun.

Copernicus pointed out in the fifteenth century that one can define two periods of revolution for each planet. The actual period he called the sidereal period, the other he referred to as the synodic period. This latter period is what can be observed from the Earth, and it is affected by the Earth’s motion as well as the planet’s motion. For an inferior planet the synodic period can be defined as the time between two inferior conjunctions and for a superior planet, as the time between two oppositions.

The Morning and Evening "Stars"

The planets Mercury and Venus, closer to the Sun than the Earth, are called the inferior planets. Recall that inferior planets (Figure 8.3) go through the same phases as the Moon.

Figure 8.3 Inferior Planet Phases

As an inferior planet orbits the Sun, the angle between it and the Sun changes. The angle between the Sun and planet is called the angle of elongation. This angle is greatest when an inferior planet is at either maximum western elongation (first quarter) or at maximum eastern elongation (third quarter). The maximum angles of elongation are about 28 degrees for Mercury and 48 degrees for Venus. So these planets are never seen very far from the Sun.

Looking south, a planet at eastern elongation would be to the left of the Sun while at western elongation it would appear to the right of the Sun. An inferior planet east (left) of the Sun rises after the Sun and sets after the Sun. Because it is visible in the evening sky around sunset it is sometimes referred to as an evening "star." If the planet is west (right) of the Sun it rises before the Sun, and being visible in the morning is often called a morning "star."

Retrograde Motion

Recall that in previous projects you’ve learned that Mercury and Venus, the inferior planets, go through the same phases as the Moon while the superior planets, such as Mars, exhibit only the full and gibbous phase.

Although ancient astronomers could not see the phases of the planets, they closely followed their changing positions. By the time of the Babylonians it was known that planets do not always move eastward through the Zodiac but from time to time back up and move westward. This westward motion is called retrograde motion. Inferior planets retrograde around inferior conjunction while superior planets retrograde near opposition (see Figures 8.1 and 8.2).

The Geocentric Theory

Ancient astronomers could account for not only retrograde motion but the related fact that planets seemed brightest when they were retrograding. One early explanation was suggested by the Alexandrian mathematician Apollonius and later refined by the great Greek astronomer Claudius Ptolemy. The Ptolemaic theory was very clever and quite complex.

Like most early theories, Ptolemy’s was a geocentric theory in which the Earth, at the center of the universe, neither rotated nor revolved. Each planet moved around a small circle called an epicycle as the center of the epicycle revolved around a larger circle, the deferent, centered on the Earth. This combination of circular motions caused a planet to move in a path such as that shown in Figure 8.4.

Notice that usually the planet is moving eastward around the Earth but from time to time its direction of motion reverses and it moves westward. During this retrograde motion, it is closest to the Earth and is therefore brightest.

Figure 8.4 Retrograde Motion in the Ptolemaic System

This brilliant theory survived for centuries. During this time it was revised, becoming ever more complex, but also more accurate. Although it seemed to explain all of the observed planetary motions, it was, of course, incorrect. The Earth is not at the center of the solar system and there are no epicycles and deferents.

The Heliocentric Theory

The Ptolemaic system was eventually replaced by a simpler and more accurate explanation: the heliocentric theory. One of the first advocates of this theory was the Greek astronomer Aristarchus. It was not, however, until Copernicus revived this idea in the fifteenth century that it began to receive the attention it deserved. But the first accurate statement of how planets actually move was made by the German astronomer Johannes Kepler. Between 1609 and 1618 Kepler, using the observations of the Danish astronomer Tycho Brahe, discovered three laws that describe planetary motions (see Chapter 1).

In the modern heliocentric theory, planets revolve around the Sun in elliptical orbits with periods of revolution that increase with increasing distance from the Sun. Mercury takes only 88 days to move about the Sun while the most distant planet, Pluto, takes some 247 years. It is this relationship between period and distance that results in the retrograde motion of planets (Figure 8.5).

Figure 8.5 Retrograde Motion in the Heliocentric Theory

Because the Earth moves faster than any of the superior planets, it overtakes and passes these planets at regular intervals. This occurs when the planet is at opposition (position 3 in Figure 18.2). At opposition, the Earth and planet are relatively close together and the planet, therefore, appears brighter than at any other time. As the Earth passes the planet, the planet seems to back up, just as a car that you speed by on an expressway seems momentarily to be going backwards. Thus, superior planets retrograde and appear brightest when they are near opposition. At this time they are also in a full phase and rise about sunset. This happens every 2.1 years for Mars and about every year for the other superior planets.

The time between oppositions is known as the synodic period. The synodic period of Mars is 779.9 days or 2.1 years, but for more distant planets the synodic period is smaller, approaching 1 year for the most distant planets. Jupiter, for example, is at opposition every 398.9 days while Pluto is at opposition every 366.7 days.

The inferior planets, Mercury and Venus, also retrograde and vary in brightness. However, for these two planets the retrograde motion occurs when they overtake and pass the slower moving Earth near inferior conjunction. The synodic period for the inferior planets, defined as the time between two inferior conjunctions, is 115.9 days for Mercury and 584.0 days for Venus.

A Different Point of View

From the Earth’s point of view, Mercury and Venus are the inferior planets while the superior planets are those from Mars outward (see Project 16). But from the point of view of Mars, the inferior planets are Mercury, Venus, and the Earth while the superior planets are those from Jupiter outward. In previous projects you have learned about the phases and retrograde motion of the planets as seen from the Earth. Viewed from Mars, the planets also retrograde and go through phases with the inferior planets exhibiting the same phases as the Moon and the superior planets having only full and gibbous phases.

Because the Earth revolves around the Sun in 1 year while Mars requires 1.88 years, the faster-moving Earth overtakes Mars at regular time intervals. At such times an observer on Mars would say that the Earth was at inferior conjunction. The Earth’s synodic period would be the time between two of these inferior conjunctions.