When people in ancient times looked up at the sky, they saw the Sun, Moon, and stars rise in the east and set in the west and appear to move around Earth. The ancient peoples were aware of five planets (planet means “wandering star”) because from one night to the next they moved in a generally eastward direction among the stars, whose positions appeared fixed on the celestial sphere. One thing the ancients did not know, however, was that Earth was similar to those planets. Developing a successful theory of how Earth and the planets move and how Earth fits in with its neighbors in the Solar System was the first step to understanding Earth’s place in the universe. The history of how those ideas evolved—from Earth at the center of all things to Earth as just an ordinary planet—is a good example of how science is self-correcting.
The Geocentric Model
Looking up at the sky, early astronomers saw that the Sun, Moon, planets, and stars appeared to move around Earth. Greek astronomers developed a geocentric (Earth-centered) model of the Solar System to explain these observations. In this model, which persisted into the 17th century, the Sun, Moon, and known planets all moved in circles around a stationary Earth. Figure 3.1 illustrates the geocentric model of the Alexandrian astronomer Ptolemy (Claudius Ptolemaeus, 90–168 CE).
Figure 3.1 In the Ptolemaic view of the heavens, Earth is at the center, orbited by the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn.
The geocentric model, though, did not account for all observations. Ancient astronomers knew that the planets usually have an eastward prograde motion, in which each night they move a little eastward with respect to the background stars. Sometimes, however, the planets had apparent retrograde motion, in which the planets appear to move westward for a time before resuming their normal eastward travel. Figure 3.2 shows this behavior for Mars as it moves across the sky. Mars enters this field of view from the west (the right side of the image), makes a loop, and leaves the field of view to the east (the left side of the image) about seven months later.
Figure 3.2 This time-lapse photographic series shows Mars as it moves in apparent retrograde motion.
★WHAT AN ASTRONOMER SEES An astronomer will notice from the dates shown that the photographic series begins with Mars on the right side of the image. As time passes, Mars moves toward the left, then completes the loop, and leaves the image on the left, about 7.5 months later. An astronomer will also notice that Mars is larger and brighter on the image in the retro- grade part of the loop, indicating that Earth and Mars are closer together at that time. This color image clearly shows that some stars are red and some stars (like the ones in the group of stars called M44) are blue.
The apparent retrograde motion of the five “naked eye” planets—Mercury, Venus, Mars, Jupiter, and Saturn—created a puzzling problem for Ptolemy’s geocentric model, as it stood in 150 CE. Because the geocentric model in its simplest form failed to explain the apparent retrograde motion of the planets, Ptolemy added an embellishment called an epicycle—a small circle superimposed on each planet’s larger circle (Figure 3.3). As the planet travels along its larger circle around Earth, it also moves along its epicycle. When moving along the smaller circle in the opposite direction of the forward motion of the larger circle, the planet’s forward motion would be reversed and it would appear to move backward in the sky. This embellishment made the model reasonably successful at predicting the positions of planets in the sky. For nearly 1500 years, Ptolemy’s model, in which the Sun, Moon, and planets all moved in perfect circles around a stationary Earth, with the “fixed stars” located far beyond the planets, was the accepted paradigm in the Western world.
Figure 3.3 To reconcile retrograde motion with the geocentric model of the Solar System, Ptolemy added loops called epicycles to each planet’s circular orbit around Earth.
CHECK YOUR UNDERSTANDING 3.1a
How did the ancients know the planets were different from the stars?
AnswerAnswer
While the stars always remained in the same location, the planets moved against those stars.
Copernicus Proposes a Heliocentric Model
Nicolaus Copernicus (1473–1543—Figure 3.4) was not the first person to suggest that the Sun might be at the center of the Solar System. A few ancient Greek and medieval Arab astronomers, such as Aristarchus of Samos (310–230 BCE), had briefly considered the idea when they saw problems with the Earth-centered model. These astronomers lacked the observational or mathematical tools to test the Sun-centered hypothesis, and most astronomers found the fact that they could not feel Earth’s motion around the Sun to be a powerful argument in favor of the Earth-centered model.
Figure 3.4 Nicolaus Copernicus rejected the ancient Greek model of an Earth-centered universe and replaced it with a model that centered on the Sun.
Copernicus, however, was the first to develop a comprehensive mathematical model with the Sun at the center and that later astronomers could test. That heliocentric (Sun-centered) model was the beginning of the Copernican Revolution. Through the work of 16th- and 17th-century scientists such as Tycho Brahe, Galileo Galilei, Johannes Kepler, and Isaac Newton, the heliocentric model of the Solar System became one of the best-corroborated theories in all of science.
what if . . .
What if we launch an Earth satellite that orbits at half the distance to the Moon? Would astronauts aboard that satellite observe retrograde motion of the Moon?
Copernicus was multilingual and highly educated: he studied philosophy, canon (Catholic) law, medicine, economics, mathematics, and astronomy in his native Poland and in Italy. He conducted astronomical observations from a small tower, and sometime around 1514 he started writing about a heliocentric model. Eighteen years later, he completed his manuscript. He did not publish the book because he knew his ideas would be controversial: philosophical and religious views of the time held that humanity, and thus Earth, must be the center of the universe. Late in his life, Copernicus was finally persuaded to publish his ideas, and his great work De revolutionibus orbium coelestium (“On the Revolutions of the Heavenly Spheres”) appeared in 1543, the year he died.
Figure 3.5 shows Copernicus’s model with the planets orbiting in perfect circles around the Sun. That model explained the observed motions of Earth, the Moon, and the planets, including apparent retrograde motion, much more simply than the geocentric model did. In this model, relative motion is important; when you are in a car or train and you pass a slower-moving car or train, the other vehicle seems as though it is moving backward.
Figure 3.5 The Copernican heliocentric view of the Solar System (II–VII) and the fixed stars (I). The Sun is at the center, orbited by Mercury, Venus, Earth, Mars, Jupiter, and Saturn. The Moon orbits Earth.
Similarly, in the Copernican model, planets farther from the Sun appear to have retrograde motion when Earth overtakes them in their orbits. Figure 3.6 illustrates that effect for Mars; compare this diagram to the observations shown in Figure 3.2. Conversely, planets closer to the Sun than Earth is—Mercury and Venus—appear to have retrograde motion when overtaking Earth. Except for the Sun and the Moon, all Solar System objects exhibit apparent retrograde motion. The effect diminishes with increasing distance from Earth. Apparent retrograde motion is caused by the relative motion between Earth and the other planets.
Figure 3.6 The Copernican model explains the apparent retrograde motion of Mars (see Figure 3.2) as seen in Earth’s sky when Earth passes Mars in its orbit. (Not drawn to scale.)
Although Copernicus correctly placed the Sun at the center of the Solar System, he still conceived of the planets as moving in perfectly circular orbits at constant speeds, so he needed to use some epicycles to match the observations. His model made testable predictions of the location of each planet on a given night. Those predictions were at least as accurate as those of the geocentric model. Overall, however, the heliocentric model was simpler than the geocentric model and became the basis for further refinements in understanding how Earth moved. As copies of De Revolutionibus and Copernicus’s ideas slowly spread across Europe, other scientists began to consider and then accept the heliocentric model, and a scientific revolution began.
Scaling the Solar System
From his observations, Copernicus deduced the correct order of the planets and concluded that planets closer to the Sun travel faster than planets farther out. He also realized that he needed to consider two categories of planets: inferior planets, which are closer to the Sun than Earth is, and superior planets, which are farther from the Sun than Earth is.
In Copernicus’s model, Earth, another planet, and the Sun periodically align in space to form either a line or a right triangle. There are special words for each of these alignments, as shown in Figure 3.7. When a superior planet is in line with the Sun and Earth but on the other side of the Sun from Earth, the planet is in conjunction (Figure 3.7a) A superior planet in conjunction rises and sets in the sky with the Sun. When a superior planet is in conjunction, it is at its farthest from Earth, so it is at its faintest, too. Exactly at conjunction, however, you won’t see the superior planet at all because it’s behind the Sun in the sky.
Figure 3.7 Planetary configurations for a. superior (outer) planets and b. inferior (inner) planets.
In contrast, when a superior planet is in line with the Sun and Earth on the same side of the Sun as Earth, the configuration is an opposition (Figure 3.7a). At opposition, the superior planet is “opposite” the Sun in the sky. Like a full Moon, the planet rises when the Sun sets and sets when the Sun rises. When the superior planet is in opposition, it is at its closest to Earth during that orbit and thus at its brightest; therefore, opposition is the best time to observe the planet in the sky. Opposition occurs during the time when the planet exhibits retrograde motion because that is exactly when Earth is overtaking the planet in its orbit. Quadrature occurs when Earth, the Sun, and a superior planet form a right triangle in space (Figure 3.7a).
For an inferior planet, the configurations are slightly different (Figure 3.7b). When the inferior planet is between Earth and the Sun, it is closest to Earth and the configuration is called inferior conjunction. If the inferior planet is on the other side of the Sun from Earth, it is farthest from Earth, and the configuration is called a superior conjunction. Greatest elongation occurs when the inferior planet forms a right triangle with Earth and the Sun, and thus is the farthest it gets from the Sun in the sky. The inner planets are always close to the Sun in the sky, so Mercury and Venus are visible only within a few hours of sunrise or sunset. The best time to observe those planets is at greatest elongation because they will have the greatest separation from the Sun in the sky.
Copernicus realized that two types of orbital periods existed. We name these periods with terms similar to those used for lunar orbits. A planet’s sidereal period is how long the planet takes to make one orbit around the Sun with respect to the stars and return to the same point in space. A planet’s synodic period is how long the planet takes to return to the same configuration with the Sun and Earth, such as from inferior conjunction to inferior conjunction or from opposition to opposition.
Reading Astronomy News
Jupiter and Saturn Will Come within 0.1 Degrees of Each Other, Forming the First Visible “Double Planet” in 800 Years
Sophie Lewis, cbsnews.com
Some planetary alignments are rare, but noteworthy. In December of 2020, a particularly unusual alignment attracted a lot of attention.
Jupiter and Saturn will be so close today that they will appear to form a "double planet." Such a spectacular great conjunction, as the planetary alignment has come to be known, hasn't occurred in nearly 800 years.
When their orbits align every 20 years, Jupiter and Saturn get extremely close to one another. Jupiter orbits the sun every 12 years, while Saturn’s orbit takes 30 years, so every few decades Jupiter laps Saturn, according to NASA.
The 2020 great conjunction is especially rare—the planets haven’t been this close together in nearly 400 years, and haven't been observable this close together at night since medieval times, in 1226.
“Alignments between these two planets are rather rare, occurring once every 20 years or so, but this conjunction is exceptionally rare because of how close the planets will appear to one another,” Rice University astronomer Patrick Hartigan said in a statement. “You’d have to go all the way back to just before dawn on March 4, 1226, to see a closer alignment between these objects visible in the night sky.”
Aligning with the winter solstice on December 21, 2020, the two planets will be just 0.1 degrees apart—less than the diameter of a full Moon, EarthSky said. The word “conjunction” is used by astronomers to describe the meeting of objects in our night sky, and the great conjunction occurs between the two largest planets in our Solar System: Jupiter and Saturn.
The planets will be so close, they will appear, from some perspectives, to overlap completely, creating a rare “double planet” effect. So close, that a "pinkie finger at arm's length will easily cover both planets in the sky," NASA said.
However, while they may appear from Earth to be very, very close, in reality, they are still hundreds of millions of miles apart.
During the last great conjunction in 2000, Jupiter and Saturn were so close to the Sun that the event was difficult to observe. But skywatchers should have a clearer view of the celestial event this time around. The great conjunction will be shining bright shortly after sunset, low in the southwestern sky, as viewed from the Northern Hemisphere, NASA said.
Saturn will appear slightly above and to the left of Jupiter, and will even look as close to the planet as some of its own moons, visible with binoculars or a telescope. Unlike stars, which twinkle, both planets will hold consistent brightness, easy to find on clear nights.
The event is observable from anywhere on Earth, provided the sky is clear. “The further north a viewer is, the less time they’ll have to catch a glimpse of the conjunction before the planets sink below the horizon,” Hartigan said.
The planets will appear extremely close for about a month, giving skywatchers plenty of time to witness the spectacular alignment throughout the holiday season. The event coincidentally aligns with the December solstice, marking the shortest day of the year in the Northern Hemisphere.
This will be the “greatest” great conjunction for the next 60 years, until 2080. Hartigan said that, following that conjunction, the duo won’t make such a close approach until sometime after the year 2400.
QUESTIONS
The use of the word “conjunction” in this context is more general than the formal usage introduced in the text of this chapter. In the chapter, we use “conjunction” to mean “solar conjunction.” Compare that usage with the usage in this article. What does the term mean more generally?
How long had it been since Jupiter and Saturn were in alignment?
How long had it been since Jupiter and Saturn were this closely aligned?
The author of the article states that while the planets appear quite close, “in reality, they are still hundreds of millions of miles apart.” How can that be?
Make a sketch of this conjunction, showing the relative positions of Jupiter, Saturn, Earth, and the Sun.
The synodic period is what can be observed directly from Earth. In Figure 3.8a, Earth and the superior planet are in opposition at point A. Superior planets move around the Sun more slowly than Earth does, so Earth orbits the Sun once and then catches up to the superior planet to form the next opposition at point B. In Figure 3.8b, Earth and the inferior planet are in inferior conjunction at point A. An inferior planet moves around the Sun faster than Earth does, so it completes one sidereal period and then must continue in its orbit to catch up to Earth for the next inferior conjunction at point B.
Figure 3.8 The synodic periods of planets indicate how long they take to return to the same configuration with Earth and the Sun. a. Earth completes one orbit around the Sun first and then catches up to the superior planet. b. Inferior planets complete a full orbit around the Sun first and then catch up to Earth.
Copernicus used the geometry of these alignments along with his observations of the positions of the planets in the sky, including their altitudes and the times they rose and set, to estimate the planet–Sun distances. He could not figure this out in terms of meters or feet, but instead determined these distances in multiples of the Earth–Sun distance. The average distance from Earth to the Sun is so useful that it has its own unit, the astronomical unit (AU). Table 3.1 shows that the relative distances Copernicus calculated are remarkably close to the distances modern methods yield. Working It Out 3.1 describes the numerical details. Copernicus’s model not only predicted planetary positions in the sky but also could be used to accurately compare the distances between the planets and the Sun.
Table 3.1
Copernicus’s Scale of the Solar System
Planet
Copernicus’s Value (AU)
Modern Value (AU)
Mercury
0.38
0.39
Venus
0.72
0.72
Earth
1.00
1.00
Mars
1.52
1.52
Jupiter
5.22
5.20
Saturn
9.17
9.58
AU = Astronomical Unit.
working it out 3.1
How Copernicus Computed Orbital Periods and Scaled the Solar System
Orbital Periods
Copernicus calculated the sidereal period by observing the synodic period. Let P be the sidereal period of a planet and S, its synodic period. E is Earth’s sidereal period, which equals 1 year, or 365.25 days. By thinking about the distance that Earth and the planet move in one synodic period, and noting that an inferior planet orbits the Sun faster than Earth does, we can show that
for an inferior planet, with P, E, and S all in the same units of days or years. Similarly, Earth orbits the Sun faster than a superior planet does, so the planet has traveled only part of its orbit around the Sun after 1 Earth year. The equation for a superior planet is
For Saturn, the time that passes between oppositions—the date of maximum brightness—shows that Saturn’s synodic period (S) is 378 days, or 378 ÷ 365.25 = 1.035 years. Then, to compute Saturn’s sidereal period (P) in years, we use S= 1.035 yr and E= 1 yr in the equation for a superior planet:
Thus,
Saturn’s sidereal period is 29.4 years, which means that Saturn takes 29.4 years to travel around the Sun and return to where it started in space.
Scaling the Solar System
Copernicus used the configurations of the planets shown in Figure 3.7 along with their sidereal periods to compute the relative distances of the planets. For the superior planets, he measured the fraction of the circular orbit that the planet completed in the time between opposition and quadrature, and then he used trigonometry to solve for the planet–Sun distance in astronomical units (see Figure 3.7a). For the inferior planets, he had a right triangle at the point of greatest elongation, and then he used right-triangle trigonometry to solve for the planet–Sun distance in astronomical units (see Figure 3.7b). Copernicus’s values are impressively similar to modern values (see Table 3.1). Copernicus still did not know the actual value of the astronomical unit in miles or kilometers, but he was the first to accurately compute the relative distances of the planets from the Sun.
CHECK YOUR UNDERSTANDING 3.1a
The planet Uranus will be observed in retrograde motion when: (a) Uranus is closest to the Sun; (b) Uranus is farthest from the Sun; (c) Earth overtakes Uranus in its orbit; (d) Uranus overtakes Earth in its orbit.
1. Rotational or orbital motion of a moon that is in the same direction as the planet it orbits. 2. The counterclockwise orbital motion of Solar System objects as seen from above Earth’s orbital plane. Compare retrograde motion.
1. Rotation or orbital motion of a moon that is in the opposite direction to the rotation of the planet it orbits. 2. The clockwise orbital motion of Solar System objects as seen from above Earth’s orbital plane. Compare prograde motion. 3. Apparent retrograde motion is a motion of the planets with respect to the “fixed stars,” in which the planets appear to move westward for a time before resuming their normal eastward motion.
Answer
Answer
