Earth Centered to Sun Centered Universe

The idea of an Earth-centered universe was firmly established by Claudius Ptolemaeus, known more commonly as Ptolemy, in the second century A.D. Ptolemy's universe had Eratosthenes's spherical Earth at its center, around which moved the Sun, Moon, planets, and stars. It was inconceivable that man, God's favored creation, should live anywhere other than at the center of the cosmos! Furthermore, by similar reasoning, it was supposed that these heavenly bodies, far removed from the imperfections of earthly life, should move along perfect circular paths.

However, there were problems with the model, which even the astronomers in Ptolemy's time could detect with their limited observational capabilities. The planets had been discovered centuries before—the Romans worshiped them as gods—and they could be distinguished not only by their brightness, but also by their movement across the sky relative to the fixed stars. Mars in particular appeared to challenge Ptolemy's model by moving erratically, performing loops in its motion among the stars, as shown in Figure 1.2. Ptolemy struggled to explain this behavior by introducing epicycles into his model. An epicycle is essentially a smaller circle around which a planet moves, which in turn is superimposed upon the larger circle representing the planet's motion about Earth. Throughout his lifetime, Ptolemy continued to tweak his model, introducing many epicycles in an attempt to fit observations.

Despite its evident weaknesses, the Earth-centered model survived for 1300 years or so, primarily because of the power and influence of the Church over this period. To challenge the notion that Earth was the center of the universe would have been considered foolhardy, a crime against God that could attract the severest penalty.

The person credited with making this challenge was Nicolaus Copernicus, a Polish Catholic cleric who was born in 1473. The main feature of Copernicus's universe was that he relegated Earth to be just one of a number of planets orbiting the Sun. At the time, this Sun-centered model was an extraordinary shift in our worldview, but Copernicus boldly swept away the old ideas, writing explicitly about the inadequacy of the previous arguments and refuting them. Copernicus waited until the year of his death, 1543,

before going public, presumably to avoid the consequences of religious persecution. Unkind contemporaries of Copernicus labeled him the "restorer" of the Sun-centered universe, in deference to Aristarchus, who held this belief around 280 B.C. However, the world was not ready for this idea in the third century B.C. Copernicus is remembered not just for establishing the idea of a Sun-centered solar system; many other related contributions secure his place in history:

• An understanding of the rising and setting of the heavenly bodies in terms of the daily rotation of the Earth.

• An explanation of the seasons due to Earth's annual journey around the Sun. Copernicus deduced that Earth's spin axis was not perpendicular to the orbit plane. Consequently, the Northern Hemisphere would be tilted toward the Sun during the Northern Hemisphere's summer, and conversely tilted away during the winter months.

• A mechanism to explain the looping motion of the planets among the fixed stars (Fig. 1.3).

• The estimation of the size of the planets' orbits in "astronomical units,'' and their periods (that is, the time taken to orbit the Sun). In this process, Copernicus assumed that the orbits were circular.

The last item on this list was a staggering achievement, and deserves further attention. First of all, what is an astronomical unit (AU)? In modern terms, it is the average distance between Earth and the Sun, taking into account that the distance varies a bit as the Earth orbits the Sun. Numerically

Figure 1.3: Copernicus's explanation of the apparent looping motion of Mars among the fixed stars. He assumed that Earth and Mars moved along circular orbits with different periods, so that Earth moved from point 1 to point 5 in the same time that Mars moved from point A to point B.

1 AU is around 150 million km (93 million miles). Copernicus had no way of determining this, but with careful thought he could devise ways of estimating the distance of the known planets from the Sun as multiples of the Earth-Sun distance—that is, in astronomical units. Therefore, he was able to construct the scale of the known solar system relative to the size of Earth's orbit, but its absolute size escaped him.

The explanation of his methods is a little complicated, but I hope the reader will come along for the ride! For the planets Mercury and Venus, closer to the Sun than Earth, the basics of this method are illustrated in Figure 1.4. Taking Venus as an example, Copernicus could observe its orbital motion around the Sun, as we can today, by watching its track in the sky at the time

Figure 1.4: (a) The motion of Venus in the evening sky over a period of weeks, allowing the measurement of the maximum angle (angle a) between the planet and the Sun. (b) The orbital geometry of Earth and Venus at the time of maximum angular separation.

Earth

Figure 1.4: (a) The motion of Venus in the evening sky over a period of weeks, allowing the measurement of the maximum angle (angle a) between the planet and the Sun. (b) The orbital geometry of Earth and Venus at the time of maximum angular separation.

Figure 1.5: Copernicus estimated the radius RJ of Jupiter's orbit, again using 'simple' trigonometry.

Jupiter

Figure 1.5: Copernicus estimated the radius RJ of Jupiter's orbit, again using 'simple' trigonometry.

of sunset over a number of weeks (Fig. 1.4a). To estimate the size of the orbit, Copernicus just needed to note the maximum angle between the Sun and the planet over this period, and he could then translate this to the orbital geometry shown in Figure 1.4b. The problem then reduces to a simple one, involving solving the lengths of the sides of a right-angled triangle using trigonometry. Most readers will have come across trigonometry in school mathematics lessons and probably will have forgotten it! However, referring to the triangle in Figure 1.4b, all that needs to be understood is that if Earth's orbit radius (RE is 1 AU) and the maximum angle (angle a) are known, then the radius Rv of Venus's orbit can be calculated. Adopting this simple process, Copernicus found that Rv was approximately 0.7 AU, and a corresponding analysis of Mercury's motion gave its orbit radius as about 0.4 AU.

The process for estimating the orbit sizes of the outer planets known to Copernicus (Mars, Jupiter, and Saturn) was a little more involved. There are a number of ways of looking at this, but they all boil down to the same thing, and ultimately reduce again to a simple trigonometrical problem.Taking the planet Jupiter as an example, Copernicus measured the time it took for Earth to "lap" Jupiter in their respective orbits. He noted that approximately every 400 days Jupiter returned to the same position, due south in the sky at midnight. Translating this into orbital position, he realized that this happened when Earth was precisely between the Sun and Jupiter, and was about to overtake Jupiter. He then went on to deduce that a quarter of this lapping period—approximately 100 days—after this alignment, Earth would be 90 degrees ahead of Jupiter in its orbit, giving the orbital geometry shown in Figure 1.5. The measurement of the angle between the Sun and Jupiter at this time, an observation best made at sunset, completed the puzzle and allowed Copernicus to calculate the radius of Jupiter's orbit at about 5.2 AU. Similar calculations gave estimates of the radii of Mars's and Saturn's orbit, at around 1.5 AU and 9.5 AU, respectively.

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