Earth was the center of the universe… until it was not. The shift from the geocentric to the Copernican model of the solar system is one of the most interesting stories in science. The geocentric model was fixed in people’s minds. It originated with the Ancient Greeks, who reasoned that Earth was the center of the universe because Earth feels stable, everything falls toward Earth, and the Sun, Moon, planets, and stars appear to travel around Earth each day. Looking northward, the stars appear to rotate in a circle at the top of a sphere. Thus, the Greeks envisioned all the stars and planets rotating around the earth on celestial spheres in perfect circles; however, what our senses tell us is not necessarily true. The geocentric model is is based on an optical illusion. It looks like the sun, moon, and planets orbit the earth. There have been other cases in which scientific data contradicted what was seemingly obvious to the senses; however, this illusion was the most difficult to reject, and it led to the greatest turmoil (Section 1-10).
Figure 1‑4. Ptolemy’s celestial spheres. Celestial Spheres (1539). Image credit: Peter Apian. Used here per CC BY-SA 4.0.
Ptolemy (150 AD) was the most famous astronomer of the ancient world. Figure 1‑4 shows Ptolemy’s model of the solar system, in which the moon (Luna) is closest to Earth, followed by Mercury, Venus, and the Sun (Solis). As with all incorrect scientific models, problems began to arise with the geocentric model. One problem was that the planets intermittently moved backward in the sky (retrograde motion), with respect to the positions of the stars. For example, Mars has a retrograde motion every two years (Figure 1‑5).
Figure 1‑5. Pattern of Mars' position against the backdrop of the stars during 2003. Credit: NASA, JPL.
Figure 1‑6. Ptolemy’s epicycle of Mars (orange). No copyright.
The second problem with the geocentric model was that planets became dimmer and brighter depending on their orbital position with respect to the sun. We now know that it was because they were closer or further from Earth; however, this was difficult to explain if you thought that they were orbiting in perfect circles around Earth.
To account for retrograde motion and the brightness and dimming of planets, Ptolemy proposed that Mars and other planets were on a second sphere or rim (epicycle) attached to a primary rim, which caused it to move backward periodically (Figure 1‑6). He also proposed that Earth was orbiting around an imaginary point.
During the Renaissance, Nicolaus Copernicus (1473-1543) spent three decades plotting the positions of the planets against the background of the fixed stars. He spent night after night measuring their angular positions with a triquetrum (Figure 1‑7). He then used mathematics to calculate the paths of the planets over time. Copernicus realized that the geocentric model was incorrect and that phenomena such as the backward movement of Mars made sense if Earth and Mars orbit the Sun.
Figure 1‑7. Astronomer Copernicus. Credit: Jan Matejko.
Copernicus thought that the planets orbited the sun on celestial spheres (perfect circles). Because the planets orbit the sun in imperfect circles or ellipses, his mathematical calculations of planetary positions on perfect circles did not match the observed paths of the planets. Another weakness with Copernicus' work was that he used instruments that did not have enough precision to enable him to precisely estimate the positions of the planets. The slight error in his theory and lack of precision in his instruments justifiably led to uncertainty. Copernicus wrote a small handwritten pamphlet on the heliocentric theory for a few colleagues in 1514. He finally published his book: De Revolutionibus Orbium Coelestium (On the Revolutions of the Celestial Spheres) in 1543, the year of his death, in which he described his heliocentric model (Figure 1-8).
Figure 1‑8. Copernicus’ heliocentric model in De Revolutionibus Orbium Coelestium.
Figure 1‑9. Tycho Brahe’s observatory and instruments. Wikipedia (artist unknown)
Tycho Brahe (1546-1601) was a Danish astrologer and astronomer. His major contribution to the study of the solar system was his precise plotting of the positions of the planets over a period of 40 years. The Danish king built an estate and observatory for Brahe (Figure 1‑9) on an island in 1576. Annual funding for the observatory amounted to 1% of the Danish national budget. The king even allowed Brahe to tax the citizens of the island on which the observatory was located. His instruments were enormous in comparison to those of Copernicus, and he was able to generate much more accurate tables of planetary positions; however, Brahe could not accept the heliocentric model, so he concluded that the sun orbits Earth, and Venus and Mercury orbit the sun.
Scientists used the principle of parallax to determine distances to planets and other objects. Using the principle of parallax, Tycho looked at a supernova explosion from different locations on Earth and observed that its position did not change (no parallax), which proved that it was beyond the moon. Previously, people had thought that all the celestial spheres beyond the moon were unchanging. Brahe also noted that a comet appeared to move across the supposed celestial spheres, which showed that there were no impermeable spheres in the sky.
Brahe fell out of favor with the new king of Denmark in 1597. He immigrated to Prague, where he became the imperial astronomer for the Austro-Hungarian Holy Roman Emperor King Rudolph II. Brahe died shortly after that in 1601, but not before the great mathematician Johannes Kepler (Figure 1‑10) joined him in 1600.
Figure 1‑10. Johannes Kepler. Artist unknown.
Much to the chagrin of Brahe’s family, Kepler (1571-1630) took possession of Brahe’s data on planetary positions when Brahe died. Kepler then analyzed the data for 20 years. Kepler discovered that planets do not orbit the sun in perfect circles, that planets speed up when they are closer to the sun, and that planets closer to the sun have faster orbits in general. With the realization that the motion of the planets was elliptical, the equations that described the motions of the planets worked perfectly. Unlike Brahe, Kepler thought that Copernicus was correct and that all of the planets orbited the sun. In addition to his mathematics, Kepler is often credited for beginning the scientific revolution. He realized that the patterns of movement of the planets indicated that a physical force moved them through the sky rather than angels. Why would angels push at a faster rate when planets were closer to the sun? This led to the search for natural causes in physics and other sciences and initiated the scientific revolution.
Figure 1‑11. The Riformati Doge looking through Galileo's telescope. Fresco by Guiseppi Bertini.
Galileo improved the design of the spyglass and developed an 8X magnification astronomical telescope by which he observed moons orbiting Jupiter and the phases of Venus as it orbited the sun. The fact that Venus had phases and was larger during the "new" phase was strong proof of the heliocentric model. The fact that the moons of Jupiter orbited Jupiter disproved the geocentric model because it showed that everything did not revolve around Earth. After Galileo published his drawings of the phases of Venus and Jupiter’s moons in 1610 in The Starry Messenger, he became a celebrity, and everyone wanted to look through his telescope (Figure 1‑11). However, the fun was short-lived. Galileo encountered resistance from those who believed in geocentrism. He was put on trial by the church and ordered not to promote the heliocentric model. This was only the beginning of his problems.
Aristotle had popularized the geocentric viewpoint in Ancient Greece. St. Thomas Aquinas popularized Aristotle’s works in the Catholic Church during the 13th century because he thought he saw in Aristotle’s works a basis for Christian theology. From 1200 to 1650, the universities of Western Europe based their philosophical and scientific curriculums on the works of Aristotle.
The Scientific Revolution was the key to the development of the correct theories of matter and energy. Aristotle’s scientific theories were generally wrong because he did not believe in experiments. Aristotle thought that experiments were mundane and beneath his level of intelligence, so he developed his theories by logic alone. Logic is a key part of science, but the problem with untested logic is that it can easily go awry. Although the scientific revolution was much more than just the scientific method, Galileo’s scientific method, which included logic and experimentation, was the key to unlocking the secrets of the universe:
1. Observation and development of a question (logic)
2. Development of a hypothesis (logic)
3. Testing the hypothesis with an experiment
In addition to the scientific method, Galileo advocated a mathematical approach to science. He made the following statement in Il Saggiatore:
“the book [of nature] cannot be understood unless one first learns to comprehend the language and read the letters of which it is composed. It is written in the language of mathematics and its characters are triangles, circles and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these one wanders in a labyrinth.”[3]
One example of Galileo’s combination of the scientific method and mathematics was his discovery of the law of falling bodies, which was a key component of Newton's discovery of the law of gravity.
He had observed that objects fell at an increasing rate of speed when dropped from the tower of Pisa or other buildings (observation).
He asked the question: Is there a mathematical relationship or equation that would describe the rate of increase of speed? (question).
His hypothesis was that there is a mathematical relationship.
His experiment included a ramp that slowed the velocity of the balls so that he could measure the time that it took for balls to travel certain distances.
In his experiment, Galileo placed series of bells at increasing distances from each other along a ramp. He rolled a ball down the ramp and observed that the bells rang at equal time intervals. Thus, Galileo logically reasoned that the ball had a uniform acceleration and that the velocity of the balls could be described by the following equation: velocity = acceleration * time. He found that the uniform rate of acceleration for vertical descent is 9.8 m/sec2. This means that a free-falling object's speed increases during each second by 9.8 meters per second. Galileo did not discovery gravity, but his discovery was a basis for Newton’s realization that the acceleration of gravity is 9.8 m/s2. Isaac Newton (1642-1727) developed the law of gravity (Equation 1) and three laws of motion based on Galileo’s and other’s experiments and observations.
1. Bodies in motion tend to remain in motion and bodies at rest tend to remain at rest: inertia.
2. Force = mass * acceleration (F = m a): conservation of momentum.
3. Every action has an equal and opposite reaction.
Although Brahe’s measurements and Kepler’s equations were precise enough to provide mathematical proof of the orbit of the planets around the sun, there still was not a physical explanation for the orbit of the planets. Isaac Newton considered Kepler’s laws of planetary motion and an apple that fell from a tree and conceived of the law of gravity, providing a physical explanation for planetary motion. He realized that gravitational force would decrease with distance and increase with mass. This would cause the planets to move in elliptical orbits and move faster when they were closer to the sun. Newton determined that the principle works on the earth and anywhere in space. The force of gravity between any two objects is proportional to the mass of the two objects and the distance between them squared.
Figure 1‑13. Gravity between two masses separated by a distance.
If the mass of the objects is large, the gravitational attraction will be strong (Figure 1‑13). As the distance, d, between the two masses becomes smaller, the force of gravity will increase. If a planet is close to the sun or if the planet is large, then the force of gravity is large. In the same way, as the universe expands, everything is farther apart, and the force of gravity diminishes in the universe over time.
Newton’s law of gravity was one of the greatest and most consequential syntheses of theory and observation in the history of astronomy.
The equation for gravity includes mass, distance, and force.
where
m2 and m2 are the mass of objects 1 and 2,
G is the universal constant of gravity,
d is the distance between the two objects.
Kauai sunrise. image credit: Michael from Minnesota. Used here per CC SA 2.0