Foundations of Modern Astronomy

Nicolaus Copernicus and the Heliocentric hypothesis

Copernicus (1473–1547) was a Polish scholar who postulated an alternative description of the solar system. Like the Ptolemaic geocentric (“Earth‐centered”) model of the solar system, the Copernican heliocentric (“Sun‐centered”) model is an empirical model. That is, it has no theoretical basis, but simply reproduces the observed motions of objects in the sky.

In the heliocentric model, Copernicus assumed Earth rotated once a day to account for the daily rise and set of the Sun and stars. Otherwise the Sun was in the center with Earth and the five naked‐eye planets moving about it with uniform motion on circular orbits (deferents, like the geocentric model of Ptolemy), with the center of each offset slightly from Earth's position. The one exception to this model was that the Moon moved about Earth. Finally, in this model, the stars lay outside the planets so far away that no parallax could be observed.

Why did the Copernican model gain acceptance over the Ptolemaic model? The answer is not accuracy, because the Copernican model is actually no more accurate than the Ptolemaic model—both have errors of a few minutes of arc. The Copernican model is more attractive because the principles of geometry set the distance of the planets from the Sun. The greatest angular displacements for Mercury and Venus (the two planets that orbit closer to the Sun, the so‐called inferior planets) from the position of the Sun ( maximum elongation) yield right angle triangles that set their orbital sizes relative to Earth's orbital size. After the orbital period of an outer planet (a planet with an orbital size larger than the orbit of Earth is termed a superior planet) is known, the observed time for a planet to move from a position directly opposite the sun ( opposition) to a position 90 degrees from the Sun ( quadrature) also yields a right‐angle triangle, from which the orbital distance from the Sun can be found for the planet.

If the Sun is placed in the center, astronomers find that planetary orbital periods correlate with the distance from the Sun (as was assumed in the geocentric model of Ptolemy). But its greater simplicity does not prove the correctness of the heliocentric idea. And the fact that Earth is unique for having another object (the Moon) orbiting around it is a discordant feature.

Galileo Galilei and the invention of the telescope

Settling the debate between the geocentric versus heliocentric ideas required new information about the planets. Galileo did not invent the telescope but was one of the first people to point the new invention at the sky, and is certainly the one who made it famous. He discovered craters and mountains on the Moon, which challenged the old Aristotelian concept that celestial bodies are perfect spheres. On the Sun he saw dark spots that moved about it, proving that the Sun rotates. He observed that around Jupiter traveled four moons (the Galilean satellites Io, Europa, Callisto, and Ganymede), showing that Earth was not unique in having a satellite. His observation also revealed that the Milky Way is composed of myriads of stars. Most crucial, however, was Galileo's discovery of the changing pattern of the phases of Venus, which provided a clear‐cut test between predictions of the geocentric and heliocentric hypotheses, specifically showing that the planets must move about the Sun.

Johannes Kepler

Because the heliocentric concept of Copernicus was flawed, new data were required to correct its deficiencies. Tycho Brahe's (1546–1601) measurements of accurate positions of celestial objects provided for the first time a continuous and homogeneous record that could be used to mathematically determine the true nature of orbits. Johannes Kepler (1571–1630), who began his work as Tycho's assistant, performed the analysis of planetary orbits. His analysis resulted in Kepler's laws of planetary motion, which are as follows:

  • The law of orbits: All planets move in elliptical orbits with the Sun at one focus.

  • The law of areas: A line joining a planet and the Sun sweeps out equal areas in equal time.

  • The law of periods: The square of the period ( P) of any planet is proportional to the cube of the semi‐major axis ( r) of its orbit, or P 2G (M (sun) + M) = 4 π 2 r 3, where M is the mass of the planet.

Isaac Newton. Isaac Newton (1642–1727), in his 1687 work, Principia, placed physical understanding on a deeper level by deducing a law of gravity and three general laws of motion that apply to all objects:

  • Newton's first law of motion states that an object remains at rest or continues in a state of uniform motion if no external force acts upon the object.

  • Newton's second law of motion states that if a net force acts on an object, it will cause an acceleration of that object.

  • Newton's third law of motion states that for every force there is an equal and opposite force. Therefore, if one object exerts a force on a second object, the second exerts an equal and oppositely directed force on the first one.

Beyond Newton: Relativity Theories

Newton's Laws of Motion and Gravity are adequate for understanding many phenomena in the universe; but under exceptional circumstances, scientists must use more accurate and complex theories. These circumstances include relativistic conditions in which a) large velocities approaching the speed of light are involved (theory of special relativity), and/or b) where gravitational forces become extremely strong (theory of general relativity).

In simplest terms, according to the theory of general relativity, the presence of a mass (such as the Sun) causes a change in the geometry in the space around it. A two‐dimensional analogy would be a curved saucer. If a marble (representing a planet) is placed in the saucer, it moves about the curved rim in a path due to the saucer's curvature. Such a path, however, is the same as an orbit and nearly identical with the path that would be calculated by use of a Newtonian gravitational force to continually change the direction of motion. In the real universe, the difference between Newtonian and relativistic orbits is usually small, a difference of two centimeters for the Earth‐Moon orbital distance ( r = 384,000 km on average).