History of Astronomy: Part 2
Previously, we discussed the history of astronomy, focusing on developments prior to Newtonian mechanics. In this section, we will continue our exploration of the history of astronomy, focusing on developments from the time of Newton to the present day.
Table of Contents
Galileo and Newton
The invention of the telescope in the early 17th century revolutionized astronomy. Galileo Galilei (1564–1642) was one of the first to use a telescope to observe the heavens. He was the first to propose a version of Newton's first law, as well as the kinematic principles of acceleration. Using his telescope, Galileo made several important discoveries, including:
- The Milky Way is actually composed of a vast number of individual stars, instead of being a nebulous cloud as previously thought.
- The four largest moons of Jupiter (now known as the Galilean moons: Io, Europa, Ganymede, and Callisto) orbit the planet, providing strong evidence against the geocentric model of the universe.
- The phases of Venus, which could only be explained by a heliocentric model (as the sun's light illuminates different portions of Venus as it orbits the sun).
- The rough and uneven surface of the Moon, which contradicted the Aristotelian idea of perfect celestial spheres.
- Sunspots on the surface of the Sun, indicating that the Sun is not a perfect, unchanging body.
Galileo's observations provided strong evidence in favor of the heliocentric model proposed by Copernicus, and they challenged the prevailing Aristotelian view of the cosmos. The Catholic Church, which held significant influence over intellectual life in Europe at the time, challenged Galileo's findings. In 1616, The Holy Office declared heliocentrism to be "foolish and absurd in philosophy, and formally heretical." Galileo was also warned by Cardinal Roberto Bellarmine not to "hold, teach, or defend" the heliocentric view.
In 1623, however, his friend and admirer Cardinal Maffeo Barberini became Pope Urban VIII, and Galileo was given permission to write about heliocentrism as a hypothesis. He published his findings in "Dialogue Concerning the Two Chief World Systems" in 1632, which presented arguments for both the geocentric and heliocentric models. While it was technically neutral, the book was clearly biased in favor of heliocentrism. The character representing the heliocentric view was named "Salviati," after Galileo's friend and supporter, while the character representing the geocentric view was named "Simplicio," which was interpreted as a derogatory term meaning "simpleton." As a result, Galileo was tried by the Roman Catholic Inquisition in 1633 and found "vehemently suspect of heresy." He was forced to recant his views and spent the rest of his life under house arrest.
Despite the controversy surrounding Galileo's work, his observations laid the groundwork for future developments in astronomy and physics. Eventually, in 1992, Pope John Paul II formally acknowledged the errors made by the Church in its handling of the Galileo affair.
Isaac Newton (1643–1727) built upon the work of Galileo and others to develop a comprehensive theory of motion and gravitation. While the Plague ravaged Europe in 1665, Newton retreated to his family estate in Woolsthorpe, where he made several groundbreaking discoveries. His Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), published in 1687, laid the foundation for classical mechanics. In the Principia, Newton formulated his three laws of motion, the law of universal gravitation, as well as differential and integral calculus (independently developed by Leibniz). He also published his work on optics in Optiks in 1704, where he described the nature of light and color.
Newton was one of the most intelligent and influential scientists in history. When faced with the Brachistochrone problem, he solved it in a single night, inventing the calculus of variations in the process. By Newton's request, his solution was published anonymously in the 1696 edition of the Journal des Sçavans. Bernoulli, who had posed the problem, recognized Newton's solution and famously remarked, "I recognize the lion by his claw."
We should be vehemently familiar with Newton's laws of motion and gravitation, as they form the basis of classical mechanics. Nevertheless, it is worth briefly reviewing them here. We will do so by deriving Kepler's laws of planetary motion from Newton's law of gravitation. We must first establish the necessary mathematical tools.
Center-of-Mass Reference Frame
In a system of particles, the center of mass (COM) is the weighted average position of all the particles, where the weights are given by their masses.
For a system of
where
If we rearrange and differentiate this equation, we have
where
Anyways, suppose we have a binary system of two particles with masses
If we define the reduced mass
then each particle's position is
There are a few useful identities that we can derive from this.
First, Newton's third law gives
where
This means that we can treat the two-body problem as a one-body problem with mass
where
The gravitational potential energy of the system is
Kepler's First Law
Virial Theorem
One important result that we will need is the virial theorem.
For a stable, bound system of particles interacting through a potential
where
where