compiling an extensive star catalogue, assigning “magnitudes” as a measure of stellar
brightness, and calculating the length of the year to within 6.5 minutes of the correct
value. His planetary models were mathematical, not mechanical. And although Hip-
parchus did not invent it, he was probably the first person to systematically use
trigonometry, which was a necessity for most of his discoveries.What was De revolutionibus orbium coelestium?
In the year of his death, astronomer Nicolaus Copernicus (1473–1543; in Polish,
Mikol/aj Kopérnik) published De revolutionibus orbium coelestium(On the Revolu-
tions of the Heavenly Spheres). This manuscript gave a full account of his theory that
the Sun, and not the Earth, was at the center of the solar system (or universe).
Although this theory was not new, Copernicus offered the idea in all its mathematical
detail. This heliocentric (versus geocentric) view of the heavens, now known as the
Copernican system, is the foundation of modern astronomy.What are Kepler’s Laws of Planetary Motion?
A great deal of mathematics went into the formulation of Kepler’s Laws of Planetary
Motion. These laws were devised by German astronomer and mathematician (and Danish
astronomer Tycho Brahe’s [1546–1601] assistant) Johannes Kepler (1571–1630). He pre-
sented the first and second laws in his work Astronomia nova(New Astronomy) in 1609;
288 the third law was published in 1619 in Harmonice mundi. The three laws are as follows:
Who first calculated the distance
from the Earth to the Sun and Moon?A
round 290 BCE, astronomer and mathematician Aristarchus of Samos (c. 310
BCEto c. 230 BCE) used geometric methods to calculate the distances to and
sizes of the Moon and Sun. Based on his observations and calculations, he sug-
gested that the Sun was about 20 times as distant from the Earth as the Moon (it
is actually 390 times); he also determined that the Moon’s radius was 0.5 times
the radius of the Earth (it is actually 0.28 times). The numbers differ not because
Aristarchus had no geometric knowledge, but because of the poor instruments
used at that time.
These calculations were not the only contribution made by Aristarchus. He
was also the first to propose that the Earth orbits the Sun—many centuries
before Nicholaus Copernicus (see below). This concept was radical for his time,
because it conflicted with geocentric religious beliefs and Aristotle’s principle
that all objects move toward the center of the Earth.