Brief history of astronomy

Astronomy 115

Zhang Heng (78 – 139 CE)Appointed Chief Astrologer/Astronomer of the Later Han Dynasty.

Wrote Ling Xian (“Mystical Laws”, 120), a summary of what was known about astronomy during his time, including a star catalog and geocentrism. Built a water-powered armillary sphere (a 3D model of the heavens) because he was not satisfied with 2D paper drawings.

Unlike Ptolemy, Heng’s geocentrism was not really a theory and did not gain wider acceptance.

Brahmagupta (c. 598 – 670)Lived in the Gurjar Empire (now Rajasthan, India), worked as a chief astronomer for the king.

Wrote Brahmasphutasiddhanta (“Correctly Established Doctrine of Brahma”, 628) in which he applied what we would now call algebra to calculate the timing of eclipses and the motions of the planets (Greek word “ephemerides”).

Took Ptolemaic ideas and made them more rigorously mathematical; in turn, influenced Arabic astronomy.

Muhammad ibn Musa al-Khwarizmi

Lived in Persia (the part now in Uzbekistan), approximately 780 – 850.

Principally a mathematician, he introduced numerals from India to the Arabic world, and developed methods of solving quadratic equations. One method was called al-jabr (= “algebra”).

His main astronomical work, Zij al Sindhind (“Astronomical Tables of Sind and Hind”, 820), corrected a number of observational errors in Ptolemy’s Almagest.

Nicholas Copernicus (1473-1543)

Born Niklas Kopernik in Poland, studied canon law and astronomy at the University of Bologna, Italy.

Came across heliocentrism in his studies, decided to use observations to prove or disprove it.

In 1497, he predicted the occultation (blocking of light) of the star Aldebaran by the Moon using a heliocentric model.

Copernicus’s work

• De revolutionibus orbium coelestrum (“On the Revolution of the Celestial Sphere” – 1543)

Heliocentrism

Johannes Kepler (1571-1630)

Appointed the Imperial Mathematician of Prague, after the death of his mentor, Tycho Brahe.

Used Brahe’s precise observational data to determine that the orbit of Mars was, in fact, elliptical around the Sun.

Kepler’s works

• Astronomia Nova (“The New Astronomy” – 1609) contained the first two laws of planetary motion

• Harmonius Mundi (“The Harmony of the World” – 1619) contained the third law

• Epitome Astronomiae Copernicanae (1621)

Three laws of planetary motion

• First law: Planetary orbits around the Sun are ellipses, with the Sun at one focus of the ellipse

• Second law: Equal areas are swept out during a period of time by the line connecting the Sun and the planet in equal times

• Third law: The cube of the semi-major axis of a planetary orbit is proportional to the square of its orbital period

Galileo Galilei (1564 - 1642)

Educated at the University of Pisa, initially in medicine, but later in mathematics. He gained a teaching position there.

Galileo’s works• Sidereus Nuncius (“The Starry Messenger”, 1609) – Discoveries

of the moons of Jupiter and the mountains on the Moon.

Dialogo sopra i due massimi sistemi del mondo (“The Dialogue Concerning the Two Chief World Systems”, 1632) – settling the heliocentrism debate

Law of falling bodies

Isaac Newton (1642 - 1727)

Born in eastern England, educated at the University of Cambridge, where he eventually earned the Lucasian Chair in Mathematical Physics.

Credited with co-inventing calculus, though for him, it was more of a means to understand motion more precisely.

Newton’s works

• Principia Mathematica Naturalis Philosophiae (“Principia”) – 1687

• Opticks – 1704

Axioms – Three laws of motion

• First law: An object in motion tends to stay in motion in a straight line unless acted on by an outside force

• Second law: The acceleration of an object is given by the force applied to it divided by the object’s mass (F = ma)

• Third law: For every action, there is an opposite and equal reaction

Law of universal gravitation

Also note the use of Newton’s Third Law, where F1 = F2

Newton’s formulation of Kepler’s third law

Orbits

Ballistic trajectories are orbits

• The minimum speed needed by an object to achieve orbit (and not hit the Earth at some point) is given by:

Escape velocity

More recent astrodynamics

• The vis-viva equation below allows you to calculate the speed (v) of an orbiting object at any point, as long as you know its mass (m), the object that it orbit’s mass (M), its distance from the object that it orbits (r) and its orbit’s semi-major axis (a)