Transcript Copernicus, Galileo, Kepler`s laws of planetary motion, Newton`s

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)