That’s the trouble with science. You’ve
got a bunch of empiricists trying to describe things of
unimaginable wonder.
Gravity & Orbits
Solar System AstronomyChapter 3
But first… history
Solar System Astronomy
Some History Ancient cultures & astronomical
knowledge Already in the stone and bronze ages, human
cultures realized the cyclic nature of motions in the sky.
Monuments dating back to ~ 3000 B.C. show alignments with astronomical significance.
Those monuments were probably used as calendars or even to predict eclipses
Some History Ancient cultures & astronomical
knowledge Nebra sky disk
~1600 BC bronze disk ~30cm diameter sun or full moon, a lunar crescent, and stars
(including Pleiades) two golden arcs along the sides marking angle between the solstices arc at the bottom perhaps
Milky Way or Rainbow
Some History
Some History Ancient cultures & astronomical knowledge
Often timekeeping methods Some objects ‘wandered’
Greek πλανήτης, derivative of the word πλάνης "moving”
7 in the sky Sun Moon Mars Mercury Jupiter Venus Saturn
Some History Ancient cultures & astronomical knowledge
Often timekeeping methods Some objects ‘wandered’
Greek πλανήτης, derivative of the word πλάνης "moving”
7 in the sky Sun Dimanche Moon Lundi Mars Mardi Mercury Mercredi Jupiter Jeudi Venus Vendredi Saturn Samedi
Some History Ancient cultures & astronomical
knowledge Often timekeeping methods Lunar cycles gave rise to months
Some History Ancient cultures & astronomical
knowledge Often timekeeping methods When is Easter?
observed on the Sunday after the first full moon on or after the day of the vernal equinox
full moon involved is not an astronomical full moon, but an ecclesiastical moon – though it coincides more or less with the astronomical full moon
Easter falls on the first Sunday following the first ecclesiastical full moon that occurs on or after March 21 (the day of the ecclesiastical vernal equinox)
Some History Ancient cultures & astronomical
knowledge Often timekeeping methods Sirius, the Dog Star
seiros σείριος, “scorcher” Rising just before Sun marks the beginning of
summer
Some History Ancient Greece
Astronomy was a branch of mathematics Astronomers sought to create geometrical
(mathematical) models that could imitate the appearances of celestial motions
tradition began with Pythagoreans, who placed astronomy among the four mathematical arts (along with arithmetic, geometry, and music)
Our conception of astronomy (and many sciences) inherited from Ancient Greek
Some History Ancient Greece
Eudoxus Aristotle Eratosthenes Hipparchus Ptolemy
All sought to describe motion of heavenly bodies
Mathematical behavior of motion
Some History Ancient Greece
Eudoxus (4009 – 356 BC) assigned to each planet a set of 27 concentric
spheres first to attempt a mathematical description of the
motions of the planets
Some History Ancient Greece
Aristotle (384 – 322 B.C.) major authority of philosophy until late Middle Ages divided universe into two parts
imperfect, changeable Earth perfect heavens (described by spheres)
expanded Eudoxus’ model to 55 spheres Aristotle taught the Earth is round
Why would he think that?
Some History Ancient Greece
Aristotle (384 – 322 B.C.) perhaps the philosopher most respected by
European thinkers during and after the Renaissance erroneous positions taken as a given, which held
back science analysis of procreation presupposes:
active, ensouling masculine element bringing life to
inert, passive, female element assertion that objects of different mass fall
at different speeds under gravity refuted by Philoponus
Some History Ancient Greece
Aristotle (384 – 322 B.C.) held back science for 2000 years
refuted Democritus's claim Milky Way was multitude of stars
refuted stars of night sky were just like Sun calculated they would have to be
millions of times farther away than Sun thus dismissed for hundreds of years
theory of the natural slave was used to justify European domination of Native Americans
On Animals…
Some History Ancient Greece
Eratosthenes (276 BC - 194 BC) Greek mathematician, geographer and astronomer
contemporaries nicknamed him Beta (2nd letter of alphabet) –supposedly proved himself to be the second in the Mediterranean world in many fields
first known to have calculated the size of the Earth
Some History Ancient Greece
Eratosthenes (276 BC - 194 BC) Angular distance between Syene and
Alexandria is ~ 7° Linear distance ~ 5,000 stadia Earth Radius ~ 40,000 stadia
probably ~ 14 % too large
Some History Ancient Greece
Hipparchus (2nd century BC) access to Babylonian observations & predictions
used to create better geometrical models, constructed accurate models for movement of Sun & Moon
moved Earth from center of spheres compiled star catalogue
recorded the position and brightness of the stars Considered among most important Greek astronomers
(& greatest astronomer of antiquity by some) introduced the concept of exact prediction into
astronomy last innovative astronomer before Ptolemy
Some History Ancient Greece
Ptolemy (c. 90 – c. 168) compiled and extended the astronomical knowledge
and theories of the ancient Greek & Babylonian world
star catalog in Almagest lists forty-eight constellations
ancestral to the modern system of constellations geocentric model widely accepted until Copernicus
Some History Ancient Greece
Ptolemy (c. 90 – c. 168) Retrograde motion…
Some History Ancient Greece
Ptolemy (c. 90 – c. 168) Epicycles…
Some History Ancient Greece
Ptolemy (c. 90 – c. 168) Epicycles Ptolemaic system was considered the “standard
model” of the Universe until the Copernican Revolution
Some History Copernican Revolution & beyond
99 years that changed our view of the Universe
Nicolaus Copernicus Galileo Galilei Tycho Brahe Johannes Kepler Isaac Newton
Some History Copernican Revolution
Copernicus (1473-1543) one of the great Renaissance polymaths mathematician, astronomer, jurist,
physician, classical scholar, governor, administrator, diplomat, economist, and soldier
Some History Copernican Revolution
Copernican Model No center to universe Center of Solar System near sun
heliocentric Distance to Sun imperceptible vs distance to stars Earth’s motion accounts for apparent motion:
rotation accounts for daily rotation of stars annual cycle of Sun’s movements caused by Earth’s
orbit apparent retrograde motion of planets is caused by
orbit
Some History Copernican Revolution
Copernican Model arrived at correct order of the known planets Explained precession of the equinoxes correctly
slow change in the position of the Earth's rotational axis
gave a clear account of the cause of the seasons Earth's axis not perpendicular to plane of orbit
added motion to Earth, keeping axis pointed throughout the year at the same place in the heavens
Some History Copernican Revolution
Copernican Model not experimentally better than Ptolemy’s from 1543 publication until about 1700, few
astronomers were convinced by the Copernican system, though the book was relatively widely circulated
influenced Galileo & Kepler, others
ironically, this was at the behest of the Catholic Church as part of the Catholic Reformation efforts for a means of creating a more accurate calendar for its activities
Some History Copernican Revolution
Galileo (1564 – 1642) Italian
physicist astronomer astrologer philosopher
closely associated with the Scientific Revolution
Some History Copernican Revolution
Galileo (1564 – 1642) improved (but did not invent) telescope invented first known microscope observed Galilean moons
motion indicated orbits about Jupiter observed rings of Saturn observed full set of phases with Venus
Some History Copernican Revolution
Galileo (1564 – 1642) improved (but did not invent) telescope invented first known microscope observed Galilean moons
motion indicated orbits about Jupiter observed rings of Saturn observed full set of phases with Venus
Some History Copernican Revolution
Galileo (1564 – 1642) one of first Europeans to observe sunspots
Existence contradicted unchanging perfection of the heavens (Aristotle)
First to report lunar mountains & craters Concluded “rough and uneven, and just like the
surface of the Earth Not Aristotle’s perfect sphere
Observed the Milky Way Found to be multitude of distant stars
Some History Copernican Revolution
Galileo (1564 – 1642) Demonstrated equal acceleration of unequal masses
Contrary to Aristotle Determined rate objects fell Demonstrated velocity constant (not zero) without
outside force Contrary to Aristotle
Basic principle of relativity
Some History Copernican Revolution
Galileo (1564 – 1642) Early example of science conflicting with
Church/authority 1633 Heresy
required to recant heliocentric ideas idea that Sun is stationary condemned as “formally
heretical” heliocentrism was never formally or officially
condemned ordered imprisoned
sentence later commuted to house arrest Dialogue Concerning the Two Chief World Systems banned
and all past & future books
Some History Copernican Revolution
Tycho Brahe (1546 – 1602) preeminent observational astronomer of pre-telescopic
period said to own 1% of Denmark’s entire wealth at one observations of stellar/planetary positions unparalleled
accuracy observations of nova contradicted immutable heavens
Lost nose in duel 1566 Fair amount of drinking involved Replacement of silver & gold
Kept a jester (Jepp) beneath the table during dinner Believed to be clairvoyant
Tame elk (or moose)…
Some History Copernican Revolution
Kepler (1571 – 1630) German Mathematician, astronomer, astrologer,
sci-fi writer
Some History Copernican Revolution
Kepler (1571 – 1630) Used the precise observational tables of Tycho Brahe
to study planetary motion mathematically Consistent description by abandoning both
Circular motion Uniform motion
Planets move around the sun on elliptical paths, with non-uniform velocities
Some History Copernican Revolution
Kepler (1571 – 1630) Kepler’s Laws
1) The orbits of the planets are ellipses with the sun at one focus
2) A line from a planet to the sun sweeps over equal areas in equal intervals of time
3) A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed
Some History Copernican Revolution
Kepler’s Law
#1 & #2
Some History Copernican Revolution
Kepler’s Law
#3
Kepler’s Laws
Some History 99 years changed our universe
Some History Copernican Revolution
Where do Kepler’s Laws come from?
Why are they true?
We don’t know…Until
Newton.
Some History Copernican Revolution
Where do Kepler’s Laws come from?
Why are they true?
We don’t know…Until
Newton.
Sir Isaac Newton, FRS
Newton’s Laws Newton discovered laws applying to all
objects Universal Describe forces that act on all objects
Like gravity
Newton’s Laws of Motion Stationary objects stay stationary, moving
objects stay in constant motion Unless a force acts upon it “constant” refers to speed AND direction Forces change motion
No change in motion means no forces OR balanced forces
#1
Newton’s Laws of Motion Force = mass × acceleration
F = ma a = F/m
More mass » less acceleration Larger force » larger acceleration
#2
Newton’s Laws of Motion Forces always come in pairs
Same size Opposite direction
Applies to ALL forces, including gravity
#3
Newton’s Law of Gravitation The story of the apple…
Newton’s Law of Gravitation The story of the apple…
Plague years 1665-1666, Newton sat in his garden at Woolsthorpe
Wondered at the fall of an apple
Newton’s Law of Gravitation The story of the apple…
The force that drew the apple to Earth certainly extended to far greater heights
What if it reached as far as the Moon? The circling Moon and falling apple are fellow
captives of the Earth And perhaps the Sun likewise holds all the planets in
thrall
A Law of Universal Gravitation!
Newton’s Law of Gravitation The story of the apple…
The force that drew the apple to Earth certainly extended to far greater heights
Newton’s Law of Gravitation The story of the apple…
What did Newton start with? Galileo – equal acceleration of unequal masses Kepler – P2 = a3
Circular motion F = ma What is a?
Δv/Δt
Newton’s Law of Gravitation The story of the apple…
We start at circular motion
Newton’s Law of Gravitation The story of the apple…
Kepler’s Law also tells us something
Newton’s Law of Gravitation The story of the apple…
So we put them together And what else is important?
Mass(es)
Newton’s Law of Gravitation The story of the apple…
They say he derived Kepler’s rules from his law of gravity…
…but it was the other way around
Newton’s Law of Gravitation Gravity is a force between any two
objects. It depends on the objects’ masses It depends on the distance between them
Important! Gravity is a mutual force, acting on both
bodies The force on each body is the same size (but
has the opposite direction)
Newton’s Law of Gravitation Gravity is a force between any two
objects. It depends on the objects’ masses It depends on the distance between them
Variables M & m, or m1 & m2, are the two masses The force on each body is the same size (but
has the opposite direction)
Newton’s Law of Gravitation Orbital velocity Escape velocity
Newton’s Law of Gravitation The story of the apple…
Ideas… Why doesn’t the Space Shuttle fall from
space? Is gravity still acting on it?
What does weightless mean?
Einstein & Relativity Special Relativity General Relativity
Confirmation
Albert Einstein (1879 – 1955) Annalen der Physic 1905
“On a Heuristic Viewpoint Concerning the Production and Transformation of Light”
“On the Motion — Required by the Molecular Kinetic Theory of Heat — of Small Particles Suspended in a Stationary Liquid”
“On the Electrodynamics of Moving Bodies” “Zur Elektrodynamik bewegter Körper”
Annus Mirabilis papers
Albert Einstein (1879 – 1955)
Who cares about Einstein Anybody who wants to pass this course… Anyone who want to use GPS…
Moving clocks slow (-7 ms/day) Orbiting clocks fast (+45 ms/day) Net 38 ms fast each day
GPS would stop working in 2 minutes 10 km error adds up each day
Albert Einstein (1879 – 1955)