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Announcements
HW#1 due today
Study guide and other comments about Quiz #1 on Monday and Wednesday
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A comet has an orbit with a semi-major axis of 15 AU. What can you conclude?
a) The comet’s orbit is circular
b) The comet is always closer to the Sun than the Earth is
c) The comet’s orbital period is longer than 1 Earth year
d) The comet will be moving slowest at perihelion
e) The comet will crash into Earth
Exploding Star in M82!
Lecture 6:Copernican Revolution Completed
Astronomy 1143 - Spring 2014
Key Ideas:Demonstrations of the Earth's Rotation:
• The Coriolis Effect
• The Foucault Pendulum
Demonstration of the Earth's Revolution:
• Stellar Parallaxes
• Aberration of Starlight
Measuring the Scale of the Solar System
• Distance from Earth to Sun first accurately measured using Transits of Venus
• Full scale of the Solar System revealed
Copernican Revolution completed
The work of Galileo and Kepler had overthrown the geocentric view of the Universe
However, none of the observations of theoretical work actually proved that the Earth moved
Geocentric models could be made to work, though not attractively
See for example Tycho’s hybrid system from the reading.
Does the Earth move?
A rotating & revolving Earth seems to disagree with the senses• Constituted the main scientific objection to the
Heliocentric System• Geocentric versions can be made that agree
with positions and phases
How do you prove that the Earth really rotates about its axis and revolves? (orbits) around the Sun?
As you go north or south of the Equator:
• East-West parallels gets smaller
• Takes 24h to go around
Speed of Rotation:• Fastest at the Equator
(1670 km/h)• Gets slower with latitude:
Columbus (40ºN):
1280 km/h
Arctic Circle (66.5ºN): 666 km/h
Riding a Rotating Sphere
Coriolis Force
Gustave Coriolis (1835)
Deflection due to Earth's Rotation:• Fire a cannonball North from the Equator• The cannon is moving east with the Earth's
rotation at 1670 km/hr• As it flies North, the Earth’s rotation is slower
beneath its flight.
Result: a slight eastward deflection from its original northward trajectory.
A little to the right (or left)…The result of the Coriolis force is:
• Projectiles swerve right at northern latitudes• Projectiles swerve left at southern latitudes.
Long-range artillery and guided missiles are designed to correct for the Coriolis force.
Also affects weather systems:• Hurricanes rotate counter-clockwise in the
Northern Hemisphere.• Cyclones rotate clockwise in the Southern
Hemisphere.
Typhoon Nagi (North)
Tropical Cyclone Edzani (South)
Flushing an Urban Legend
The Coriolis force does not determine the direction water swirls down drains (or toilets)
• Size of a sink, tub, toilet, etc. is too small
• Coriolis effect is much smaller than other motions, (water jets, swirling with hands)
Toilets do not flush clockwise in Australia
(or any other place south of the Equator).
Foucault Pendulum
Built by Léon Foucault in 1851.
Hung a 67-meter pendulum insidethe dome of the Paris Pantheon.
• Started it swinging North-South
• A few hours later, it was swinging NE-SW
• Later it was swinging East-West.
The change in the direction of the swing is due to the rotation of the Earth.
The Pole and the PendulumBuild a pendulum at the North Pole and set it
swinging towards the star Betelgeuse:An observer on Betelgeuse would see:
• Direction of the pendulum's swing is constant.• Earth rotates eastward every 24 hours.
Observer at the North Pole would see:• Earth doesn't rotate relative to the observer.• Pendulum's swing rotates clockwise every 24hrs
What is rotating depends on your point of view.
Towards Betelgeuse
You Tube video of Foucault’s pendulum
Off of the Spinning Earth
Stellar Parallaxes
As Earth orbits around the Sun, it moves 2 AU from one side to another in 6 months.• A nearby star would appear to shift position
with respect to more distant stars.• The apparent shift is the "stellar parallax"
It was not observed in Copernicus' time:• Principal objection to the Copernican system• The stars are too far to have large enough
parallaxes to measure without telescopes
December
Trigonometric Parallaxes
June
Distant Stars
ForegroundStar
p = parallax angle
Parallaxes of Stars
Stellar parallaxes are very small• All are smaller than 1 arcsecond• 1 arcsecond = the angle spanned by a dime at
2.5 miles• Large distances to stars = not observed before
telescopes and specialized instruments• First parallax observed in 1837 (Bessell) for the
star 61 Cygni.• Copernicus’ explanation for why stellar
parallaxes were not easily observed is correct
What’s the nearest star?(
Proxima Centauri, a not-too-bright star in the constellation Centaurus
p = 0.77 arcseconds
Nearest Star after the Sun
Where is the rain coming from?
Aberration of Starlight
Stars also appear to shift their positions because of the aberration of starlight
This effect happens because the motion of the Earth around the Sun + the finite speed of light makes stars appear to come from a slightly different direction
Effect is similar to “horizontal rain” if traveling at highway or airplane speeds through a rain storm
First shifts detected
1680 – Jean Picard measured shifts in the positions of stars by using crosshairs in his telescope
40 arcseconds for Polaris
~20 arcseconds in general
1728 – James Bradley identifies the cause as the motion of the Earth
1675 – Ole Romer estimates the speed of light from the timing of Jupiter’s moons
The Cosmic AnticlimaxFirm observational proofs of the rotation and
revolution of the Earth did not come until more than 2 centuries after the death of Copernicus.
By then, the use of the telescope and the revolution in thought started by Isaac Newton's laws of motion and gravitation had made the heliocentric version of the solar system the accepted version.
Measuring Distances: Parallax
Kepler’s Third Law
Transits of Venus
If we know the distance between the Earth and Venus (in km, or miles, etc), we can determine the distance to the Sun using Kepler’s Third Law
Currently, we bounce radar signals off of Venus to determine the distance to Venus.
But the first measurements of the distance to Venus came from measuring transits of Venus.
1882 Transit of VenusVenus appears as a small black dot on the Sun
Every ~ 100 years, there are two eclipses separated by 8 years
Last ones were in 2004, 2012
Next one Dec 2117
Transit of Venus – June 6, 2012
Parallax of VenusObservations of Venus from North and South will appear at different
places on the Sun
A’B’AB
A’B’ AB
Earth Sun
Venus
Parallax of Venus
Measuring the distance between AB and A’B’ is very difficult
Measuring the time it takes to go from A to B vs. A’ to B’ is simpler (but not simple!)
Need widely spaced north-south observations of the transit of Venus
Major expeditions were launched in 1761 and 1769 to time the transits of Venus.
In the Name of Science…..Guillaume Le Gentil
• 1761: couldn’t observe on a ship near India• 1769: couldn’t observe due to clouds in India
(but Phillipines clear!)• Returned home to find that he had been
declared dead, estate gone
Jean Chappe• 1769: died of fever in Baja California
(Charles) Mason and (Jeremiah) Dixon successfully observed the 1761 transit together
The Size of the Solar System
From Greek measurements
1 AU=7.5 million kilometers
From 1761 and 1769 transits
1 AU=153 million kilometers
From 1761, 1769, 1874, 1882 transits
1 AU=149.59 million kilometers
From modern radar measurements
1 AU=149.60 million kilometers
In-Class Scale Models
A Scale Model of the Sun-Proxima Centauri
By the mid-1800sConfirmation that the Earth rotated on its axis and
revolved around the Sun
Correct scale for the Solar System known
Can use this to find the Sun’s radius, mass, and luminosity
Sun not 5x bigger than the Earth, but 110x bigger than the Earth!
Astronomy was moving from looking at motions in the sky to understanding the physical nature of bodies
Astronomy to Astrophysics – universal laws of nature