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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