Astronomy 171
Solar System Astronomy
Prof. Paul Martini

Lecture 20: Rotation and Revolution of the Earth

Key Ideas:

Demonstrations of the Earth's Rotation: Coriolis Effect; Foucault's Pendulum
Demonstration of the Earth's Revolution: Stellar Parallaxes

Eppur si muove (?)

A rotating and revolving Earth was an absurdity to strict Aristotelians: Constituted the main scientific objection to the Heliocentric System
Question:: How do you prove that the Earth really rotates about its axis and revolves (orbits) around the Sun?

Dizzying Implications

A major conceptual barrier was the enormous speed
Rotation at the Equator:: Circumference of the Earth: 40,000 km; Time for 1 Rotation: 24 hours; Speed = Distance/Time = 40,000/24 = 1,670 km/hr!

Revolution of the Earth

Orbital Motion:: Radius of the Earth's Orbit = 1 AU = 150,000,000 km; Circumference = 2 pi r = 942,000,000 km; Time for one Orbit: 365.24 days = 8,766 hours
Speed of Revolution: Distance/Time = 942,000,000/8,766 = 107,000 km/hr (or 30 km/sec)

Riding a Rotating Sphere

As you go North or South of the Equator: The East-West parallels get smaller; Still takes 24 hours to go around
Speed of rotation is fastest at the Equator: Gets slower with latitude; In Columbus it is 1,280 km/hour; Arctic Circle (66.5 degrees North) = 670 km/hour

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 1,670 km/hr; As it flies North, the Earth's rotation is slower beheath its flight
Result: a slight eastward deflection from its original northward trajectory

A litttle 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
The Coriolis force also affects weather systems: Hurricanes rotate counter-clockwise in the Northern Hemisphere; Cyclones rotate clockwise in the Southern Hemisphere

Flushing an Urban Legend

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 (e.g. water jets, swirling with hands)
The Coriolis force does not cause toilets to flush clockwise in the southern hemisphere.

Foucault's Pendulum

Built by Jean Foucault in 1851
Hung a 67 meter pendulum inside the dome of the Paris Pantheon: Started it swinging North-South; A few hours later it was swinging NE to SW; Later still 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 Pendulum

Build a pendulum at the North Pole and set it swinging toward the star Betelgeuse
An observer on Betelgeuse would see:: Direction of the pendulum's swing is constant; Earth rotates eastward one revolution per 24 hours
An observer at the North Pole would see: Earth doesn't rotate relative to the observer; Pendulum's swing rotates clockwise every 24 hours
What is rotating depends on your point of view

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

Measuring Parallaxes

Stars are more distant than peoples thought: All stellar parallaxes are less than 1 arcsecond; Nearest Star, alpha Centauri, is 0.76 arcsecond; Cannot measure parallaxes with the naked eye
First observed in 1837 by Friedrich Wilhelm Bessel for the star 61 Cygni: Used a telescope; Measured a parallax of 0.3 arcseconds
Its distance is therefore ~10 light years

The Cosmic Anticlimax

Firm observational proofs of the rotation and revolution of the Earth did not come until more than two 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 swept away the last vestiges of the Aristotelian view of the world.

See A Note about Graphics to learn why some of the graphics shown in the lectures are not reproduced with these notes.