Our Place in the Cosmos Our Place in the Cosmos Rotation of the - - PDF document

Our Place in the Cosmos Our Place in the Cosmos and and Introduction to Introduction to Astrophysics Astrophysics

Lecture 3 Patterns in the Sky - The Earth’s Rotation

Rotation of the Earth

The most familiar, literally “everyday”,

astronomical phenomenon, the passage of night and day, is due to the fact that the Earth spins on its axis [not that the Sun orbits around the Earth, as Ptolemey and others thought]

As viewed from above the North pole, Earth

rotates in a counterclockwise direction, completing one rotation in 24 hours

Rotation of the Earth

As the rotating Earth carries us from west to

east, objects in the sky appear to move in the

• pposite direction, from east to west

The meridian is an imaginary line running

directly north-south, passing through the point directly overhead, the zenith

True local noon occurs when the Sun appears

to cross the meridian at our location

Midnight is 12 hours later when we face the

• pposite direction

Location, location, location

What we see depends strongly on our latitude

(degrees north or south of the equator)

At the North Pole, you are standing on the

Earth’s rotation axis

The point directly overhead remains stationary

while everything else appears to rotate counterclockwise around this point, which is called the north celestial pole

Stars at greater angular distance from the

pole appear to follow larger circular paths

View from the North Pole

horizon

Location, location, location

Whatever your location, you can only see one half of

the sky at any given time, that half above the horizon

The half below the horizon is blocked by the Earth For most locations the visible half of the sky is

constantly changing as Earth rotates

However at the poles, one always sees the same half

• f the sky: nothing rises or sets

Objects near the horizon will follow a circular path

that keeps them the same distance above the horizon

At the South Pole, one observes the opposite

hemisphere, and stars appear to move clockwise

Latitude

Latitude measures how far north or south of the

equator a point is

Any point on the equator is at 0° latitude, the North

Pole is at +90°, South Pole -90° [we are at 50° 52’]

As one travels south from the North Pole, horizon tilts

and zenith moves away from north celestial pole

At 60° latitude, north celestial pole (NCP) is at 60°

above the horizon, the altitude of the NCP

NB pole stays fixed, it is the horizon which changes Altitude of NCP is same as northern latitude - useful

navigational aid!

Celestial poles and equator are directions in space not locations

Size of the Earth

Location of north celestial pole can be used to

measure the size of the Earth!

• Measure altitude of NCP at current location
• Head north and repeat measurement
• 290 km north NCP will have risen by 2.5°
• This is 1/144 of a complete circle (360°)
• We have therefore travelled 1/144th way round the

Earth’s circumference, which is thus 144 290 km = 42,000 km

• Actual value just over 40,000 km (radius 6,400 km)

Changing Night Sky

Apart for an observer at the poles, the visible part of

the night sky is constantly changing as Earth rotates

For observer at latitude b, stars within b degrees of

the pole are always above the horizon - they are described as circumpolar

Stars within b degrees of opposite pole are never

visible - they are always below the horizon

The remaining stars are visible for part of each night From the equator, one can observe the entire sky over

a 24 hour period

Italy Tanzania Sahara Dan Heller Photography

Celestial Sphere

An imaginary sphere centred on the Earth,

with the stars on its surface

Real stars are at varying distances, so a point

• n the celestial sphere represents a direction

in space

The celestial sphere is divided into northern

and southern halves by the celestial equator - the projection of the Earth’s equator onto the sky

The celestial equator intersects the horizon at

points due east and due west

Measuring Earth’s Spin

A point on the equator moves at 1,674

km/h due to Earth’s spin (circumference

• f earth divided by rotation period)

Not normally noticeable, apart from two

measurable effects:

• Foucault Pendulum
• Coriolis effect

Foucault Pendulum

Jean-Bernard-Léon Foucault made a 67

metre long pendulum in the Panthéon dome in Paris in 1851

A pendulum normally swings within a

fixed plane, but Foucault noticed that the plane of motion rotated in a clockwise direction (viewed from above)

Foucault realised this is because the

Earth is rotating beneath the pendulum

Foucault Pendulum

At the North Pole, a Foucault pendulum will

make a complete rotation in 24 hours

On the equator, the Earth is no longer spinning

under a pendulum and no rotation is seen

At intermediate latitudes, a pendulum will

take longer than one day to complete a rotation

Foucault’s pendulum in Paris, at a latitude of

49°, took about 32 hours to complete one period

Viewed from space Viewed from Earth Equatorial pendulum - no rotation

Coriolis Effect

Due to different speeds between different

latitudes

• Fire a cannon directly north from a point in

northern hemisphere

• Ball has west-east motion due to movement of

cannon

• Because rotation slows away from the poles, ball is

moving eastward faster than its target

• For a ground-based observer, ball appears to curve

eastward more and more the further north it travels

• Opposite effect if you fire to the south

Coriolis Effect

Coriolis effect causes counterclockwise

rotation of northern hurricanes, clockwise rotation of southern ones

Imagine a low-pressure system in the north

• Air flowing up from lower latitudes will be

deflected to the right of the system

• Air flowing down from higher latitudes will be

deflcted to the left

• Result is counterclockwise rotating wind pattern

Summary

Night and day, and the apparent motion of the

Sun and stars are due to the Earth’s rotation

Latitude may be determined from the altitude

• f the celestial poles

Changing altitude of pole with latitude

provides estimate of Earth’s radius

Earth’s rotation demonstrated directly by two

• bservable effects: Foucault pendulum and

Coriolis effect

Next Friday, 12 October

Peter Thomas will give the 9am lecture and

hold the 10am workshop for Intro to Astrophysics

The 10am workshop for Our Place in the

Cosmos is postponed until later in the term for a multiple-choice quiz

Instead, I will pose a few questions for

discussion on the Study Direct Open Forum