Sunlight on Earth

Movement and shape of the planet

GEOLOGYTWO

JD Price

Optimist: Glass is half full

Pessimist: Glass is half empty

Scientist: Right conical container, h

= 14 cm, u.d. = 10 cm, l.d. = 8

cm, made of Na-Ca-Si-O glass

contains 250 ml of a white-colored

lipid-protein aqueous colloid

overlain by 265 ml of air

(transparent N-O dominated gas

mixture).

h

u.d.

l.d.

air

colloid

Energy

There are only two sources of energy

1. The EarthHeat from interior

Gravitational potential (topography)

Earth materialsRadioactive elements

Lunar interactions (tides)

2. The SunRadiation from surface

Storage in buried hydrocarbons

In biomass

Weather (wind)

UV radiation - NASA

The Sun

Much of the emitted

energy within the sun is

produced by fusion of

elements in the core

(principally H into He).

Heat is moved outward

radiatively in the deep

interior, convectively in

the near surface.

It’s magnetic field limits

the escape of charged

particles.

Graphic - UCal Berkeley

EM Spectrum

Visible light

Wavelengths (!)- in nm and Angstroms

! and velocity are related v = !f, and v = c

FREQUENCY (f) number of cycles per unit time [units = Hertz (Hz)]

1 Hz = 1 cycle/s

Period T = 1/f; f = 1/T; T f = 1

WAVELENGTH (!) is the distance occupied by one cycle [units=meters]

Waves

Objects radiate light because of their high temperatures -

incandescentincandescent.

Light (EM) is produced whenever a charge is accelerated by an

external force...

electromagnetic wave model Image by E.B. Watson

Electromagnetic radiation

The wavelength distribution of an object is a function of its surface

temperature. Hot things emit more radiation at shorter wavelengths.

Blackbody radiation

v = !f,

and v = c

5487oC

Surface

of the

Sun

Seeing the light

Peak solar

%

Intensity

Slide by EB Watson

Sunlight

Not all sunlight makes it to the surface of the planet. The gasses in the

atmosphere absorbs appreciable amounts of the spectrum (specific wavelengths

and much of the intensity at shorter wavelengths.

Orbit – gravitational movement

Revolution is counter clockwise (from

top)

Not constant velocity

Mercury 0.24 years

Pluto 248.6 years

Revolution

Earth Revolution

ravg = 150 E 6 km (93 E 6 mi) = 1 A.U.

Closest in January

perihelion (- 2.5 E 6 km)

Furthest in July

aphelion (+ 2.5 E 6 km)

Inclined at 23.5o to the ecliptic (orbit) plane

Equinoxes and Solstices – seasonal variation

Aphelion

Shape of the Earth

• What observations do you have?

• Are you able to explain these?

• Could you predict behavior not

observed?

• Are you able to validate your

predictions?

More about rotation later…

Axis of rotation

Please note: axis of rotation is constant

23.5o throughout the year!

Revolution with tilt – reason for seasons

Precession

Result of oblate shape and the moon

Axis wobble with a 26,000 year period

Vega will be the North Star in another 12,000 years

Helical PathHelical Path

RotationRotation

Mercury 58.65 days

Venus 243.01 days (r)

Earth 23 h 56 min 4.1 s

Mars 24 h 37 min 22.6s

Jupiter 9 h 50.5 min

Saturn 10 h 39 min*

Uranus17 h 14 min (r)

Neptune 16 h 3 min

Pluto 6.39 days (r)

Planets need not rotate, but all do

Duration of one rotation

Earth’s moon does not rotate

with respect to the Earth

2004 Cassini’s observations

10 hr 45 min 45 ± 36 sec.

1980-81 Voyager flybys

10 hr 39 min 24 ± 7 sec

6 minutes slower now - Three

options

1. Saturn is slowing

2. Voyager or Cassini

measurement is incorrect

3. Decoupling of the rotation

signal

Saturn

http://www-pw.physics.uiowa.edu/space-audio/

50 to 500 kHz electromagnetic wave called Saturn

Kilometric Radiation (SKR)

Measuring Rotation on Gaseous Planets

Rotation

Photo © F. Giovannangeli

Apparent Sidereal Movement

Careful observation of

the night sky show

rotation around a pole

(pole star currently).

This famous time-lapse

photograph shows this

progression over the

course of the night.

Foucault Pendulum

Once started, the pendulum moves back and forth in the

same plane. If the surface beneath it is rotating, then the

plane’s trace on that surface will change.

The earth's rotational velocityObjects moving north or south pass over the surface that is

rotating at a lesser velocity - deflection in the object path.

French engineer-

mathematician Gustave-

Gaspard Coriolis

calculated the effect of

the changing velocity on

the ground as one

changes latitude

Hypothetical Spain-Ivory Coast missile exchange

v at poles = 0 km/hr v at equator = 1,670 km/hrv at poles = 0 km/hr v at equator = 1,670 km/hr

Intended path

Actual path

DetailsKeep in mind that rocket is

launched moving with earth

at the velocity of the

latitude - example equator.

On the diagram, I show the

“overshoot” of this missile

as a function of its velocity

in 10º increments

Simply "e = V - Vi

A more sophisticated

treatment:

!

ac =ve

vn

"

# $

%

& ' 2( sin)

# is angular momentum

$ is latitude

Ve is the velocity to the

east

Vn is velocity to the north

The small force due to the decreasing v in rotationThe small force due to the decreasing v in rotation

as one moves north or south from equator.as one moves north or south from equator.

Northern hemisphere Northern hemisphere –– right deflection, right deflection,

counterclockwisecounterclockwise

Southern hemisphere Southern hemisphere –– left deflection, clockwise left deflection, clockwise

You can see thisYou can see this air travel, satellite air travel, satellite

movement, winds and related weathermovement, winds and related weather

phenomena, a really specialized basin-phenomena, a really specialized basin-

drain system.drain system.

You canYou can’’t see thist see this the draining of water the draining of water

in average bathroom fixturesin average bathroom fixtures

Coriolis Effect

Greek naturalist

Eratosthenes – 250 B.C.

Alexandria

Syene (Aswan)

Highest latitude of direct

sunlight (June 21), Tropic of

Cancer

Copyright © 1998 Oriental Institute, University of Chicago

http://www-oi.uchicago.edu/OI/INFO/MAP/SITE/

Size of the Earth

Noon, Summer Solstice

7o / 360o = 1 / 51.4

5,000 stadia between cities

Circumference of the Earth =

257 kstadia

Spherical Earth

Great, what’s a stadium?

~185m

842 km between Syene and Alexandria

So Ce = 47,545 km

Actual modern measurement of Ce = 43,278 km –

Not bad

Circumference of theCircumference of the

Earth = 257 Earth = 257 kstadiakstadia

Stadia

The cosmos of the Zetetics.

Picture © 1992 by Robert Schadewald

"The facts are simple, the earth is flat…sunrise and sunset are

optical illusions."Charles K. Johnson

the late president of the International

Flat Earth Research Society.

Aristotle's proof ~330 BCE

1. Things fall straight down -

a nonspherical earth

requires attraction

towards the center, which

is not always straight

below.

2. The shadow of the Earth

on the Moon is circular

Round Earth

The Earth is actually an oblate

spheroid

•de = 12,756 km (7,926 mi)

•dm = 12,714 km (7,900 mi)

•Asymmetrical – North pole is

higher than average surface,

South pole is lower.

18-351

Meridians – great circles

Longitude – arc angle from

prime

Polar Coordinates

Parallels – small circles &

equator

Latitude – arc angle from

equator

Please note: 23.5o is the same as 23o 30’

Important Latitudes

GNU free license image

Chester A. Arthur’s

most enduring legacy*

(1884)

*Not considering his ridding the White House of Federalist-era antiques.

Important Longitude

http://rubens.anu.edu.au/

John Harrison’s H4

First “accurate” sea-worthy

chronograph

Latitude is a no-brainer: the position of the sun or a

star and days since solstice

Longitude is much trickier.

Accurate time keeping to a known

solar reference point

-or-

Detailed calculations on the positions

of planets and moons

More on time later…

Apparent Solar Day

One rotation = 86,164 s

Mean solar day = 86,400 s

The length of a day

depends on what you’re

watching. The time

between seeing the sun

appear at its highest point

in the sky is longer than

the time between seeing

a star appear at its highest

point in the sky. The sun

is much closer than any

other star, as such the

earth has to rotate a little

further to bring it back to

the same place in the sky.

The elliptical nature of the earth’s orbit means that the time between sightings of the

sun overhead is shorter in early April and later in October. If their were no tilt to the

earth, the sun would always shine directly on the equator, and the distribution of times

between the sun passing its highest point in the sky would look like the graph above.

Orbit Effect

Tilt is also affects the time between sightings of the sun at local noon. If the earth

moved around the sun in a circular orbit (not elliptical), the time between the sun’s

appearance at its highest point in the sky would look like this graph.

Tilt Effect

Orbit and Tilt Variation

-20

-15

-10

-5

0

5

10

15

20

21-

Dec

20-

Jan

19-

Feb

21-

Mar

20-

Apr

20-

May

19-

Jun

19-

Jul

18-

Aug

17-

Sep

17-

Oct

16-

Nov

16-

Dec

Late

(M

inu

tes)

Earl

y

However, earth is rotating at a tilt and moving along and elliptical orbit. The net

effect of both motions produces the above distribution of times between local noon

events.

Photographing the sun or marking the location of a sunbeam on the floor

of a room with a skylight every 24 hours over the course of a year results

in a shape known as the analemma. The analemma was an important

navigational tool in the pre-GPS world, and was commonly included on

maps of the time.

Solar position

Of course, solar energy applications

require understanding the analemma. It is

also useful in areas such as

architecture, landscaping,

photography, and outdoor graphic

design.

Standing Still?

Minor changes in Earth orbit, tilt,Minor changes in Earth orbit, tilt,

time of time of parihelionparihelion

360,000 mi/hr360,000 mi/hr580,000 km/hr580,000 km/hrGalactic movementGalactic movement

700,000 mi/hr700,000 mi/hr1,000,000 km/hr1,000,000 km/hrStar group movement relative toStar group movement relative to

othersothers

230,000 mi/hr230,000 mi/hr370,000 km/hr370,000 km/hrSolar system movement aroundSolar system movement around

Milky Way coreMilky Way core

~66,000 mi/hr~66,000 mi/hr106,000 km/hr106,000 km/hrRevolution Revolution vvavgavg

~30 mi/hr~30 mi/hr50 km/hr50 km/hrRevolution around Earth-MoonRevolution around Earth-Moon

gravitational centergravitational center

~1,040 mi/hr~1,040 mi/hr1,670 km/hr1,670 km/hrRotation at equatorRotation at equator

In terms of absolute motion – all historical locations on Earth

are grossly inaccurate

The Home Planet

•Third planet from the sun

•Fifth in diameter and mass

•First in density

•Strong magnetic field

•Atmosphere rich in oxygen (O), carbondioxide (CO2), and nitrogen (N)

•Surface temperatures and pressurespermit liquid H2O.

NASA Clementine

Insolation

As we will see, a number

of atmospheric factors

affect the distribution of

sunlight on the Earth.

The top graphic shows

the distribution on top of

the atmosphere. The

bottom shows the

amount received on the

surface.

We will spend the next

few weeks evaluating

this.