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PTYS 214 – Spring2011 Homework #3 DUE in class TODAY Class website: http://www.lpl.arizona.edu/undergrad/classes/spring2011 /Pierazzo_214/ Useful Reading: class website “Reading Material” http://en.wikipedia.org/wiki/Sun http://www.solarviews.com/eng/sun.htm Announcements

PTYS 214 – Spring2011 Homework #3 DUE in class TODAY Class website: Useful

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Page 1: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

PTYS 214 – Spring2011

Homework #3 DUE in class TODAY

Class website: http://www.lpl.arizona.edu/undergrad/classes/spring2011/Pierazzo_214/

Useful Reading: class website “Reading Material”http://en.wikipedia.org/wiki/Sun

http://www.solarviews.com/eng/sun.htm

Announcements

Page 2: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Classification of living organisms by carbon and energy sources

Plants are… Humans are…

Nutritional Type Energy Source Carbon Source

Photo-autotrophs Light CO2

Chemo-autotrophs Inorganic Compounds

(H2, NH3, NO2, H2S)

CO2

Photo-heterotrops Light Organic Compounds

Chemo-heterotrops Organic Compounds Organic Compounds

Page 3: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Life needs energy

Photosynthesis:

6CO2 + 6H2O + h (Energy) → C6H12O6 + 6O2

99.9% of energy at the Earth’s surface is from

Solar Radiation

Page 4: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

The Sun

~4.6 billion years old

G2 class star (~8% of stars are G class) based on photospheric temperature

In our galaxy >100 million stars are of the same class

Sun in X-rays NASA/ESA SOHO

Page 5: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

The Sun – Basic FactsDistance from Earth 1 AU = 1.5×108 km Mass

333,000 Earth Masses99% mass of the Solar

system

Diameter109 Earth Diameters

Composition (by mass)74% Hydrogen24% Helium<2% other elements

Average Density1410 kg/m3

Sun and Planets to scale

Page 6: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

The size of the Sun is due to the overall balance between two main forces:

Sun Size: Hydrostatic Equilibrium

1) Gravity: Tremendous weight of the mass of the Sun that presses inward under the force of gravity

2) Pressure: Enormous pressure inside the Sun (generated by nuclear fusion) that pushes outward

The life of any star is a constant balancing of

Gravity & Pressure

Page 7: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Solar Structure

(7 Million K)

(2 Million K)

Nuclear Fusion

Page 8: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Fusion Reactions

Combine atomic nuclei to form a heavier nucleus (a heavier element)

12C + 1H→13N + γ (Energy)

(C and H combine to form a new element, N)

Very different from Chemical Reactions:

Deal with electrons binding atoms of certain elements into molecules, but the elements (nuclei) do not change:

6CO2 + 6H2O + h (Energy) → C6H12O6 + 6O2

(number of C, H and O atoms does not change)

Page 9: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Nuclear fusion reactions can happen only under very high temperatures and pressures

Energy released in nuclear fusion reactions is ~1,000,000 times larger than in chemical reactions

Hydrogen bomb

Page 10: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

The Sun’s Energy Source is NuclearFusion in its Core

Nuclear fusion occurs only at the very high temperatures and pressures at the Sun’s core

Proton-proton chain

Four hydrogen nuclei “fuse” to form a single helium nucleus

It will continue to heat the Sun for another 5 billion years

Page 11: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Proton-Proton Chain

One He nucleus has 99.3% of the weight of four H nuclei

Excess 0.7% mass is converted into energy: E=mc2

Page 12: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Energy Transfer in the Solar Interior

The convection zone is a region right below the visible surface of the Sun

Here, turbulent convective motions occur, similar to a pot of boiling water

These bubbling motions are responsible for the granulation pattern seen on the Sun’s surface (photosphere)

Core: Nuclear Fusion 1.57107 K ~28,000°F

Convection zone:2.2106 K

Solar surface: 5,800 K

Page 13: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

(in the photosphere)

They are 100s to1000s

of km wide

Solar Granulation

Page 14: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Photosphere: Visible surface of the Sun

Mean surface temperature

5,800K (~10,000 oF)

The most obvious features on the surface of the Sun, sunspots have been observded since the 17th century (Galileo)

Page 15: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Sunspots

Sunspots vary greatly in size; typical ones measure a few tens of thousands of kilometers

A Sunspot's life can be as short as an hour or two or as long as several months

They clearly show the Sun’s 27-day rotation!

Regions of low temperature and intense magnetic fields

Page 16: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

The Corona Outermost layer of the solar

atmosphere, made of very high-temperature gases at extremely low density

It is extremely hot: temperatures reach up to about 2 million K

What heats the corona remains an open question!

Material (charged particles) from the corona is continuously blown away from the Sun towards space: Solar wind

Visible light

X-rays

Page 17: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Energy from the SunOnce energy reaches the Sun’s surface, it is radiated

outward, into space

Solar Luminosity: Total energy emitted by the Sun per second

L = 3.84 x 1026 W = 3.84 x 1026 J/s

Page 18: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Energy Conversion

The biggest hydrogen bomb ever exploded (Tsar Bomba) was ~50 Megatons of TNT (>3000 times Hiroshima) 1 ton TNT = 4.184×109 J

How many Tsar bombs would be necessary to explode per sec to obtain Solar Luminosity?

1 Tsar bomb = 2.1×1017 J

~ 1.8 billion Tsar bombs per sec!

/s101.8Tsar# 9s

Page 19: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Solar Flux - Luminosity divided by the area over which it is distributed (energy per sec per unit area)

The area over which solar luminosity is distributed increases with distance from the Sun

How?

How does the solar flux change with distance from the Sun?

Why is Earth not destroyed by the energy coming from the Sun?

)A(m

L(J/s)S

2

Page 20: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

As energy moves away from the Sun, it is spread over a greater area

Inverse Square Law

Solar constant:

Page 21: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

The Solar Constant

1. Determine the area of distribution at the Earth’s orbit

A=4πdE2

1 AU = 1.496×1011 m

2. Divide L by A

23223

26

W/m101.37m102.81

W103.84

A

LS

Page 22: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Each planet has its own solar constant…

…depending on its distance from the Sun

Page 23: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

SE ~ 1370 W/m2

dE = 1 AU

We can relate the inverse square law to the Earth’s solar constant:

SE

SdE

d

2

EE d

dSS

A more convenient form of the inverse square law:

Page 24: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

SMars = ?

SVenus = ?

SJupiter = ?

dMars orbit=1.52 AU

dVenus orbit= 0.72 AU

dJupiter orbit = 5.2 AU

SEarth = 1370 W/m2

Page 25: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

2642 1370 593 51

D= 0.72 1 1.52 5.2 AU

Planetary Solar Constant, W/m2

Page 26: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

The Sun is not really constant

Solar luminosity varies, e.g. sunspots

Solar flares can release hundreds of millions megaton of energy in a few minutes

Prominences/coronal loops eject large amounts of charged particles into space in a few minutes

What causes this variability is an active area of research

Page 27: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Solar Activity

Any type of variation in the appearance or energy output of the sun

Sunspots

Flares

Prominences

Can solar activity affect the Earth?

Page 28: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful
Page 29: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Solar Activity and Earth

Aurora from Space Shuttle

Solar activity releases large amounts of plasma, charged particles (gases) and electromagnetic radiation moving at up to 3 million miles per hour, making up the Solar Wind

Variation in solar activity results in variation of solar wind intensity

This can affect Earth’s atmosphere and climate, and disrupt telecommunications on Earth

Earth’s magnetic field deflects most incoming charged particles toward Earth's north and south poles

Solar wind

Earth’s magnetic field

Page 30: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Polar Auroras

Aurora over Circle, Alaska

Charged particles deflected toward Earth's poles collide with atmospheric molecules causing them to give off light

Each atmospheric gas emit light of a particular wavelength that depend on its electrical state and on the energy of the particle that hits it

The light emitted by atmospheric gases appears as the northern and southern lights, a.k.a. auroras

Page 31: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

How does the Sun Influence Earth? Provides energy for life, warms the planet, drives the

dynamic atmosphere and oceans UV light can cause mutations in living organisms

Geomagnetic storms (high solar activity)– Aurora– Power-grid failures (Canada, 1989);

Telecommunications failures

High-energy solar particles (solar wind)– can destroy ozone– dangerous radiation dosages to astronauts and

passengers/pilots on polar air-travel routes

Page 32: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Solar Luminosity Varies in Time

Faint Young Sun

The sun was probably 20-25% cooler about 3.5 Gyr ago

Yet, there is no evidence of a cold (freezing) Earth surface

The “Faint Young Sun” is important for climate - not so critical for photosynthesis

3.843.8410102626 W/m W/m22

Page 33: PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website:   Useful

Why the Sun gets brighter with time

H fuses to form He in the core

Core slowly loses mass

Core contracts and heats up

Fusion reactions proceed faster

More energy is produced more energy needs to be emitted

warmer!