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Page 1: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested
Page 2: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

During the nineteenth During the nineteenth century, scientists century, scientists suggested that the Earth suggested that the Earth was hundreds of millions was hundreds of millions of years old.of years old.

Today we know the Earth Today we know the Earth is 4.5 Billion years old.is 4.5 Billion years old.

PROBLEM – HOW CAN PROBLEM – HOW CAN THE SUN BURN SO HOT THE SUN BURN SO HOT FOR SO LONG A FOR SO LONG A TIME????TIME????

Page 3: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

In the 1800’s Lord Kelvin and Hermann von In the 1800’s Lord Kelvin and Hermann von Helmholtz suggested that as gravity collapsed Helmholtz suggested that as gravity collapsed the Sun, the gases would heat up. the Sun, the gases would heat up. (Kelvin-(Kelvin-Helmholtz contraction)Helmholtz contraction) Kinda like a bicycle pump heats up compressed air.Kinda like a bicycle pump heats up compressed air.

PEPEgravgrav Thermal Energy as star contracts Thermal Energy as star contracts This process cannot be This process cannot be

Calculations show that the sun would have had to Calculations show that the sun would have had to start its contraction no more that 25 million years ago.start its contraction no more that 25 million years ago.

THE SOLAR SYSTEM IS MUCH, MUCH OLDERTHE SOLAR SYSTEM IS MUCH, MUCH OLDER

Page 4: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

A stars power output is called its LUMINOSITY.A stars power output is called its LUMINOSITY. What energy source produces this power???What energy source produces this power???

Page 5: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Recall that Einstein Recall that Einstein predicted that there is an predicted that there is an equivalence of mass and equivalence of mass and energy according to energy according to

E = mcE = mc22

Consider the meaning of Consider the meaning of this. this.

A small amount of mass A small amount of mass can release a tremendous can release a tremendous amount of energyamount of energy

Page 6: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Fusion Requires Extreme Fusion Requires Extreme ConditionsConditions

Fusion occurs during collisionsFusion occurs during collisionslong range electrostatic forces work to keep long range electrostatic forces work to keep

positively charged nuclei apartpositively charged nuclei apartif nuclei come sufficiently close to one if nuclei come sufficiently close to one

another, the stronger but shorter range another, the stronger but shorter range nuclear forces work to pull nuclei togethernuclear forces work to pull nuclei together

Fusion requires high Fusion requires high temperatures: ~10 million Ktemperatures: ~10 million Kso that particles have the velocities or so that particles have the velocities or

energies required to overcome electrostatic energies required to overcome electrostatic repulsionrepulsion

the higher the electrostatic force the harder a the higher the electrostatic force the harder a species is to fusespecies is to fuse

Fusion requires high densitiesFusion requires high densitiesso that collisions are very commonso that collisions are very common

Particle Separation

Rep

uls

ive

For

ce

Strong electrostatic repulsionat intermediate separation.

Strong nuclear attraction atvery small separation.

Page 7: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Figure from Foundations of Astronomy by M. Seeds

Page 8: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Each proton has a certain

mass

The resulting Hydrogen atom is less massive. Note that one of

the protons converted into a

neutron

The mass defect is converte

d into energy

Positron – electron

annihilation

Page 9: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Another proton can now combine with deuterium to form a low mass isotope of

Helium

A gamma ray is given off

Page 10: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Fusion and Mass DefectFusion and Mass Defect

Consider this,Consider this,

If 1kg of Hydrogen is converted into Helium, the If 1kg of Hydrogen is converted into Helium, the helium will have a mass of 993 grams.helium will have a mass of 993 grams.

The mass defect is converted to 6.3 x 10The mass defect is converted to 6.3 x 101414J of J of energy. energy.

(like burning 20,000,000 kg of coal)(like burning 20,000,000 kg of coal)

Page 11: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Finally the Helium isotopes combine to produce Helium

and 2 new protons

Page 12: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested
Page 13: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested
Page 14: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Consider Consider the picturethe picture

Recall Recall Hydrostatic Hydrostatic Pressure Pressure

Page 15: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Now consider a “slab” Now consider a “slab” of solar material. Aka of solar material. Aka a layer of the Sun.a layer of the Sun.

The Suns interior is in The Suns interior is in hydrostatic hydrostatic equilibrium. equilibrium.

In general there is a In general there is a balance betweenbalance between

Radiation pressure and Radiation pressure and Gravitational pressureGravitational pressure

Page 16: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested
Page 17: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested
Page 18: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested
Page 19: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Each layer of a star is in thermal equilibrium. Otherwise the star

would become too hot or too cold. ENERGY MUST BE

TRANSPORTED TO THE SURFACE by radiative diffusion

and convection

Page 20: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

A diagram of the Sun

Page 21: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested
Page 22: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested
Page 23: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

All stars have a certain All stars have a certain Luminosity (L)Luminosity (L)

Power output in WattsPower output in Watts

This information can tell This information can tell

us a lot about a stars us a lot about a stars history and current state.history and current state.

First we need to First we need to understand the inverse understand the inverse square nature of EM square nature of EM radiation.radiation.

Page 24: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

d=1

d=2

d=3

B=1

B=1/9

B=1/4

Page 25: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested
Page 26: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

How does the amount of paint caught by a 1 How does the amount of paint caught by a 1 square unit area change with distance?square unit area change with distance?

Page 27: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

LUMINOSITY = THE AMOUNT OF ENERGY EMITTED IN 1 SECOND

Page 28: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

IF YOU DIVIDE THE LUMINOSITY BY THE SURFACE AREA OF A SPHERE (where the detector would be)YOU GET...

Page 29: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

bL

d

4 2 " A p p aren t B rig h n ess"

[W m [J s m-2 -1 -2] o r ]

(PSRT)

Page 30: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

EXAMPLE PROBLEMEXAMPLE PROBLEM

A long time ago in a galaxy farfar away

Darth Vader is observing two different stars. Both stars are equally bright as observed from his location, but Star A is 10 pc away and star B is 20 pc away.

Which star is more luminous? By how much?

Page 31: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Summary - Luminosity and BrightnessSummary - Luminosity and BrightnessLuminosity Luminosity is an absolute value that measures the total is an absolute value that measures the total power radiated by a star. Luminosity is measured in power radiated by a star. Luminosity is measured in watts and tells us the rate that energy radiates from a watts and tells us the rate that energy radiates from a star in all directions. Our Sun has a luminosity of about star in all directions. Our Sun has a luminosity of about 3.90 x 103.90 x 102626 W. Luminosity is very important in W. Luminosity is very important in providing information about star structure and age.providing information about star structure and age.

Apparent brightness Apparent brightness is a relative value. As observers is a relative value. As observers on Earth, we perceive star brightness as the fraction of on Earth, we perceive star brightness as the fraction of the luminosity received by us. We measure brightness the luminosity received by us. We measure brightness in watts per square meter.in watts per square meter.

Page 32: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Luminosity and Apparent BrightnessLuminosity and Apparent Brightness

Apparent Brightness Apparent Brightness

Apparent brightness is proportional to the Apparent brightness is proportional to the luminosity of the starluminosity of the star..

Apparent brightness is inversely proportional to Apparent brightness is inversely proportional to the square of the distance between the star the square of the distance between the star and the observer.and the observer.

24L

bd

Apparent brightness depends on two variables:Apparent brightness depends on two variables:

Page 33: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Luminosity and Apparent BrightnessLuminosity and Apparent Brightness

This means that a brighter star is not necessarily closer This means that a brighter star is not necessarily closer to Earth, or larger, or hotter. to Earth, or larger, or hotter.

A high luminosity star that is A high luminosity star that is farther from Earth can still farther from Earth can still appear brighter. appear brighter.

Page 34: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

Luminosity and Apparent BrightnessLuminosity and Apparent BrightnessWhen comparing two stars the When comparing two stars the same distancesame distance from from Earth, the star with the greatest luminosity will appear Earth, the star with the greatest luminosity will appear brighter. brighter.

Both the surface Both the surface temperature and size of temperature and size of a star affect luminosity. a star affect luminosity. These relationships are These relationships are the topics of Wien’s and the topics of Wien’s and the Stefan-Boltzmann the Stefan-Boltzmann Laws Laws

Page 35: During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested

EXAMPLESEXAMPLES

Tsokos 5ed - # 1-3 pg. 504Tsokos 5ed - # 1-3 pg. 504


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