Energy from the Sun
Energy
Energy is a quantity that describes how much force an object has experienced
over a distance or can potentially experience in a given situation.
Energy can be transferred from one object to another, or transform from one
form to another. It can neither be created nor destroyed.
Kinetic Energy: energy that an object has because of it’s motion
Potential Energy: energy that an object has because of it’s position
What is the Sun?
The Sun IS NOT an average, yellow star.
Size and Distance of the Sun
• The Sun is 109 times the diameter of
Earth
• Over 1,000,000 Earths could fit inside
the Sun.
Earth
• The Sun is 150 million kilometers away
from Earth.
Moon
• It takes light 8 minutes to travel to Earth
from the Sun.
• This distance is defined as 1
Astronomical Unit (AU)
Mass of the Sun
Kepler’s 3rd Law of Planetary Motion
2
𝑃 =
4𝜋2
𝐺(𝑀+𝑚)
𝑑3
P is the period of the orbit,
d is the average distance of the planet from the Sun,
G is the gravitational constant of the Universe
M is the mass of the Sun
m is the mass of the planet
When the planet mass is totally insignificant compared to the mass of the Sun:
𝑀≫𝑚
4𝜋 2 𝑑 3
𝑀=
𝐺𝑃2
For Earth, d = 1.496x1011 m, P = 1 sidereal year
MSun = 2 x 1030 kg
333,000 times Earth’s mass
Rotation of the Sun
Galileo saw sunspots that
appear to move across the face
of the Sun.
Conclusion: the Sun rotates on
its axis.
Rotation rate:
27 days (equator) to
31 days (poles)
Movie made from Galileo’s sunspot drawings
from June 2 – July 8, 1613
Luminosity of the Sun
Luminosity is the total energy output per unit time. It is related to
brightness by the distance:
𝐿
𝐵=
4𝜋𝑑 2
So
𝐿 = 4𝜋𝑑 2 𝐵
We’ve measured the distance to be 1.496x1011 m
Brightness is also a directly observable quantity. The Sun’s
brightness at Earth is 1,361.5 W/m2
So
L = 3.8 x 1026 watts
10 trillion times the power consumption of all Earth’s nations
combined
The Spectrum of the Sun
•Visible light is a tiny fraction of the
Electromagnetic Spectrum
•Gamma rays--billions of waves per inch
•Radio waves--up to miles-long wavelengths
Low Energy
Waves
High Energy
Waves
Surface Temperature
5800 K Thermal Spectrum
Composition of the Sun
The spectrum of the Sun’s light reveals its composition.
The Sun is White
The Sun produces all the
colors of the rainbow in
roughly equal amounts, which
is white light.
If the Sun were yellow, then
white T-shirts would look
yellow in the mid-day
sunshine.
When you observe the Sun
safely, by projecting its image
through a pinhole camera or a
telescope, you see that it is
white.
Don’t stare directly at the Sun!
The UV radiation can damage your eyes.
Magnetic Field
When an external magnetic field is present, single
energy levels in an atom/ion/molecule split into
additional levels.
The amount of splitting and the new energy levels
present depend on the strength and direction
(north or south) of the external magnetic field.
Examining the solar spectrum for the “Zeeman
Effect” allows us to map the magnetic field on the
surface of the Sun.
The Sun’s Layers
Looking at the Sun in
different wavelengths of
light reveals different
parts of the Sun.
Radio light:
Wavelength = 17.6 cm
See radiation from
Sun’s atmosphere,
Corona
The Sun’s Layers
Looking at the Sun in
different wavelengths of
light reveals different
parts of the Sun.
Visible light (white light):
Wavelength = 400-700
nm
See radiation from
Sun’s “surface”,
Photosphere
The Sun’s Layers
Looking at the Sun in
different wavelengths of
light reveals different
parts of the Sun.
Visible light (H-α):
Wavelength = 656.3 nm
See radiation from layer
just above Sun’s
surface,
Chromosphere
The Sun’s Layers
Looking at the Sun in
different wavelengths of
light reveals different
parts of the Sun.
Extreme Ultraviolet
light:
Wavelength = 30.4 nm
See radiation from
Sun’s atmosphere,
Corona
Image from STEREO mission
The Sun’s Layers
Looking at the Sun in
different wavelengths of
light reveals different
parts of the Sun.
Extreme Ultraviolet
light:
Wavelength = 17.1 nm
See radiation from
Sun’s atmosphere,
Corona
Image from STEREO mission
The Sun’s Layers
The Different Parts of the Sun
During a total eclipse of the Sun, the
very bright Photosphere is blocked
and the Sun’s outer atmosphere
becomes visible (in white light). We
call it the Corona
Spacecraft, like SOHO and
STEREO, place a disk in front of
their cameras to create an eclipse.
They are then able to take images
with a larger view of the Sun’s
Corona
It extends far out into the Solar
System, in fact we live in it!
Hydrostatic Equilibrium
There is no evidence that the Sun has
changed its size, temperature, or luminosity
in billions of years.
We therefore conclude that it is in a state of
equilibrium.
The forces acting on it are:
• Gravity from its mass
• Pressure from its temperature
These forces must be in balance to create
equilibrium.
Internal Structure
Use the Doppler Effect to measure
motions on the surface.
Seismic (acoustic) waves can be
mapped out by their appearance on
the surface. Just like seismology on
Earth.
Helioseismology reveals changes in
density and pressure at different
depths inside the Sun.
The Different Parts of the Sun
Core
•T = 15,700,000 K
•Density = 162 g/cm3
Radiative Zone
• Energy transported by light
• T = 10,000,000 K
Convective Zone
• Energy transported by convection
Photosphere
• Visible surface
• Far less dense than Earth’s atmosphere
• T = 5,800 K
• Sunspots: T = 4,000 K
Chromosphere
• Thin layer above photosphere
• Produces most of Sun’s UV light
• T = 10,000 K
Corona
• Tenuous, extends out millions of kilometers
• Emits X-rays
• T = 1,000,000 K
Energy Source
The Sun’s luminosity has been
sustained for billions of years
(geologic and fossil evidence
suggest at least 3.8 billion years).
What energy source could last
that long?
Chemical Burning?:
If the Sun were made of coal,
burning (oxidizing: chemical
potential energy → thermal
energy) it could only sustain the
luminosity for ~1,000 years.
Energy Source
The Sun’s luminosity has been
sustained for billions of years. What
energy source could last that long?
Gravitational contraction?:
compression of gas from gravity
heats the gas.
gravitational potential energy →
thermal energy (randomized kinetic
energy of the gas particles)
original source of energy for the
Sun.
could only sustain the Sun’s
luminosity for ~10 million years.
Current energy source for
Jupiter and Saturn.
Nuclear Fusion
proton-proton chain
most common nuclear reaction for
Sun-like stars.
4 protons → a helium nucleus,
positrons, neutrinos, and gamma
rays
mass of the 4 protons > the mass of
the helium nucleus, the positrons,
and the neutrinos combined.
mass → gamma ray photons:
the energy equivalent to the missing
mass by the equation E = mc2
Random Walk
Photons bounce off of electrons – imparting
energy to the plasma (pressure and
temperature increase)
Plasma is very dense in core and radiative
zone
Can take 10,000 -100,000 years for the
energy generated in the core to escape to
the surface.
Extra Slides
Age of the Sun
We think that the Sun and Solar System formed
from a single interstellar cloud all at the same
time. So the oldest rocks in the Solar System
should gives us an approximate age for the Sun
as well.
Rocks are dated using their relative abundances
of radioactive elements and their decay products.
The oldest rocks on Earth are 4.6 billion years old
as are the oldest meteorites ever examined.
So the Sun is at least 4.6 billion years old. The
oldest fossils of life on Earth are 3.8 billion years
old. So the Sun must have reached equilibrium by
at least that age.
It burns through fuel at the rate of its luminosity.
We figure that about less than 1% of its mass is
available to convert to energy through fusion. This
gives a total lifetime of the Sun at about 10 billion
years.
Sun
The Sun is Above Average
Most stars in the Universe are
small, cool, low-mass dwarfs.
The Sun is larger, hotter, and
more massive than these.
There are stars that are much
larger, very hot, and many times
more massive than the Sun. But
these stars are quite rare
compared to the Sun or the lowmass stars.
The Sun is also not median,
mid-range, or most frequent
(mode) in the measures of size,
temperature, brightness, or
mass.
Energy Comparisons
Food Calories
Joules
Lifting a lemon 1 meter
2.388 X 10-4
1
Car moving at 60 mph
86
3.6 x 105
Burning a liter of oil
287
1.6 x 106
Human daily diet
2 X 103
8.4 x 106
Lightening bolt
106
1010
Heat a house (1 year)
107
1011
1-megaton H-bomb
1 x 1012
5 x 1015
Major geomagnetic storm
1012
1016
Earthquake (magnitude 8.0)
6 x 1012
2.5 x 1016
Annual U.S. energy usage
1016
1020
Impact of dinosaur extinction
asteriod
1019
1023
Annual sunlight on Earth
1021
1025
Large solar flare
1022
1026
Earth spinning
1025
1029
Earth moving in orbit
1029
1033
Annual solar energy output
1030
1034
Supernova (exploding star)
1040
1044
Nuclear Fusion
neutrinos (ν) have very little mass, and travel
near the speed of light. They hardly react with
anything. They can escape directly from the
core, unlike photons. Hence we can observe
them to probe directly the conditions in the
core of the Sun.
To do this we build giant tanks filled with
different liquid compounds and put them far
underground. Since neutrinos hardly react to
anything we expect to detect only 1 neutrino
per day interacting with the liquid in the tank!
After decades of experiments we’ve
now actually detected the amount that we
expect. But found that we were detecting all
the types of neutrinos, not just those
produced by the proton-proton chain. This
means that neutrinos must have some mass in
order to be able to oscillate between the
different types.
Sun’s Orbit
The Sun’s orbit is 3D.
It takes the Sun about 250 million years to orbit the Galaxy.
So the Sun has completed about 18 orbits since its birth (4.5 billion/ 250
million).