The Sun and Special Relativity - Guided Notes update
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Dec 6, 2023
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Guided Notes – The Sun and Special Relativity
Name:
Leah Walker
Please type or handwrite notes as you watch the video lecture and answer the
included questions.
Interior Structure – Observations:
There are two methods used by astronomers to learn about the inner parts of the Sun.
o
One way is to analyze the slight movements of small areas on the Sun's surface.
o
The other is to measure the neutrinos that are given off by the Sun.
Helioseismologists can use the amplitude and cycle length of these motions to learn about the
temperature, density, and composition of the layers that the waves passed through before they
reached the surface.
Test Yourself – Measuring Mass
How do we tell the mass of the Sun?
A. From its size and density
B. From the speed that it moves around the galaxy
C. From the motions of the planets orbiting it
D. From the Sun’s spectrum
Your answer: B. From the speed that it moves around the galaxy
Interior Structure – Physical Models:
The Sun's interior is divided into four domains: the core, radiative layer, convective layer, and
surface atmospheres.
Astronomers use their observations to create a computer program that contains everything they
know about the physical processes occurring in the Sun's interior.
o
This program calculates the temperature and pressure at every point inside the Sun, and
determines whether any nuclear reactions are taking place.
o
This program is known as the standard solar model, which is a mathematical model used
to determine the interior structure of the Sun, including the temperature, density, and
composition of its layers.
Test Yourself – Pressure Changes in a Fluid
As a submarine goes down in the ocean, the pressure
A. Increases
B. Decreases
Your answer:
A. Increases
Your Turn – Calculating Pressure Changes in Fluid
If the pressure at sea level is 1 atmosphere, what is the pressure at depth A?
Your answer:
Click or tap here to enter text.
What is the pressure at depth B?
Your answer:
Click or tap here to enter text.
Modeling Pressure in the Sun:
The pressure within the sun is modeled using the standard solar model, which assumes the sun
evolves in hydrostatic equilibrium - a local balance between pressure and gravity.
o
The pressure can be expressed as dP/dr = - G m (r) ρ r 2, where P is the pressure, r is the
radius, G is the gravitational constant, rho is the density, and m is the mass of the sun
contained at that radius
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Solar Interior:
The Sun is divided into four regions: the core, radiative zone, convective zone, and outer layer. The core
generates energy through nuclear fusion, while the radiative zone moves energy outward through
radiation. The convective zone moves energy outward through convection. The outer layer is composed
of photosphere, chromosphere, transition region, and corona. The Sun's temperature is 15 million
degrees Celsius, and it is stable.
Heat Flow:
Heat Flow in the Sun:
Sunspots:
Sunspots are dark spots on the Sun caused by magnetic flux concentrations. They are cooler than the
surrounding areas and often come in pairs of opposite magnetic polarity. Solar flares are sudden
outbursts of energy that release radiation, interfering with our radio communications. Coronal mass
ejections (CMEs) are massive bubbles of radiation and particles from the Sun that can trigger auroras.
Test Yourself – Sunspot Heat Flow
Sunspots are darker because of lower temperatures. This suggests that in sunspots interior heat
A. is rapidly rising to the surface
B. is blocked from rising to the surface
C. is radiated rapidly away from the surface
D. is transmitted rapidly through the surface
Your answer:
B. is blocked from rising to the surface
Sunspots and Magnetism:
Test Yourself – Sunspot Cycle:
Sunspot numbers increase and decrease in a cycle that is not perfectly regular. Right now, sunspot
numbers are probably
A. near a maximum
B. near a minimum
C. increasing
D. decreasing
Your answer: B. near a minimum
Special Relativity:
Albert Einstein introduced the scientific theory of special relativity in 1905. This theory explains
how space and time are related. It's based on two main ideas. First, the laws of physics are the
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same for everyone, regardless of how they're moving. Second, the speed of light is always the
same, no matter who's measuring it or how fast they're moving.
Special relativity is essential to modern physical theories, including quantum field theory, string
theory, and general relativity. Scientists have tested it, and it's been confirmed. The theory has
several important implications, including the relativity of simultaneity, length contraction, time
dilation, the relativistic velocity addition formula, the relativistic Doppler effect, relativistic mass,
a universal speed limit, mass-energy equivalence, the speed of causality, and the Thomas
precession.
Time:
Time dilation is a concept in special relativity that explains how time can appear different
depending on the observer's perspective. This difference can be caused by the relative velocity
between two objects or the difference in gravitational potential between their locations.
Special relativity predicts that if an observer is in an inertial frame of reference, a clock that is
moving relative to them will appear to tick slower than a clock that is at rest in their frame of
reference. This is called special relativistic time dilation.
Distance:
Other Implications:
Test Yourself – Mass Energy
The mass-energy relation can be reversed. This means:
A. A small amount of energy can be turned into a huge amount of matter
B. A huge amount of energy can be turned into a small amount of matter
C. A small amount of energy can be turned into a small amount of matter
D. A huge amount of energy can be turned into a huge amount of matter
Your Answer:
B. A huge amount of energy can be turned into a small amount of matter
Nuclear Fusion in the Sun:
The Sun's core is a nuclear fusion reactor that converts hydrogen nuclei into helium nuclei. This process
is responsible for the enormous amount of energy that the Sun radiates and keeps it hot. The
temperature at the core of the Sun is around 14 million kelvin. Every second, the Sun fuses
approximately 620 million metric tons of hydrogen, producing 616 million metric tons of helium.
Test Yourself – Products of Fusion
Which of the following products of the Proton-Proton Chain escape the Sun directly (i.e., unchanged by
interaction with the outer layers of the Sun)?
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A. gamma ray photons
B. neutrinos
C. helium atoms
D. kinetic energy
Your answer:
B. neutrinos
Your Turn: Sun’s Interior
Imagine that the Sun’s mass increased.
A. What would this do to the temperature in the Sun’s interior? Explain your reasoning.
Your answer:
In the event that the Sun's mass were to undergo an increase, the temperature within the Sun's core
would rise substantially. This escalation in temperature could potentially have significant effects on the
Sun's overall behavior and could impact other celestial bodies within the solar system.B. What would
this do to the rate of nuclear fusion? Explain your reasoning.
Your answer:
As the Sun continues to burn through its fuel, its mass gradually increases. This increase in mass causes
an increase in the rate of nuclear fusion, the process that powers the Sun. As a result, the Sun emits
greater amounts of heat and light, which can be observed from Earth as a steady source of warmth and
brightness..
C. How would the nuclear fusion affect the Sun’s luminosity (total energy radiated)? Explain your
reasoning.
Your answer:
The process of nuclear fusion in the Sun is responsible for producing the heat and light that we receive
on Earth. By increasing the rate of this process, we can expect a significant enhancement in the Sun's
luminosity, which would result in a much brighter and hotter Sun. This could potentially have far-
reaching effects on our planet and the entire solar system.