Helioseismology in an Alternate Universe 0 points possible (ungraded) Stars, like planets, can vibrate. On Earth, we call these vibrations earthquakes, and their study is called seismology. The study of the vibrations of the sun is called helioseismology. Earth's crust is made up of solid, rigid rock, so elastic forces are largely responsible for the propagation of earthquake vibrations. Stars, however, are made of hot plasma, so elastic forces are negligible. Instead, the relevant force in an oscillating star is gravity. In our universe, the force of gravity between two objects is F, (r) = Gm1m₂ where G is the Newton's gravitational constant, m₁ and m₂ are the masses of the two objects, and is the distance between the objects. Imagine that we are in an alternate universe in which the force of gravity is instead given by Fg (r) = Zm1m₂ Mass, distance, and force all have the same units in this alternate universe, i.e. kilograms, meters, and Newtons (kg-m/s²), respectively, and Z is Notwen's gravitational constant, which is analogous to G. (Part a) What are the dimensions of Z? Express your answer in terms of some or all of the following: M for mass, I for length, and T for time. (Part b) Since the stellar oscillations are governed by the gravitational force, the frequency of a star's oscillations will depend the gravitational constant Z and the star's density, p, and radius, R, i.e. w=w (p, R, Z). Using dimensional analysis, find a combination of p, R, and Z that has the units of frequency, i.e. s-¹. Your answer may contain some or all of the following: p, R, and Z. Note that you could do the exact same analysis to find the frequency of oscillations of a star in our universe, and the answer that you'd get would actually be quite accurate!
Helioseismology in an Alternate Universe 0 points possible (ungraded) Stars, like planets, can vibrate. On Earth, we call these vibrations earthquakes, and their study is called seismology. The study of the vibrations of the sun is called helioseismology. Earth's crust is made up of solid, rigid rock, so elastic forces are largely responsible for the propagation of earthquake vibrations. Stars, however, are made of hot plasma, so elastic forces are negligible. Instead, the relevant force in an oscillating star is gravity. In our universe, the force of gravity between two objects is F, (r) = Gm1m₂ where G is the Newton's gravitational constant, m₁ and m₂ are the masses of the two objects, and is the distance between the objects. Imagine that we are in an alternate universe in which the force of gravity is instead given by Fg (r) = Zm1m₂ Mass, distance, and force all have the same units in this alternate universe, i.e. kilograms, meters, and Newtons (kg-m/s²), respectively, and Z is Notwen's gravitational constant, which is analogous to G. (Part a) What are the dimensions of Z? Express your answer in terms of some or all of the following: M for mass, I for length, and T for time. (Part b) Since the stellar oscillations are governed by the gravitational force, the frequency of a star's oscillations will depend the gravitational constant Z and the star's density, p, and radius, R, i.e. w=w (p, R, Z). Using dimensional analysis, find a combination of p, R, and Z that has the units of frequency, i.e. s-¹. Your answer may contain some or all of the following: p, R, and Z. Note that you could do the exact same analysis to find the frequency of oscillations of a star in our universe, and the answer that you'd get would actually be quite accurate!
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Transcribed Image Text:Helioseismology in an Alternate Universe
0 points possible (ungraded)
Stars, like planets, can vibrate. On Earth, we call these vibrations earthquakes, and their study is called seismology. The study
of the vibrations of the sun is called helioseismology. Earth's crust is made up of solid, rigid rock, so elastic forces are largely
responsible for the propagation of earthquake vibrations. Stars, however, are made of hot plasma, so elastic forces are
negligible. Instead, the relevant force in an oscillating star is gravity.
In our universe, the force of gravity between two objects is
Fg (r):
Gm1m2
p2
where G is the Newton's gravitational constant, m₁ and m₂ are the masses of the two objects, and r is the distance between
the objects. Imagine that we are in an alternate universe in which the force of gravity is instead given by
Fg (r)
Zm1m2
p3
Mass, distance, and force all have the same units in this alternate universe, i.e. kilograms, meters, and Newtons (kg - m/s²),
respectively, and Z is Notwen's gravitational constant, which is analogous to G.
(Part a) What are the dimensions of Z? Express your answer in terms of some or all of the following: M for mass, L for
length, and T for time.
(Part b) Since the stellar oscillations are governed by the gravitational force, the frequency of a star's oscillations will depend
the gravitational constant Z and the star's density, p, and radius, R., i.e. w=w (p, R, Z). Using dimensional analysis, find a
combination of p, R, and Z that has the units of frequency, i.e. s-¹. Your answer may contain some or all of the following: p,
R, and Z.
Note that you could do the exact same analysis to find the frequency of oscillations of a star in our universe, and the answer
that you'd get would actually be quite accurate!
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