Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Chapter 16, Problem 27E
Why do you suppose so great a fraction of the Sun’s energy comes from its central regions? Within what fraction of the Sun’s radius does practically all of the Sun’s luminosity originate (see Figure 16.16)? Within what radius of the Sun has its original hydrogen been partially used up? Discuss what relationship the answers to these questions bear to one another.
Figure 16.16 shows how the temperature, density, rate of energy generation, and composition vary from the center of the Sun to its surface.
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Assuming that (1) the solar luminosity has been constant since the Sun formed, and (2) the Sun was initially of uniform composition throughout, as described by Table 9.2, estimate how long it would take the Sun to convert all of its original hydrogen into helium. [Hint: Calculate the mass of hydrogen in the sun and then divide it by the rate of hydrogen fusion (PPT slide 47.)]
The Sun’s luminosity (or power) is 4 x 1026 Watts (=J/s). How many kilograms of hydrogen must be fused every second to maintain this luminosity? (hint: work backwards from the energy per second to the mass released to the amount of hydrogen required, using the results from the previous question.)
The Sun’s mass is ~2x1030 kg. If 10% of this is Hydrogen available in the core, how long will the Sun be able to continue fusing hydrogen at this rate? This is considered the Sun's "lifetime". If the Sun is 4.6 billion years old (and assuming it's power output is constant), how many years does it have left?
a) At solar maximum sunspots might cover up to 0.4% of the total area of the Sun. If the sunspots have a temperature of 3800 K and the surrounding photosphere has a temperature of 6000 K, calculate the fractional change (as a percentage) in the luminosity due to the presence of the sunspots.
b) A star of the same stellar class as the Sun is observed regularly over many years, and a time series of its bolometric apparent magnitude is collected. What would be the signal in this time series which indicated that the star had a magnetic dynamo similar to the Sun? Briefly describe two or three possible sources of other signals which could confuse the interpretation of the data.
Chapter 16 Solutions
Astronomy
Ch. 16 - How do we know the age of the Sun?Ch. 16 - Explain how we know that the Sun’s energy is not...Ch. 16 - What is the ultimate source of energy that makes...Ch. 16 - What are the formulas for the three steps in the...Ch. 16 - How is a neutrino different from a neutron? List...Ch. 16 - Describe in your own words what is meant by the...Ch. 16 - Two astronomy students travel to South Dakota. One...Ch. 16 - What do measurements of the number of neutrinos...Ch. 16 - Do neutrinos have mass? Describe how the answer to...Ch. 16 - Neutrinos produced in the core of the Sun carry...
Ch. 16 - What conditions are required before proton-proton...Ch. 16 - Describe the two main ways that energy travels...Ch. 16 - Someone suggests that astronomers build a special...Ch. 16 - Earth contains radioactive elements whose decay...Ch. 16 - The Sun is much larger and more massive than...Ch. 16 - A friend who has not had the benefit of an...Ch. 16 - Which of the following transformations is (are)...Ch. 16 - Why is a higher temperature required to fuse...Ch. 16 - Earth’s atmosphere is in hydrostatic equilibrium....Ch. 16 - Explain what it means when we say that Earth’s...Ch. 16 - What mechanism transfers heat away from the...Ch. 16 - Suppose you are standing a few feet away from a...Ch. 16 - Give some everyday examples of the transport of...Ch. 16 - Suppose the proton-proton cycle in the Sun were to...Ch. 16 - Do you think that nuclear fusion takes place in...Ch. 16 - Why is fission not an important energy source in...Ch. 16 - Why do you suppose so great a fraction of the...Ch. 16 - Explain how mathematical computer models allow us...Ch. 16 - Estimate the amount of mass that is converted to...Ch. 16 - How much energy is released when a proton combines...Ch. 16 - The Sun converts 4109 kg of mass to energy every...Ch. 16 - Assume that the mass of the Sun is 75% hydrogen...Ch. 16 - In fact, the conversion of mass to energy in the...Ch. 16 - Now suppose that all of the hydrogen atoms in the...Ch. 16 - Models of the Sun indicate that only about 10% of...Ch. 16 - Show that the statement in the text is correct:...Ch. 16 - Every second, the Sun converts 4 million tons of...Ch. 16 - Raymond Davis Jr.’s neutrino detector contained...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Let's examine how we know that the Sun cannot power itself by chemical reactions. Using the fact that an average chemical reaction between two atoms releases 1.6×10-19 J of energy, estimate how long the Sun could emit energy at its current luminosity. Compare that estimate to the known age of Earth.arrow_forwardWhat is the average density of the Sun? How does it compare to the average density of Earth?arrow_forwardFrom the information in Figure 15.21, estimate the speed with which the particles in the CME in parts (c) and (d) are moving away from the Sun. Figure 15.21 Flare and Coronal Mass Ejection. This sequence of four images shows the evolution over time of a giant eruption on the Sun. (a) The event began at the location of a sunspot group, and (b) a flare is seen in far-ultraviolet light. (c) Fourteen hours later, a CME is seen blasting out into space. (d) Three hours later, this CME has expanded to form a giant cloud of particles escaping from the Sun and is beginning the journey out into the solar system. The white circle in (c) and (d) shows the diameter of the solar photosphere. The larger dark area shows where light from the Sun has been blocked out by a specially designed instrument to make it possible to see the faint emission from the corona. (credit a, b, c, d: modification of work by SOHO/EIT, SOHO/LASCO, SOHO/MDI (ESA & NASA))arrow_forward
- Show that the statement that 92% of the Sun’s atoms are hydrogen is consistent with the statement that 73% of the Sun’s mass is made up of hydrogen, as found in Table 15.2. (Hint: Make the simplifying assumption, which is nearly correct, that the Sun is made up entirely of hydrogen and helium.)arrow_forwardAssuming an average sunspot cycle of 11 years, how many revolutions does the equator of the Sun make during that one cycle? Do higher latitudes make more or fewer revolutions compared to the equator?arrow_forwardNeutrinos produced in the core of the Sun carry energy to its exterior. Is the mechanism for this energy transport conduction, convection, or radiation?arrow_forward
- How would the interior temperature of the Sun be different if the strong force that binds nuclei together were 10 times as strong?arrow_forwardA Crude Analysis: In about 5 billion years, the Sun is going to look a lot different. Our sun is going to turn into a red-giant, a bigger star whose core temperature is much higher than the Sun's current core temperature (you will learn about the red giants in the coming weeks). Assume the core temperature of the red-giant phase of the Sun does not go beyond 100 million degrees. Do you think the temperature is high enough for helium fusion to occur? Note that this question is about helium fusion not hydrogen fusion. How are you going about proving your claim? Question: What temperature in degrees Kelvin must the red-giant sun be at to allow for the helium-helium interactions to take place not considering the Quantum Mechanical effects (i.e. what temperature would allow helium atoms to breach the helium-helium potential wall without help from Quantum Mechanics)? Use wolfram alpha to find the values for the constants. Round your answer to two decimal places. Your answer i [ Select ] 1.47…arrow_forwardThe average density of the sun is 1. 4 g/cm3 What do you expect the density to be at 0.25 of Rsun? 2) The average density of the sun is 1.4 g/cm3. The following resource claims that the sun's core has a density of 150 g/cm3 and a radius of 25% of the sun's radius. Assume the core has a constant density and calculate it's mass. What fraction of the sun's mass is in the core according to that resource?arrow_forward
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