21ST CENT.AST.W/WKBK+SMARTWORK >BI<
6th Edition
ISBN: 9780309341523
Author: Kay
Publisher: NORTON
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Chapter 16, Problem 32QP
To determine
The percentage of Sun’s mass that is turned from hydrogen into helium over its lifetime.
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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.)]
In the model shown in the table below, what fraction of the Sun's mass is hotter than 5,000,000 K?
R/R SunT (106 K) Density (g/cm³)
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.006
0.60
1.2
2.3
3.1
4.9
5.1
6.9
9.3
13.1
15.7
0.00
0.009
0.035
0.12
0.40
1.3
4.1
13
36
89
150
M/M Sun L/L Sun
1.00
0.999
0.996
0.990
0.97
0.92
0.82
0.63
0.34
0.073
0.000
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.99
0.91
0.40
0.00
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.
Chapter 16 Solutions
21ST CENT.AST.W/WKBK+SMARTWORK >BI<
Ch. 16.1 - Prob. 16.1CYUCh. 16.3 - Prob. 16.3CYUCh. 16.4 - Prob. 16.4CYUCh. 16.5 - Prob. 16.5CYUCh. 16 - Prob. 1QPCh. 16 - Prob. 2QPCh. 16 - Prob. 3QPCh. 16 - Prob. 4QPCh. 16 - Prob. 5QPCh. 16 - Prob. 6QP
Ch. 16 - Prob. 8QPCh. 16 - Prob. 9QPCh. 16 - Prob. 10QPCh. 16 - Prob. 11QPCh. 16 - Prob. 12QPCh. 16 - Prob. 13QPCh. 16 - Prob. 14QPCh. 16 - Prob. 15QPCh. 16 - Prob. 16QPCh. 16 - Prob. 17QPCh. 16 - Prob. 18QPCh. 16 - Prob. 19QPCh. 16 - Prob. 20QPCh. 16 - Prob. 21QPCh. 16 - Prob. 23QPCh. 16 - Prob. 24QPCh. 16 - Prob. 25QPCh. 16 - Prob. 26QPCh. 16 - Prob. 27QPCh. 16 - Prob. 28QPCh. 16 - Prob. 29QPCh. 16 - Prob. 30QPCh. 16 - Prob. 31QPCh. 16 - Prob. 32QPCh. 16 - Prob. 33QPCh. 16 - Prob. 34QPCh. 16 - Prob. 35QPCh. 16 - Prob. 36QPCh. 16 - Prob. 37QPCh. 16 - Prob. 38QPCh. 16 - Prob. 39QPCh. 16 - Prob. 40QPCh. 16 - Prob. 41QPCh. 16 - Prob. 42QPCh. 16 - Prob. 43QPCh. 16 - Prob. 44QPCh. 16 - Prob. 45QP
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- From 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_forwardShow 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_forwardNow suppose that all of the hydrogen atoms in the Sun were converted into helium. How much total energy would be produced? (To calculate the answer, you will have to estimate how many hydrogen atoms are in the Sun. This will give you good practice with scientific notation, since the numbers involved are very large! See Appendix C for a review of scientific notation.)arrow_forward
- What is the average density of the Sun? How does it compare to the average density of Earth?arrow_forwardDescribe the reaction that powers the sun during its main sequence lifetime. Be sure to include the basic ingredients and the basic products.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
- 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?arrow_forwardIn a typical solar oscillation, the Sun’s surface moves up or down with a speed of 0.1m/s . If you were to try to measure this speed using the Doppler shift of the absorption line for Iron which has a wavelength of 557.6099nm, what is the longest wavelength you will see?arrow_forwardLet's calculate how much mass will be lost by the Sun during the course of its main-sequence lifetime. While it is on the main sequence, a star converts about 10% of the hydrogen initially present into helium (remember that it is only the core of the star that is hot enough for fusion). During nuclear fusion, the Sun converts about 0.7% of the core hydrogen mass into energy. The total mass of the Sun is 2 × 1030 kg. How many kilograms of mass will be converted to energy during the main sequence stage of the Sun's life? What is the ratio of this lost mass to the Earth's mass (6 × 1024 kg)? In other words, how many Earths of mass will be turned into energy?arrow_forward
- If the sun expanded to a radius 200 times it's present radius, what would the average density be (in g/cm^3?)arrow_forwardCan you solve the problem, according to the information provided?arrow_forwarda) 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.arrow_forward
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