21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Question
Chapter 14, Problem 45QP
To determine
The time period up to which sun’s luminosity lasts.
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If the Sun expanded to a radius 160 times its current size and its temperature decreased by 55%, how would its luminosity change?
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?
Given the Sun's present rate of energy generation (i.e. its present luminosity), how long will the Sun's energy source last (from beginning to end)? Answer in years.
Chapter 14 Solutions
21st Century Astronomy
Ch. 14.1 - Prob. 14.1ACYUCh. 14.1 - Prob. 14.1BCYUCh. 14.2 - Prob. 14.2CYUCh. 14.3 - Prob. 14.3CYUCh. 14.4 - Prob. 14.4CYUCh. 14 - Prob. 1QPCh. 14 - Prob. 2QPCh. 14 - Prob. 3QPCh. 14 - Prob. 4QPCh. 14 - Prob. 5QP
Ch. 14 - Prob. 6QPCh. 14 - Prob. 7QPCh. 14 - Prob. 8QPCh. 14 - Prob. 9QPCh. 14 - Prob. 10QPCh. 14 - Prob. 11QPCh. 14 - Prob. 12QPCh. 14 - Prob. 13QPCh. 14 - Prob. 14QPCh. 14 - Prob. 15QPCh. 14 - Prob. 16QPCh. 14 - Prob. 17QPCh. 14 - Prob. 18QPCh. 14 - Prob. 19QPCh. 14 - Prob. 20QPCh. 14 - Prob. 21QPCh. 14 - Prob. 22QPCh. 14 - Prob. 23QPCh. 14 - Prob. 24QPCh. 14 - Prob. 25QPCh. 14 - Prob. 26QPCh. 14 - Prob. 27QPCh. 14 - Prob. 28QPCh. 14 - Prob. 29QPCh. 14 - Prob. 30QPCh. 14 - Prob. 31QPCh. 14 - Prob. 34QPCh. 14 - Prob. 35QPCh. 14 - Prob. 36QPCh. 14 - Prob. 37QPCh. 14 - Prob. 38QPCh. 14 - Prob. 39QPCh. 14 - Prob. 40QPCh. 14 - Prob. 41QPCh. 14 - Prob. 42QPCh. 14 - Prob. 43QPCh. 14 - Prob. 44QPCh. 14 - Prob. 45QP
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- If a T Tauri star is the same temperature as the Sun but is eighteen times more luminous, what is its radius relative to the Sun? (Hint: Use the luminosity-radius-temperature relation: L L = R R 2 T T 4 .) R R =arrow_forwardIf a T Tauri star is the same temperature as the Sun but is seventeen times more luminous, what is its radius relative to the Sun? (Hint: Use the luminosity-radius-temperature relation:L/L=(R/R)^2(T/T)^4)arrow_forwardIf the Sun were replaced by a white dwarf with a surface temperature of 10,000 K and a radius equal to Earth’s, how would its luminosity compare to that of the Sun?arrow_forward
- In about 5 billion years, the sun will evolve to a red giant. Assume that its surface temperature will decrease to about half its present value of 6000 K, while its present radius of 7.0108 m will increase to 1.51011 m (which is the current Earth-sun distance). Calculate the ratio of the total power emitted by the sun in its red giant stage to its present power.arrow_forwardIf a 100 solar mass star were to have a luminosity of 107 times the Sun’s luminosity, how would such a star’s density compare when it is on the main sequence as an O-type star, and when it is a cool supergiant (M-type)? Use values of temperature from Figure 18.14 or Figure 18.15 and the relationship between luminosity, radius, and temperature as given in Exercise 18.47. Figure 18.15 Schematic HR Diagram for Many Stars. Ninety percent of all stars on such a diagram fall along a narrow band called the main sequence. A minority of stars are found in the upper right; they are both cool (and hence red) and bright, and must be giants. Some stars fall in the lower left of the diagram; they are both hot and dim, and must be white dwarfs. Figure 18.14 HR Diagram for a Selected Sample of Stars. In such diagrams, luminosity is plotted along the vertical axis. Along the horizontal axis, we can plot either temperature or spectral type (also sometimes called spectral class). Several of the brightest stars are identified by name. Most stars fall on the main sequence.arrow_forwardModels of the Sun indicate that only about 10% of the total hydrogen in the Sun will participate in nuclear reactions, since it is only the hydrogen in the central regions that is at a high enough temperature. Use the total energy radiated per second by the Sun, 3.81026 watts, alongside the exercises and information given here to estimate the lifetime of the Sun. (Hint: Make sure you keep track of the units: if the luminosity is the energy radiated per second, your answer will also be in seconds. You should convert the answer to something more meaningful, such as years.)arrow_forward
- Our Sun, a type G star, has a surface temperature of 5800 K. We know, therefore, that it is cooler than a type O star and hotter than a type M star. Given what you learned about the temperature ranges of these types of stars, how many times hotter than our Sun is the hottest type O star? How many times cooler than our Sun is the coolest type M star?arrow_forwardAccording to the text, a star must be hotter than about 25,000 K to produce an H II region. Both the hottest white dwarfs and main-sequence O stars have temperatures hotter than 25,000 K. Which type of star can ionize more hydrogen? Why?arrow_forward
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