Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 11, Problem 7P
To determine
Compare the luminosity of protostar with that of Sun.
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If a contracting protostar is seven times the radius of the Sun and has a temperature of only 2030 K, how luminous will it be relative to the Sun? (Hint: Use the luminosity-radius-temperature relation: (L/L) = (R/R.)^2 (T/T.)^4 The surface temperature of the Sun is 5800 K.)
(L/L.) = ?
If a contracting protostar is eight times the radius of the Sun and has a temperature of only 2190 K, how luminous will it be relative to the Sun? (Hint: Use the luminosity-radius-temperature relation)
For a main sequence star with luminosity L, how many kilograms of hydrogen is being converted into helium per second? Use the formula that you derive to estimate the mass of hydrogen atoms that are converted into helium in the interior of the sun (LSun = 3.9 x 1026 W).
(Note: the mass of a hydrogen atom is 1 mproton and the mass of a helium atom is 3.97 mproton. You need four hydrogen nuclei to form one helium nucleus.)
Chapter 11 Solutions
Foundations of Astronomy (MindTap Course List)
Ch. 11 - Prob. 1RQCh. 11 - Prob. 2RQCh. 11 - Prob. 3RQCh. 11 - Prob. 4RQCh. 11 - During free-fall collapse, what keeps the...Ch. 11 - Prob. 6RQCh. 11 - Prob. 7RQCh. 11 - Prob. 8RQCh. 11 - Prob. 9RQCh. 11 - Prob. 10RQ
Ch. 11 - Prob. 11RQCh. 11 - Prob. 12RQCh. 11 - Prob. 13RQCh. 11 - Describe the three ways thermal energy can be...Ch. 11 - Prob. 15RQCh. 11 - Prob. 16RQCh. 11 - How does the CNO cycle differ from the...Ch. 11 - Prob. 18RQCh. 11 - Prob. 19RQCh. 11 - Prob. 20RQCh. 11 - Prob. 21RQCh. 11 - Prob. 22RQCh. 11 - Prob. 23RQCh. 11 - Prob. 24RQCh. 11 - Prob. 1PCh. 11 - Prob. 2PCh. 11 - Prob. 3PCh. 11 - Prob. 4PCh. 11 - If a protostellar disk is 200 AU in radius and the...Ch. 11 - Prob. 6PCh. 11 - Prob. 7PCh. 11 - Prob. 8PCh. 11 - Prob. 9PCh. 11 - Prob. 10PCh. 11 - Prob. 11PCh. 11 - Prob. 12PCh. 11 - If the Orion Nebula is 8 pc in diameter and has a...Ch. 11 - Prob. 14PCh. 11 - Prob. 1SOPCh. 11 - Prob. 2SOPCh. 11 - Prob. 1LTLCh. 11 - Prob. 2LTLCh. 11 - Prob. 3LTLCh. 11 - Prob. 4LTLCh. 11 - Prob. 5LTLCh. 11 - Prob. 6LTL
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- Suppose a protostar has a luminosity of 157,341 Lo and a surface temperature of 4,540 K (Kelvins). What is the radius of this protostar? [Enter your answer as a multiple of the Sun's radius. I.e., if you find R = 20 Ro enter 20. This problem is easier if you start with the relevant equation and create a ratio using the Sun's values. Recall that the Sun has a surface temperature of 5778 K. ]arrow_forwardIf a contracting protostar is 0.5 times as luminous as the Sun and has a temperature of only 1,500 K, how does its radius compare to that of the Sun?arrow_forwardA protostar evolves from a temperature T = 3500 K and a luminosity L = 5000 times that of the Sun to T = 5000 K and L = 3 solar units. What is its radius (a) at the start, and (b) at the end of the evolution? (need full step)arrow_forward
- Assuming that at the end of the He burning phase of the stellar core (r < R_core) has no H or He or other metals and is composed completely of Carbon, X=Y=0, X_c = 1 ; The envelope above the core has a normal stellar composition ( r > R_core). Calculate the length of time in years that a 1M_sol and 10M_sol star will live on the horizontal branch or the time between the start and end of the He burning phase. Assume that the normal relationship between mass and luminosity holds for horizontal branch stars. Please be as detailed as possiblearrow_forwardA 46M Sun main sequence star loses 1 Msun of mass over 105 years. (Due to the nature of this problem, do not use rounded intermediate values in your calculations including answers submitted in WebAssign.) How many solar masses did it lose in a year? By how much will its luminosity decrease if this mass loss continues over 0.8 million years? Due to the nature of this problem, for all parts, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign. To determine the number of solar masses lost per year, divide the mass lost by the number of years over which it was lost. Mlost tlost-yr Part 1 of 3 dM = dM = MSun/yrarrow_forwardIf a contracting protostar is three times the radius of the Sun and has a temperature of only 3000 K , how luminous will it be relative to the Sun?arrow_forward
- The Orion Nebula is a gas-rich region in which stars are being born. The nebula is at a distance of about 1344 lyr from Earth.Suppose you observe a star in the Orion Nebula to have an apparent magnitude of 6.75. Calculate the absolute magnitudeof the star. Also calculate the luminosity of the star in units of the solar luminosity (knowing that the absolute magnitude ofthe Sun is 4.8).arrow_forwardA planetary nebula expanded in radius 0.3 arc seconds in 30 years. Doppler measurements show the nebula is expanding at a rate of 35 km/s. How far away is the nebula in parsecs? First, determine what distance the nebular expanded in parsecs during the time mentioned. Δd = vpc/sTs So we first need to convert the rate into pc/s and the time into seconds: vpc/s = vkm/s (1 pc / 3.09 x 1013km) vpc/s = ? Ts = (Tyr)(365 days/yr)(24 hrs/day)(3600 s/hr) Ts = ? s Δd= vpc/sTs Therefore, Δd = ? pcarrow_forwardIf the hottest star in the Carina Nebula has a surface temperature of 51,000 K, at what wavelength (in nm) does it radiate the most energy? Hint: Use Wien's law: ?max = 2.90 ✕ 106 nm · K T How does that compare with 91.2 nm, the wavelength of photons with just enough energy to ionize hydrogen? -The wavelength calculated above is shorter than 91.2 nm. Photons at this calculated wavelength will have more than enough energy to ionize hydrogen. -The wavelength calculated above is longer than 91.2 nm. Photons at this calculated wavelength will have more than enough energy to ionize hydrogen. -The wavelength calculated above is shorter than 91.2 nm. Photons at this calculated wavelength will not have enough energy to ionize hydrogen. -The wavelength calculated above is longer than 91.2 nm. Photons at this calculated wavelength will not have enough energy to ionize hydrogen.arrow_forward
- If a contracting protostar is five times the radius of the sun and has a temperature of only 2000 K, how luminous will it be?arrow_forwardFor the PP chain 0.7% of the mass participating in nuclear fusion is liberated as energy which produces a star's luminosity. Assume that the core of a main sequence star consists of 10% of its total mass. Hence, estimate the lifetime of a star on the main sequence in terms of its luminosity L/L. Give your answer in years. You may use the observed mass-luminosity relation L x M³.5, where M is the star's total mass. Using typical values, calculate estimates for the main sequence lifetime of a KO star and a 05 star. Describe briefly why your estimate might be more accurate for K stars compared to O stars.arrow_forwardA protostar evolves from a temperature T = 3500 K and a luminosity L = 5000 times that of the Sun to T = 5000 K and L = 3 solar units. What is its radius (a) at the start, and (b) at the end of the evolution? [Hint: Week 6 slide 13]arrow_forward
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