UNDERSTANDING THE UNIVERSE(LL)-W/CODE
3rd Edition
ISBN: 9780393869903
Author: PALEN
Publisher: NORTON
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Chapter 13, Problem 29QAP
To determine
The difference in speed of Type II supernovae blast material and expansion of Crab Nebula.
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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.)
A 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 = ? pc
Assume that the mass of the core of a star that just went Supernova type II is $2.5 \mathrm{M}_{\odot}$ before and after the collapse, while the Radius changes from $10^3 \mathrm{~km}$, before the collapse, to 12 km , after the collapse respectively.(a) What is the change in potential energy of the core between the two stages before and after the collapse?(b) Knowing that the luminosity of the Sun is $4 \times 10^{26} \mathrm{~W}$ how many years would it take the Sun to release the same amount of energy?
Chapter 13 Solutions
UNDERSTANDING THE UNIVERSE(LL)-W/CODE
Ch. 13.1 - Prob. 13.1CYUCh. 13.2 - Prob. 13.2CYUCh. 13.3 - Prob. 13.3CYUCh. 13.4 - Prob. 13.4CYUCh. 13.5 - Prob. 13.5CYUCh. 13.6 - Prob. 13.6CYUCh. 13 - Prob. 1QAPCh. 13 - Prob. 2QAPCh. 13 - Prob. 3QAPCh. 13 - Prob. 4QAP
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- Why do nebulae near hot stars look red? Why do dust clouds near stars usually look blue?arrow_forwardA supernova's energy is often compared to the total energy output of the Sun over its lifetime. Using the Sun's current luminosity, calculate the total solar energy output, assuming a 1010 year main-sequence lifetime. Using Einstein's formula E = mc? calculate the equivalent amount of mass, expressed in Earth masses. [Hint: The total energy output of the Sun over its lifetime is given by its current luminosity times the number of seconds in a year times its ten billion-year lifetime; Week 5 slide 4; mass of earth = 6x1024kg; c = 3x10®m/s. Your answer should be 200-300 Earth masses.]arrow_forwardA supernova’s energy is often compared to the total energy output of the Sun over its lifetime. Using the Sun’s current luminosity, calculate the total solar energy output, assuming a 1010 year main-sequence lifetime. Using Einstein’s formula E=mc2 calculate the equivalent amount of mass, expressed in Earth masses. [Hint: The total energy output of the Sun over its lifetime is given by its current luminosity times the number of seconds in a year times its ten billion-year lifetime; ; mass of earth = 6×1024kg; c = 3×108m/s. Your answer should be 200-300 Earth masses.]arrow_forward
- . The radius of the nebula is about 0.401 light-years. The gas is expanding away from the star at a rate of about 37 kilometers/second . Considering that distance = velocity x time, calculate how long ago the gas left the star if its speed has been constant the whole time. Make sure you use consistent units for time, speed, and distance. Answer in years.arrow_forwardThe Orion Nebula is about 20 light-years (20 × 1018 cm) across, enclosing a roughly spherical area with a volume of 4.19 × 1057 cm3. Calculate the number of 0.1 solar mass stars that might be formed in such a nebula. Assume that the nebula has a density of 1000 atoms/cm3.arrow_forwardA planetary nebula expands at 32 km/s. How far will it expand (in km) in 0.6 million years?arrow_forward
- Suppose a planetary nebula is 4.3 pc in diameter, and Doppler shifts in its spectrum show that the planetary nebula is expanding at 31 km/s. How old is the planetary nebula? (Note: 1 pc = 3.1 ✕ 1013 km and 1 yr = 3.2 ✕ 107 s.)arrow_forwardA main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say “mass vanish '' what we really mean is “gets converted into energy and leaves the star as light”. Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.arrow_forwardWhat is the escape velocity (in km/s) from the surface of a 1.5 M neutron star? From a 3.0 M neutron star? (Hint: Use the formula for escape velocity, Ve = 2GM r ; make sure to express quantities in units of meters, kilograms, and seconds. Assume a neutron star has a radius of 11 km and assume the mass of the Sun is 1.99 ✕ 1030 kg.) 1.5 M neutron star km/s3.0 M neutron star km/sarrow_forward
- If a neutron Star has a radius of 12 km and a temperature of 8.0 x 10^6 K, how luminous is it? Express your answer in watts and also in solar luminosity units. (Hint: Use the relation L/L= (R/R)^2(T/T)^4 . Use 5,800 K for the surface temperature of the Sun. The luminosity of the sun is 3.83 x 10^26W) luminosity in watts ________ W luminosity in solar luminosity units ______ Larrow_forward(a)What type of supernova is most luminous in light? (b) What kind of star results in such an explosion? (c) What type of supernova is most luminous in neutrino emission? (d) What kind of star results in such an explosion?arrow_forwardA distant Nebula is now 2.35 pc in radius and is expanding at 1100 km/s. Approximately when did the supernova occur?arrow_forward
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