if the nuclear fusion reaction of converting 4 H → He occurs at anefficiency of 0.7%, and that mass is converted into energy accordingto the equation E = mc2, then estimate the Main Sequence lifetime of the Sun (spectral type G2)in years if the Sun (⊙) has a surface luminosity L⊙ = 3.839×1033erg. Assume the Sun’s core (10% of the total mass) is convertedfrom H into He. The Sun’s mass is M⊙ = 1.9891 × 1033 g
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if the nuclear fusion reaction of converting 4 H → He occurs at an
efficiency of 0.7%, and that mass is converted into energy according
to the equation E = mc2, then estimate the Main Sequence lifetime of the Sun (spectral type G2)
in years if the Sun (⊙) has a surface luminosity L⊙ = 3.839×1033
erg. Assume the Sun’s core (10% of the total mass) is converted
from H into He. The Sun’s mass is M⊙ = 1.9891 × 1033 g
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- If the nuclear fusion reaction of converting 4 H → He occurs at an efficiency of 0.7%, and that mass is converted into energy according to the equation E = mc2, then estimate the Main Sequence lifetime of the Sun (spectral type G2) in years if the luminosity of the Sun is 3.83 × 1033 ergs s−1. Assume the Sun’s core (10% of the total mass) is converted from H into He. The Sun’s mass is M⊙ = 1.9891 × 1033 g.The Sun and all Main Sequence stars derive their luminosity by fusing hydrogen to helium; in particular 4 1H ® 1 4He + Energy (photons) The mass of a proton is 1.0078 AMU, while the mass of a helium nucleus is 4.0026 AMU. a) How much mass is ``lost'' (in AMU and kg) in fusing four H atoms to one helium? This is called the mass defect. b) Mass isn't really lost, of course. It is converted to energy via E=mc2. How much energy in joules (J) is liberated in a single reaction? c) How many reactions per second are required to account for the entire luminosity of the Sun?A 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.
- = 2000 K and a radius of R, A young recently formed planet has a surface temperature T Jupiter radii (where Jupiter's radius is 7 x 107 m). Calculate the luminosity of the planet and 2 determine the ratio of the planet's luminosity to that of the Sun.what is the answer for sub-item (b) if the radius of the neutron star is 6.676 km? (express your answer in the proper SI unit and without scientific notation) (b)What is the average density of a neuron star that has the same mass as the sun but a radius of only 20.0 km?A nova dwarf has: mass 0.85 Mʘ, radius 0.0095 Mʘ, transfer rate ofmass 5.0 × 10-10 Mʘ / year during its active phase lasting 10 days. Estimate the total energy released and the absolute brightness of dwarf nova during the active phase.
- (a) Estimate the Eddington luminosity of a 0.072 M, star and compare your answer to the main-sequence luminosity given in Problem 21. Assume k = 0.001 m² kg¯'. Is radia- tion pressure likely to be significant in the stability of a low-mass main-sequence star? (b) If a 120 Mo star forms with log1o T. = 4.727 and log1o(L/Lo) = 6.252, estimate its Eddington luminosity. Compare your answer with the actual luminosity of the star.International Astronomical Union reported on 24 Feb 1987: An object was discovered on Feb. 24.37 UT (position R.A. = 5h35m.8, Decl. = -69 18'), obtained m = 4.8 on Feb. 24.454 UT. This object proved to be the most famous supernova (SN) in the 20th Century and the brightest visible from Earth since 1604. It is classified as a SN of the type Il in the Large Magellanic Cloud (SN1987A). Its brightness peaked in May 1987, with an apparent magnitude of m = 2.8. a) Find the absolute magnitude M of the SN1987A at maximum. Distance of the LMC is 51,400 pc. b) The progenitor (before SN explosion) star was a blue supergiant of the apparent magnitude m = 12.8. How much brighter (in terms of flux density) this SN was at maximum compared to the progenitor star. Find the ratio FSN / EbeforeThe typical core-collapse supernova has an energy budget of about 1046 J. This energy comes from the gravitational potential energy of an inner core with mass Mic, which collapses from an initial radius of 5 x 106 m down to the final radius of 50 km. Estimate Mic, in solar masses, for this to be a realistic energy source of the core-collapse supernova. You may assume that the density before the collapse is uniform. Discuss briefly how a Type la supernova is different from a core-collapse supernova from a massive star?
- A G0 III star with a mass of about 1 M⊙ sits on the horizontal branch. Horizontal branch stars are in the helium-burning phase of stellar evolution. For this process, 3He→C +energy If the star has a luminosity of 100 L⊙, estimate the size of this star assuming it has a temperature of 6000 K. What is the thermal time scale (time for the star to radiate away all its potential energy) if only 10% of the star’s mass is in the form of helium?A star with mass m, period Ti = 30 days, and radius ri = 1E4 km collapses into a neutron star (Links to an external site.) with a radius of rf = 3 km. Our goal will be to determine the period Tf of the neutron star. Useful formulae: Li=Lf; L=Iω; ω=2πf=2π/T; Isphere=2/5mr^2. 1.How much angular momentum Li does the star have before it collapses? 2. What is the rotation rate ωi of the star before collapsing? 3. Suppose we model the star as a solid sphere of radius ri with moment of inertia 2/5mri2 (a good assumption). What does our description of Li read now? 4.How much angular momentum Lf does the star have after it collapses? 5. What is the rotation rate ωf of the star after collapsing? 6.The new object, a neutron star, is also shaped like a sphere. What does Lf read? Group of answer choices 7.Assuming angular momentum is conserved during collapse (also a good assumption), what is our prediction for the period of the neutron star, Tf? 8. What is Tf in units of days? 9. What…Using the HR diagram what is the approximate range of relative luminosities covered for a main sequence star at 10 000 K?