Integrate the first equation over all wavelengths to find an expression for the total luminosity of a black body star. (See the second equation for a hint)
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- As we read in the book, a star that appears to be 1 magnitude brighter will have approximately 2.5 times as much flux hitting an observer's detector/telescope/eye (i.e. a star with an apparent magnitude of 4 has approximately 2.5 times more flux hitting the detector as a star with an apparent magnitude of 5). With this in mind what is the approximate ratio of the flux hitting the a detector for a star with an apparent magnitude of 3 compared to a star with an apparent magnitude of 7? (hint: remember that magnitudes follow a logarithmic scale, not a linear one)If a T Tauri star is the same temperature as the sun but is ten times more luminous, what is its radius?In a laboratory, the Balmer-beta spectral line of hydrogen has a wavelength of 486.1 nm . If the line appears in a star’s spectrum at 485.8 nm , what is the star’s radial velocity? Is it approaching or receding? Is this a blueshift or a redshift?
- 2If the Sun was producing its energy by slow contraction as suggested by Helmholtz and Kelvin, estimate the amount by which the radius of the Sun has to decrease every year to produce the observed luminosity."H-R" Diagram pg. 118, question 7 Stars of the same spectral type have the same: absolute magnitude number temperature luminosity
- 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 =We will take a moment to compare how brightly a white dwarf star shines compared to a red giant star. For the sake of this problem, lets assume a white dwarf has a temperature roughly twice as large as a red giant star. As for their stellar radii, the white dwarf has a radius about 1/10000th that of a red giant star. With this in mind, how does the luminosity of a red giant star compare to that of a white dwarf? (Put differently, find the ratio of their luminosities a.k.a. how many times more luminous is the red giant than the white dwarf? An answer of less than 1 means the white dwarf is more luminous, an answer of 1 means they have the same luminosity, and an answer greater than 1 means the red giant is more luIf a star has M = 100Msun and L = 10^6Lsun, how long can it shine at that luminosity if it started as pure hydrogen and is able to convert 10% of its H to He? If a star has M = 0.5Msun and L = 0.1Lsun, how long can it shine under the same conditions?
- Sirius is the brightest star in the sky (but is located in the Southern hemisphere). It has a luminosity of 25.4 LSun and is 2.67 parsec away (1 parsec= 3.086 ×1016 m). What flux is received on Earth from Sirius? How manytimes smaller is this than the flux from 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.Show that if two stars of the same luminosity form a close binary pair, the magnitude apparent light of the pair measured together is about 0.75 magnitudes brighter than any of the individual stars.