The longest wavelength of light humans can see is around 750 nm, deep red. If we were to observe a green - colored space probe approaching a stellar black hole of 20 solar masses, how close to the event horizon would it be when it just turned invisible? Green light has a wavelength around 520 nm. Answer
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- 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.An interstellar cloud is observed at a wavelength of 2.898 µm. Estimate the temperature of the cloud.Infrared radiation from the center of our galaxy with a wavelength of about 2 μm (2 × 10-6 m) comes mainly from cool stars. Use this wavelength as Amax and find the temperature of the stars.
- The three most prominent spectral lines of hydrogen are H-α at 656 nm, H-β at 486 nm, and H-γ 434 nm. If we observe an object with H-α at a wavelength of 700 nm, what wavelength will we observe H-β and H-γ? Is the object moving toward or away from us, and how do you know? Suppose we observe another object with H-α at 585 nm. Is this object moving toward or away from us? Is it moving slower or faster than the first object?You are the leader of the international Event Horizon Telescope, a collaboration of radio astronomers who want to take a picture of the black hole at the center of the Milky Way (Sag. A*). That black hole has a mass of about 4.1 million solar masses and is about 8 kpc away. If you are observing with a radio wavelength of about 1 mm, what effective diameter of your radio interferometric array is needed in order to just resolve the diameter of the Sag. A* black hole event horizon. (Assume the black hole is non-spinning, so its diameter is twice the event horizon radius.) Express your answer as a multiple of the Earth's radius. [Hint: you will need to recall and combine three formulas introduced throughout this course, including one about how big a black hole is, one about the criterion for resolving objects, and another that relates distance, sizes, and angles.] There really is an Event Horizon Telescope, and they are responsible for the first image of a black hole in the galaxy M87…Imagine a planet orbiting a star. Observations show a Doppler shift in the star's spectrum of 58 m/s over the 3.3 day orbit of the planet. What is the mass of the planet in kg? Assume the star has the same mass as the Sun (2.0 x1030 kg), there are 365.25 days in a year, and 1AU = 1.5 x 1011 m.
- Calculate the redshift of a star if H-ß line of hydrogen from the star is observed to be 800 nm.Studying the spectrum of a star, we see that the Haline (l= 656.285nm) has been shifted to 656.286 nm. Is the star moving towards us or away (explain your answer) How fast is the star moving with respect to us?11. Bob is traveling in a space ship and observes emission from a cloud of atomic hydrogen gas a few light years away. He identifies the Balmer-beta emission line (from the n = 4 to n = 2 transition) and measures its wavelength to be 322 nm. How fast is Bob moving relative to the cloud of hydrogen? Is he getting closer or further away from the hydrogen cloud? (You may assume that Bob is moving directly toward or away from the hydrogen gas cloud. Recall that the ground state energy of hydrogen is -13.6 eV.)
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