Astronomy 1 / Section 3 (S. Myers)

Problem Set #3 (due Mon 26 Feb 1996 5pm)

Problems:
  1. How far is the barycenter (center-of-mass) from a star of 3 times the mass of the Sun from in a double-star system in which the other star has a mass equal to the Sun's and a distance of 4 AU from the first star? Assume a circular orbit.

    What is the period of mutual revolution of the two stars described above? (Use Newton's modification of Kepler's 3rd Law)

  2. Find the ratio of the light-gathering powers of the 2.4 meter diameter Hubble Space Telescope (HST) and the 10 meter Keck telescope.
  3. In a given time, the intensity ratio of the faintest objects that can be seen with a telescope is inversely proportional to the ratio of the light-gathering powers (bigger telescopes can see fainter objects in the same amount of time). For the HST and Keck telescopes using the powers computed above, calculate the magnitude difference corresponding to this limiting intensity ratio.

  4. Calculate and compare the resolving powers of the HST and Keck telescopes in the visible light waveband (500 nm). (Use the wavelength dependent formula:

    resolution (arcsec) = ( wavelength(meters) / diameter(meters) ) x 206265"

    In light of this, why do images taken with the HST have better resolution than those taken with the Keck even though the resolving powers would suggest the opposite? (What is special about the HST?)

  5. What is the resolving power (resolution) of the 10 meter Keck telescope were it to be used in the radio at a wavelength of 5 cm? (This is why radio telescopes have to be so big!).


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Steven T. Myers - Last revised 21Feb96