Galaxies, Redshift and the Expanding Universe · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Measuring an expanding universe

Science · Astronomy & Astrophysics · ages 21-22
Name ______________________   Date ____________

  1. A galaxy's spectral line has a rest wavelength of 500 nm and is observed at 505 nm. Ignoring local motion, estimate its recession speed with v = cz and c = 300,000 km/s.

    • About 300 km/s
    • About 3,000 km/s
    • About 30,000 km/s

  2. For a nearby standard candle, dust dimming is corrected and emission is equal in all directions. Its measured luminosity and flux give L/(4 pi F) = 36 Mpc^2. Using d = sqrt(L/(4 pi F)), what is its distance?

    • 6 Mpc
    • 18 Mpc
    • 36 Mpc

  3. Use H0 = 70 km/s/Mpc, 1 Mpc = 3.09 x 10^19 km and 1 billion years = 3.15 x 10^16 s. What is the Hubble time in billion years, rounded to the nearest whole number?

    Answer: ______________

  4. In an inverse-square model, two galaxies have equal luminosity and no dust dimming. One is ten times farther away. What is its observed flux compared with the nearer galaxy?

    • One tenth of the nearer galaxy's flux
    • One hundredth of the nearer galaxy's flux
    • The same flux as the nearer galaxy

  5. Two Cepheids obey the same calibrated period-luminosity relation in the same observing band. Their periods are 4 and 16 days. Which has greater mean luminosity?

    • The 4-day Cepheid has greater mean luminosity
    • Both Cepheids have the same mean luminosity
    • The 16-day Cepheid has greater mean luminosity

  6. For low-redshift galaxies whose local motions are small, a graph plots recession speed vertically and distance horizontally. What does the fitted slope estimate?

    • The present expansion rate H0
    • The average stellar age
    • The total mass of these galaxies

  7. A nearby star is reliably dated at 11 billion years. What does that establish about the universe's age?

    • Exactly 11 billion years
    • At least 11 billion years
    • Less than 11 billion years

  8. In a homogeneous universe with uniform expansion, different comoving observers find the same recession-speed versus distance relation at the same cosmic time. What does this model imply?

    • Our location is the unique centre of expansion
    • A fixed outer edge encloses all galaxies
    • No location is a preferred expansion centre
LightMySky · lightmysky.comW1-mt_-POhqrng-Q-s1

Answer key

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Measuring an expanding universe W1-mt_-POhqrng-Q-s1

  1. About 3,000 km/s · The shift is 5 nm, so z = 5/500 = 0.010. The small-redshift estimate is v = 300,000 x 0.010 = 3,000 km/s.
  2. 6 Mpc · The supplied ratio equals distance squared. Take its positive square root: sqrt(36 Mpc^2) = 6 Mpc.
  3. 14 · The Hubble time is (3.09 x 10^19)/70 seconds. Dividing by 3.15 x 10^16 gives about 14.01 billion years, which rounds to 14. This need not equal the exact cosmic age.
  4. One hundredth of the nearer galaxy's flux · At equal luminosity, flux is proportional to 1/d^2. A distance factor of 10 gives a flux factor of 1/10^2 = 1/100.
  5. The 16-day Cepheid has greater mean luminosity · Within the stated relation, longer period means greater mean luminosity. The 16-day period is longer.
  6. The present expansion rate H0 · In v = H0 d, H0 is the change in recession speed per unit distance. It is the slope for these axes.
  7. At least 11 billion years · The universe existed when the star formed. A reliable stellar age gives a lower bound, not an exact cosmic age or a measurement of H0.
  8. No location is a preferred expansion centre · The model treats comoving locations alike. Changing the observer does not select a special expansion centre.
Worksheet · LightMySky