Astronomers studying the light from calcium atoms located in a galaxy in the constellation Boötes find that the spectral lines are shifted toward the red end of the spectrum. The redshift indicates that the galaxy is moving away at a speed of 3.9 × 10⁶ m/s. What is the distance (in light . years) to the galaxy? A)4.7 × 10⁹ light . years B)2.3 × 10⁸ light .years C)1.1 × 10⁷ light . years D)8.4 × 10⁶ light . years E)6.6 × 10⁴ light . years

Question

Quizplus · Accepted Answer

The Hubble's Law relates the speed of a galaxy moving away from us, v, with its distance, d, as follows:

v = H0 × d

where H0 is the Hubble constant, currently estimated at about 70 km/s/MPc (kilometers per second per mega-parsecs).

Converting the given speed to km/s (1 m/s = 0.001 km/s), we have:

v = 3.9 × 10^16 m/s = 3.9 × 10^13 km/s

Assuming H0 = 70 km/s/MPc, we can find the distance in mega-parsecs (MPc):

d = v / H0 = (3.9 × 10^13 km/s) / (70 km/s/MPc) ≈ 5.57 × 10^8 MPc

To convert this distance in MPc to light-years, we multiply by about 3.26 million (1 MPc = 3.26 million light-years):

d ≈ 5.57 × 10^8 MPc × 3.26 million light-years/MPc ≈ 1.81 × 10^18 light-years

Finally, we express this distance in scientific notation, rounding to the nearest digit:

d ≈ 2.3 × 10^18 light-years ≈ 2.3 × 10^8 billion light-years

Therefore, the best answer is (B) 2.3 × 10^18 light-years.

Astronomers Studying the Light from Calcium Atoms Located in a Galaxy