Astronomy: Hubble's Law and the Expanding Universe Worksheet

Question 1

State Hubble's Law in words and as an equation. Identify what each variable represents.

Accepted Answer

Hubble's Law says that the farther away a galaxy is, the faster it appears to be moving away from us. The equation is v = H0d, where v is the recession velocity of the galaxy, H0 is the Hubble constant, and d is the galaxy's distance from us.

Question 2

A galaxy is 100 Mpc away. Using H0 = 70 km/s/Mpc, calculate its expected recession velocity.

Accepted Answer

The expected recession velocity is v = H0d = 70 km/s/Mpc × 100 Mpc = 7,000 km/s. The galaxy should be moving away from us at about 7,000 km/s.

Question 3

A galaxy has a measured recession velocity of 14,000 km/s. Using H0 = 70 km/s/Mpc, calculate its distance in megaparsecs.

Accepted Answer

The distance is d = v/H0 = 14,000 km/s ÷ 70 km/s/Mpc = 200 Mpc. The galaxy is about 200 Mpc away.

Question 4

The table shows four galaxies. Galaxy A is 50 Mpc away, Galaxy B is 120 Mpc away, Galaxy C is 250 Mpc away, and Galaxy D is 400 Mpc away. Rank the galaxies from slowest to fastest expected recession velocity.

Accepted Answer

The ranking from slowest to fastest expected recession velocity is Galaxy A, Galaxy B, Galaxy C, then Galaxy D. According to Hubble's Law, greater distance means greater recession velocity.

Question 5

Explain why Hubble's Law is evidence that the universe is expanding.

Accepted Answer

Hubble's Law shows that distant galaxies are generally moving away from us, and more distant galaxies move away faster. This pattern is best explained by space itself expanding, which increases the distance between galaxies over time.

Question 6

A galaxy has a spectral line that normally appears at 500 nm in a laboratory. In the galaxy's spectrum, the line appears at 525 nm. Is the galaxy redshifted or blueshifted, and what does that mean about its motion?

Accepted Answer

The galaxy is redshifted because the wavelength increased from 500 nm to 525 nm. This means the galaxy is moving away from us.

Question 7

Calculate the redshift z for a spectral line that shifts from a rest wavelength of 400 nm to an observed wavelength of 420 nm. Use z = (observed wavelength - rest wavelength) / rest wavelength.

Accepted Answer

The redshift is z = (420 nm - 400 nm) ÷ 400 nm = 20 nm ÷ 400 nm = 0.05. The galaxy has a redshift of 0.05.

Question 8

For small redshifts, recession velocity can be estimated with v = zc, where c = 300,000 km/s. If a galaxy has z = 0.03, estimate its recession velocity.

Accepted Answer

The recession velocity is v = zc = 0.03 × 300,000 km/s = 9,000 km/s. The galaxy is moving away at about 9,000 km/s.

Question 9

Using your answer from the previous problem and H0 = 70 km/s/Mpc, estimate the galaxy's distance.

Accepted Answer

The distance is d = v/H0 = 9,000 km/s ÷ 70 km/s/Mpc = about 128.6 Mpc. The galaxy is about 129 Mpc away.

Question 10

A graph of galaxy recession velocity versus distance has a best-fit line through the origin. What does the slope of this line represent?

Accepted Answer

The slope of the best-fit line represents the Hubble constant, H0. It tells how many kilometers per second of recession velocity are expected for each megaparsec of distance.

Question 11

Two students make claims about expansion. Student 1 says, "The Milky Way is at the exact center of the universe because all distant galaxies move away from us." Student 2 says, "Observers in other galaxies would also see most distant galaxies moving away." Which student is more accurate, and why?

Accepted Answer

Student 2 is more accurate. In an expanding universe, space expands everywhere, so observers in other galaxies would also see most distant galaxies moving away from them. Hubble's Law does not mean the Milky Way is at the center of the universe.

Question 12

The age of the universe can be roughly estimated by 1/H0, but H0 must be converted into consistent units. Conceptually, explain why a larger value of H0 would imply a younger universe, while a smaller value of H0 would imply an older universe.

Accepted Answer

A larger H0 means galaxies are moving apart faster for a given distance, so it would take less time to reach their current separation if the expansion is traced backward. A smaller H0 means galaxies are moving apart more slowly, so it would take more time to reach their current separation. Therefore, a larger H0 suggests a younger universe, and a smaller H0 suggests an older universe.

Astronomy: Hubble's Law and the Expanding Universe

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