Worksheet: The Hubble Time

In this worksheet, we will practice calculating the z-factor of distant galaxies and estimating the age of the universe from the Hubble Constant.

Q1:

An astronomer identifies a hydrogen emission line in the spectrum of light coming from a distant galaxy. The wavelength of the emitted light is 656 nm. The astronomer measures that the light has been redshifted by 9.54 nm. What is the 𝑍 -factor of the distant galaxy? Give your answer to 3 significant figures.

Q2:

The Antennae galaxies are a pair of interacting galaxies that have a recessional velocity of 1,640 km/s. By how much would the 434 nm hydrogen line be redshifted in the light from these galaxies? Give your answer to 3 significant figures.

Q3:

An astronomer observes the light coming from the Fireworks galaxy and identifies the 410 nm hydrogen emission line in the spectrum. The emission line has been redshifted by 0.0545 nm. What is the recessional velocity of the galaxy? Give your answer to 3 significant figures.

Q4:

Messier 60 is a galaxy in the constellation Virgo. It has a 𝑍 -factor of 0.00373. How far away is Messier 60? Use a value of 74.0 km/s⋅Mpc for the value of the Hubble constant. Give your answer to 3 significant figures.

Q5:

In March of 2019, the Hubble Space Telescope was used to measure the value of the Hubble constant. The value found was 2 . 4 0 × 1 0 s . Use this value to estimate the age of the universe. Give your answer in years to 3 significant figures.

  • A 6 . 6 0 × 1 0 years
  • B 2 4 . 0 × 1 0 years
  • C 1 . 3 1 × 1 0 years
  • D 1 3 . 2 × 1 0 years
  • E 4 . 1 7 × 1 0 years

Q6:

The Whirlpool Galaxy has a 𝑍 -factor of 0.00154. What is its recessional velocity? Give your answer to 3 significant figures.

Q7:

The Hubble constant is usually measured in units of km/s⋅Mpc, but in order to use the Hubble constant to calculate the Hubble time, it must be converted into units of s−1. What is 50.0 km/s⋅Mpc in units of s−1? Give your answer to 3 significant figures.

  • A 1 . 6 2 × 1 0 s−1
  • B 1 . 6 2 × 1 0 s−1
  • C 1 . 6 2 × 1 0 s−1
  • D 1 . 6 2 × 1 0 s−1
  • E 1 . 6 2 × 1 0 s−1

Q8:

The Sunflower galaxy has a 𝑍 -factor of 0.00161. By how much would the 486 nm hydrogen line be redshifted in light from the Sunflower galaxy? Give your answer to 3 significant figures.

Q9:

What is 65 km/s⋅Mpc in units of s−1? Give your answer to 3 significant figures.

  • A 2 . 1 1 × 1 0 s−1
  • B 2 . 1 1 × 1 0 s−1
  • C 2 . 1 1 × 1 0 s−1
  • D 2 . 1 1 × 1 0 s−1
  • E 2 . 1 1 × 1 0 s−1

Q10:

What is the recessional velocity of a galaxy that has a 𝑍 -factor of 0.00820? Give your answer to 3 significant figures.

Q11:

The Cartwheel Galaxy has a recession velocity of 9 . 0 5 × 1 0 m/s. What is the 𝑍 -factor of the Cartwheel Galaxy? Give your answer to 3 significant figures.

Q12:

What is the 𝑍 -factor of a galaxy that has a recession velocity of 1 . 2 7 × 1 0 m/s? Use a value of 3 × 1 0 m/s for the speed of light in free space. Give your answer to 3 significant figures.

Q13:

In 2016, the Hubble Space Telescope was used to measure the value of the Hubble constant. The value found was 7 3 . 2 4 ± 1 . 7 4 km/s⋅Mpc.

Using this value of the Hubble constant, calculate the upper limit for the Hubble time. Give your answer in years to 3 significant figures.

  • A 1 4 . 0 × 1 0 years
  • B 1 3 . 0 × 1 0 years
  • C 1 3 . 4 × 1 0 years
  • D 1 2 . 0 × 1 0 years
  • E 1 3 . 7 × 1 0 years

Using this value of the Hubble constant, calculate the lower limit for the Hubble time. Give your answer in years to 3 significant figures.

  • A 1 3 . 4 × 1 0 years
  • B 1 2 . 0 × 1 0 years
  • C 1 3 . 7 × 1 0 years
  • D 1 4 . 0 × 1 0 years
  • E 1 3 . 1 × 1 0 years

Q14:

In 2018, the Planck mission measured the value of the Hubble constant as 67.7 km/s⋅Mpc. Use this value to estimate the age of the universe. Give your answer in years to 3 significant figures.

  • A 1 4 . 5 × 1 0 years
  • B 4 5 . 9 × 1 0 years
  • C 4 5 . 9 × 1 0 years
  • D 1 4 . 5 × 1 0 y e a r s
  • E 2 1 . 9 × 1 0 years

Q15:

If the age of the universe is 13.8 billion years, how far away is the edge of the observable universe? Give your answer in light-years.

  • A 1 3 . 8 × 1 0 ly
  • B 1 3 . 8 × 1 0 ly
  • C 1 3 . 8 × 1 0 ly
  • D 1 3 . 8 × 1 0 ly
  • E 1 3 . 8 × 1 0 ly

Q16:

NGC 1097 is a galaxy in the constellation Fornax, 13.8 Mpc away. Calculate the 𝑍 -factor of the galaxy. Use a value of 74.0 km/s⋅Mpc for the value of the Hubble constant and a value of 3 . 0 0 × 1 0 m/s for the speed of light in free space. Give your answer to 3 significant figures.

Q17:

When Edwin Hubble first discovered that the galaxies in the universe were moving away from each other, he calculated the Hubble constant to be 500 km/s⋅Mpc. This value was later discovered to be very inaccurate, but what would the age of the universe be if this value had been accurate? Give your answer in years to 3 significant figures.

  • A 1 . 9 6 × 1 0 years
  • B 1 . 9 6 × 1 0 years
  • C 5 . 1 1 × 1 0 years
  • D 1 . 9 6 × 1 0 years
  • E 5 . 1 1 × 1 0 years

Q18:

A galaxy is at a distance of 8.50 Mpc away from the Solar System.

What is the recessional velocity of the galaxy? Take Hubble’s constant to be 70 km/s⋅Mpc.

What is the 𝑧 -factor of this galaxy?

  • A 3 . 3 4 × 1 0
  • B 1 . 0 4 × 1 0
  • C 1 . 9 8 × 1 0
  • D 2 . 0 1 × 1 0
  • E 6 . 2 7 × 1 0

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