Question

Suppose we were to discover that all of the galaxies are actually ten times farther away than previously thought. What effect would this have on the value of Hubble's constant?

Short answer

Hubble's constant would be ten times smaller.

Step-by-step solution

Understanding Hubble's Law

Hubble's Law relates the velocity (\[ v \]) at which a galaxy is moving away from us to its distance (\[ d \]) with the formula \[ v = H_0 imes d \], where \[ H_0 \] is Hubble's constant. This means that as we observe galaxies, their velocities and distances are proportional.

Recognizing the Change in Distance

The problem states that all galaxies are ten times farther away than previously thought. We denote the original distance as \[ d \] and the new distance as \[ 10d \].

Analyzing the Effect on Velocity

Since the problem does not mention any changes to the observable velocities of the galaxies, we assume that \[ v \] remains the same. Hence, the observable velocities of the galaxies have not been affected by the new distance measurements.

Reevaluating Hubble's Constant

With the new distance, the relationship becomes \[ v = H_{0_{new}} imes 10d \]. Since \[ v \] is unchanged, we set the new equation equal to the old equation: \[ H_{0_{old}} imes d = H_{0_{new}} imes 10d \].

Solving for the New Hubble's Constant

By canceling \[ d \] from both sides, we find \[ H_{0_{new}} = \frac{H_{0_{old}}}{10} \]. This means the new value of Hubble's constant is ten times smaller than the previous value.

Key concepts

Hubble's constant

In the study of the universe, Hubble's constant, denoted as \( H_0 \), is a crucial value that explains the expansion rate of the universe. It represents the relationship between a galaxy's recessional velocity and its distance from us. In essence, this constant tells us how fast galaxies are moving away based on their distance.
Understanding Hubble's constant is pivotal in cosmology, as it provides insights into the size, age, and future of the universe. When Edwin Hubble first discovered this relationship, it unveiled the idea of an expanding universe.

• Hubble's constant is measured in kilometers per second per megaparsec (km/s/Mpc).
• Different methods to calculate \( H_0 \) include observing the cosmic microwave background or using distant supernovae.
• Changes in the perceived distances do not affect galaxies' velocities directly but do alter our calculated \( H_0 \).

In the exercise scenario, increasing all galaxy distances by ten times would reduce the measured Hubble's constant by the same factor. This is because the perception of distance affects \( H_0 \)'s calculation directly.

galaxy distances

Galaxy distances are essential for understanding the structure and expansion of the universe. They tell us how far away galaxies are and therefore how light and other information have reached us over time. Measuring these distances accurately is notoriously challenging yet crucial for accurate cosmological conclusions.
The distance to a galaxy can be estimated through various methods, including using "standard candles," such as Cepheid variables or Type Ia supernovae. These methods rely on objects of known luminosity to infer distance based on how bright they appear to us.

• A key method involves using the redshift, where the further away a galaxy is, the more its light shifts to the red end of the spectrum.
• Redshift and other distance indicators depend on precise calibration and understanding of cosmic scales.
• Miscalculations in galaxy distances can lead to significant changes in our understanding of cosmic parameters.

By recalibrating distances as suggested in the problem, perceptions of the universe's size and expansion rate will change, highlighting the importance of accurate distance measurement.

redshift and velocity

Redshift is a phenomenon that occurs when the light from a galaxy moving away from us shifts towards the red end of the light spectrum. This shift happens because the light waves stretch as the galaxy moves away, similar to the Doppler effect with sound waves.
The redshift is directly related to a galaxy's velocity. Hubble's Law states that the velocity \( v \) is proportional to the redshift, which in turn is proportional to the distance \( d \) of the galaxy—as described by the formula \( v = H_0 \times d \).

• By measuring redshift, astronomers can determine how fast a galaxy is moving away from us.
• This information provides essential clues about the universe's rate of expansion.
• Importantly, redshift is one of the key pieces of evidence supporting the Big Bang theory.

When the exercise suggests a tenfold increase in galaxy distances, it implies no change in redshift or velocities. This scenario demonstrates how critical redshift measurements are for determining both velocity and distance accurately.