# CIE A Level Physics复习笔记25.2.3 Hubble's Law & the Big Bang Theory

### Hubble's Law & the Big Bang Theory

• Edwin Hubble investigated the light spectra emitted from a large number of galaxies
• He used redshift data to determine the recession velocities of these galaxies, and standard candles  to determine the distances
• From these measurements, he formulated a relationship, now known as Hubble’s Law
• Hubble’s Law states:

The recession speed of galaxies moving away from Earth is proportional to their distance from the Earth

• This can be calculated using:

v = H0d

• Where:
• v = the galaxy's recessional velocity (m s-1)
• d = distance between the galaxy and Earth (m)
• H0 = Hubble's constant, or the rate of expansion of the universe (s-1)
• This equation tells us:
• The further away a galaxy, the faster it’s recession velocity
• The gradient of a graph of recession velocity against distance is equal to the Hubble constant A key aspect of Hubble’s law is that the furthest galaxies appear to move away the fastest

#### Age of the Universe

• If the galaxies are moving away from each other, then they must’ve started from the same point at some time in the past
• If this is true, the universe likely began in an extremely hot, dense singular point which subsequently began to expand very quickly
• This idea is known as the Big Bang theory
• Redshift of galaxies and the expansion of the universe are now some of the most prominent pieces of evidence to suggest this theory is true
• The data from Hubble’s law can be extrapolated back to the point that the universe started expanding ie. the beginning of the universe
• Therefore, the age of the universe T0 is equal to: • Current estimates of the age of the universe range from 13 - 14 billion years
• There is still some discussion about the exact age of the universe, therefore, obtaining accurate measurements for the Hubble constant is a top priority for cosmologists Tracing the expansion of the universe back to the beginning of time leads to the idea the universe began with a “big bang”

#### Worked Example

A galaxy is found to be moving away with a speed of 2.1 × 107 m s-1. The galaxy is at a distance of 9.5 × 1024 m from Earth.Assuming the speed has remained constant, what is the age of the universe in years?

Step 1: Write down Hubble’s Law

v = H0d

Step 2: Rearrange for the Hubble constant H0, and calculate Step 3: Write the equation for the age of the universe T0, and calculate Step 4: Convert from seconds into years Therefore, the age of the universe is estimated to be about 14.3 billion years 