Measuring a galaxy: speed from redshift, distance from a supernova
Hubble constant
The ratio of the speed at which a galaxy is moving away from the Earth to its distance from the Earth.
H0=vd H_{0} = \frac{v}{d} H0=dvwith vvv in m/s\text{m/s}m/s and ddd in m\text{m}m, giving H0H_{0}H0 in per second\text{per second}per second.
- Two quantities have to be measured for each galaxy, and they come from completely separate observations.
- The speed vvv comes from redshift.
- The speed at which a galaxy is moving away from the Earth is found from the change in wavelength of the galaxy's starlight due to redshift.
- A bigger shift in wavelength means a faster recession, so the size of the shift is the measurement of speed.
- The distance ddd comes from a supernova.
- The distance of a far galaxy can be determined using the brightness of a supernova in that galaxy.
- This works because these supernovae all release about the same amount of energy, so one that looks fainter must be further away.
- Dividing one measurement by the other gives the Hubble constant H0H_{0}H0, and the striking result is that every galaxy gives roughly the same value.
- The current estimate is H0=2.2×10−18 per secondH_{0} = 2.2 \times 10^{-18}\ \text{per second}H0=2.2×10−18 per second, and that figure has to be recalled.
- A single constant working for every galaxy means speed is proportional to distance: twice as far away means moving away twice as fast.
The two measurements are independent: redshift gives the speed and supernova brightness gives the distance, which is why finding a constant ratio between them is a real discovery rather than a definition.
Running the expansion backwards gives the age of the Universe
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If a galaxy has been receding at a steady speed vvv ever since the beginning, the time it has taken to reach its present distance ddd is simply d/vd/vd/v.
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Since H0=v/dH_{0} = v/dH0=v/d, that time is the reciprocal of the Hubble constant.
dv=1H0 \frac{d}{v} = \frac{1}{H_{0}} vd=H01 -
This equation represents an estimate for the age of the Universe, the time since the expansion began.
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Every galaxy gives the same answer, near and far alike, which only makes sense if they all set off from the same place at the same moment.
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That is the evidence that all the matter in the Universe was once present at a single point.
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It is an estimate rather than an exact age, because the calculation assumes the expansion rate has stayed constant throughout.
- Do not write H0=d/vH_{0} = d/vH0=d/v, because the Hubble constant is speed divided by distance and inverting it turns the constant into the age.
- Do not give H0H_{0}H0 a unit of m/s\text{m/s}m/s, since dividing a speed by a distance leaves per second only.
- Do not swap the two measurements: redshift gives speed and supernova brightness gives distance, not the other way round.
- Do not treat 1/H01/H_{0}1/H0 as an exact age, because it rests on the assumption of a constant rate of expansion.
- The reciprocal is where marks vanish here, so write age=1/H0\text{age} = 1/H_{0}age=1/H0 on its own line and check you have divided one by the constant, not the constant by one.
- Handle the negative index carefully on the calculator, since 10−1810^{-18}10−18 typed as 101810^{18}1018 gives an answer wrong by 363636 orders of magnitude.
- Read whether the answer is wanted in seconds or years, because the equation gives seconds and the conversion is an extra step.
- When asked how H0H_{0}H0 is found, name both measurements and their sources, since one of the two is usually the mark being tested.
- How is the speed at which a galaxy is receding from the Earth found?
- How is the distance to a far galaxy determined?
- Define the Hubble constant, give its equation and state its current estimated value.
- Write the equation that estimates the age of the Universe and explain where it comes from.
- Why is this age evidence that all the matter in the Universe was once at a single point?
