Hubble’s Law
Name(s):
Hubble's law is the name for the observation in physical cosmology that:
1. Objects observed in deep space (extragalactic space, ~10 megaparsecs or more) are found to have a
Doppler shift interpretable as relative velocity away from the Earth;
2. This Doppler-shift-measured velocity, of various galaxies receding from the Earth, is approximately
proportional to their distance from the Earth for galaxies up to a few hundred megaparsecs away
Hubble's law is considered the first observational basis for the expansion of the universe and today serves
as one of the pieces of evidence most often cited in support of the Big Bang model
Finding the distance to a galaxy:
To determine a galaxy's distance, we must rely on indirect methods.
There is a chain of overlapping methods by which astronomers establish a distance scale for objects in the
universe, from nearby planets to the most remote quasars and galaxies. At every step of the distance ladder, errors
and uncertainties creep in. Each step inherits all the problems of the ones below, and also the errors intrinsic to
each step tend to get larger for the more distant objects; thus the spectacular precision at the base of the ladder
degenerates into much greater uncertainty at the very top.
Distances within the Solar System are known to extreme accuracy by using a variety of methods including the
motions of the planets in the sky, radar, and timing of signals from interplanetary probes. Distances to stars
within a couple of thousand light-years come from various geometrical methods; the most accurate values are
those based on measurements of the annual parallax of about 10,000 nearby stars made by the Hipparcos satellite.
The moving cluster method can be applied over a similar range, while main-sequence fitting works with open
clusters out to a distance of about 60,000 light-years.
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Beyond the Milky Way Galaxy, distances can be established most reliably using the period-luminosity relation of
Cepheid variables, backed by similar observations of other bright stars whose intrinsic brightness is reasonably
well-known, including RR Lyrae stars and novae. This method can be applied out to the limit at which Cepheids
and other individual stars can be distinguished inside their host galaxies - up to about 100 million light-years. For
more distant galaxies, standard candles brighter than Cepheids are needed. These include globular clusters and
Type Ia supernovae, which can be calibrated as distance indicators using Cepheids in relatively nearby galaxies
and then applied further afield-up to about 200 million light-years for globulars and out to at least 3 billion lightyears for supernovae. At the furthest limits, only whole galaxies are detectable, so methods such as the TullyFisher relation and Faber-Jackson relation are used, which link measurable properties of galaxies, or clusters of
galaxies, to their luminosity. Extragalactic distance indicators enable estimates to be made of the Hubble constant,
a measure of the rate at which the universe as a whole is expanding. Observation of the redshift of a remote
galaxy or quasar then supplies the object's distance. Over time the accuracy to which the Hubble constant is
known has improved dramatically.
Procedure (Part 1)
1. Find the Distance of the galaxy using N.E.D. (NASA/IPAC EXTRAGALACTIC DATABASE Redshift Independent Distance Data Search by Object Name) Using the Galaxy ID, go to this site:
http://ned.ipac.caltech.edu/forms/d.html and type in the name of the galaxy (i.e. NGC 1357) and click the
Search button.
 Record the following data on the Hubble’s Law Back-Up Data Sheet:
o Number of Distances Found
o Mean Distance (Mpc)
o Most Often Used Method to determine the distance
Finding the recessional velocity of a galaxy
The velocity of a galaxy is more directly measured using the Doppler effect. The radiation coming from a moving
object is shifted in wavelength:
[Eqn. (2)]
where λtrue is the rest or true wavelength of the radiation, λmeasured is the wavelength as measured at the telescope,
making
the fractional value that the velocity of the galaxy is of the speed of light.
In this case, wavelengths are measured in Ångstroms (Å), a unit equal to 1 ten-billionth of a meter. The speed of
light has a constant value of ~300,000 km/sec. The quantity on the left side of equation (2) above is usually called
the redshift, and is denoted by the letter z.
We can determine the velocity of a galaxy from its spectrum by measuring the wavelength shift of an absorption
or emission line whose wavelength is known and solve for the velocity, v.
Procedure (Part 2)
1. Find the Recessional Velocity of the galaxy using its spectrum from this website:
http://www.astro.washington.edu/courses/labs/clearinghouse/labs/HubbleLaw/galaxies.html choose a
galaxy from the list on your worksheet.
 Measure the redshifted wavelength (not the rest wavelengths) by clicking at the middle of the
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corresponding spectral line -- bottom of an absorption line, top of an emission line -- in the galaxy's
spectrum.
 Record the redshifted wavelength(s) on the Hubble’s Law Back-Up Data Sheet.
 If any of the absorption lines or the emission line isn’t clearly identifiable, don’t record it. For some
galaxies you may have 1, 2 or all 3 Spectrum Measurements
2. Repeat Procedure for Parts 1 & 2 for all of the galaxies on the worksheet.
3. After you have gathered all of you data, pick 15 Galaxies whose data you feel confident in graphing.
Using the Hubble's Law Spreadsheet, follow these directions (Recommended):
1.
Download the Hubble’s Law Speadsheet.xlsx file.
2.
Once it is downloaded, open the file and save it to your Student Network Drive
3.
REMEMBER TO SAVE YOUR SPREADSHEET OFTEN!
4.
If the spreadsheet is working correctly on your computer, it should automatically calculate the distances
to the galaxies, the redshifts, and the velocities as you enter your data on the Input Data tab.
5.
If the spreadsheet is working correctly on your computer, it should also automatically update the chart of
the data as you enter your numbers. (Look at the Data Spreadsheet and Graph tabs. Watch as you enter
your last few data points.)
6.
Once you are satisfied with all of your data, save it and then submit a copy of the file.
Background and Theory
In the 1920's, Edwin P. Hubble discovered a relationship that is
now known as Hubble's Law. It states that the recessional velocity
of a galaxy is proportional to its distance from us:
ν = Hod
where v is the galaxy's velocity (in km/sec), d is the distance to
the galaxy (in megaparsecs; 1 Mpc = 1 million parsecs), and Ho is
the proportionality constant, called "The Hubble Constant".
Hubble's Law states that a galaxy moving away from us twice as
fast as another galaxy is twice as far away. The Hubble constant
is a hotly contested quantity in astrophysics. In order to precisely
determine the value of Ho, we must determine the velocities and
distances to many galaxies, preferably those extremely far away.
Hubble’s Law Activity Analysis Questions:
1. What is your value for the Hubble constant?
2. Identify the galaxy with the highest redshift and state its recessional velocity. What fraction of the speed of
light is that galaxy receding from us? (There's a remarkably easy way to find this out as you've already
calculated it. Find the galaxy with the largest Ave. Z value in the Data Spreadsheet tab and multiply it by
100.)
3. Why does the best-fit line to your data need to go through the origin of your graph? Where is this “origin”
located in the Universe?
4. What criteria did you use to choose the 15 galaxies’ data you graphed?
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5. Why do you think you were asked to record the number of “measured” distances found for each galaxy and
the most often used method? Are there any uncertainties in these “measured” distances? Why do you think
quotations were used around the word measured?
6. Another consideration is the fact that galaxies are found in groups or clusters. The motion of these galaxies
through space as they orbit their common center of mass is called “peculiar motion.” That is, at a given
distance some galaxies will be receding more slowly than others in the cluster while others will be receding
more quickly. How does this peculiar motion affect your velocity measurements?
7. Write a scientific explanation (with a claim, evidence, and scientific reasoning) about the “Hubble's Law”
relationship.
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