![]() ![]() For nearby galaxies (in the Local Group), stars inside the Milky Way, and for objects in our Solar System, the relationship between distance and velocity does not hold. Hubble's Law only works for distant galaxies.There are a couple of important caveats that apply to Hubble's Law. Astronomers believe that Hubble's law is a direct consequence of the ongoing expansion of the universe and that the evidence suggests that the universe began in an explosion, which we call the Big Bang. The usual analogy used here is that of an explosion – the fragments of shrapnel produced are moving with a range of velocities, and the most distant objects from the source of the explosion have the largest velocities. However, if the universe is expanding, we expect a correlation between distance and velocity. If the universe is static and unchanging, there should be no correlation between distance and velocity. Hubble's law, which says simply that a galaxy's velocity (or as is sometimes plotted, its redshift) is directly proportional to its distance, also tells us something important about the state of the universe. The definition of z is that it is the left hand side of the Doppler shift equation:įor example, if you observe a galaxy with an H-alpha line at 680 nm, and you know the rest wavelength for that line is 656.3 nm, then its redshift is: ![]() For objects at large distances from Earth where the distance is determined using Hubble's Law, we do not often refer to their recession velocities (e.g., "that galaxy has a velocity of 14,000 km/sec away from us") or their distances in Mpc (e.g., "that galaxy is 247 Mpc from us"), instead, we simply refer to the object's redshift, z. The other term on the left hand side, λ 0, is the wavelength of that line in the spectrum of an object at rest. ![]() Where Δλ is the difference between the measured wavelength for a line in the spectrum of an object and the wavelength for that same line observed in the spectrum of an object at rest. The equation that you saw in Lesson 4 for the Doppler shift was: Let's quickly review how we measure velocities for objects that are receding from us. If you know H 0 and if you can calculate the velocity, v, from the spectrum, then you can use this equation to calculate the distance, d, to that galaxy. It is the slope of the line that relates the distance of a galaxy to its velocity. For the specific case of this relationship, we usually write the equation this way: Where y = the quantity plotted on the y-axis (velocity), x = the quantity plotted on the x-axis (distance), and m is the slope of the line. In algebra class, you learned that the equation for a line that passes through the point (0,0) is: ![]() What this means is that as the distance gets bigger, so does the velocity. However, it is somewhat apparent in this case that you can draw a straight line through the points. If these two quantities (distance and velocity) had nothing to do with each other, then the diagram would look like what we call a "scatter plot." That is, it would appear as a bunch of points randomly placed in different locations. On the x-axis, you plot the distance to that galaxy, in this case obtained from Cepheids. On the y-axis, you plot the velocity of the galaxy obtained from the spectrum. However, for a much more interesting search, you can go there and put in "Hubble, E" in the author field, and it will bring up the listing of Hubble's published works, including the paper in which he published the plot above. For example, if you want to find information on every article I have ever published, you can go there and stick my name in the author field. It is the SAO/NASA Astrophysics Data System, and you can use it to search the astronomical literature. Read Hubble's original articles! The astronomical community maintains an excellent resource meant primarily for practicing astronomers. ![]()
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