 To understand how we calculate that the magnetar SGR 1806-20 is 45,000 light-years away deep inside the hidden zone, we need to take a look at how kinematic distance calculations and radio astronomy were used to develop the Milky Way rotation curve that we discussed in our 2015 update on dark matter. The best way to map out the rotation curve for the galaxy's disk is to measure the orbital velocities and distances of gas clouds and star-forming regions across the galaxy. These are the H1, H2, and molecular clouds we covered in our segment on star birth nebula. These are the best objects to analyze for three reasons. One, they trace out the spiral arms, like we see here with Andromeda. Two, we can see them clearly at great distances using radio astronomy. And three, there is a good way to calculate their distance for the inner part of the galaxy. We need radio astronomy because stars are not good candidates for building a galaxy-wide map. This is because we cannot see stars in the plane of the galaxy's disk beyond 6000 light-years due to the dust in the interstellar medium. The dust absorbs and scatters the light that passes through it. The further the light has to travel, the more of this dust it encounters, and the dimmer it gets. This is called extinction. But gas clouds radiate radio waves, and radio waves pass through dust particles untouched because their wavelength is much larger than the size of these particles. We can see these clouds all across the galaxy, including the hidden area behind the central bulge. What's more, the hydrogen in these regions emit a spectral line in the radio frequency band, and this spectral line exhibits Doppler shifts, enabling us to measure the cloud's radio velocity relative to us. In this line of sight reading, we see a number of peaks. Each one represents a cloud. Clouds have different frequencies because the clouds have different radio velocities. The maximum peak is from a cloud that's radio velocity is close to its total orbital velocity. We can use the Doppler shift of dust clouds to find the kinematic distance to the object and calculate how fast it is rotating around the center of the galaxy. In order to convert this radio velocity information into rotational velocity and distance from the center of the galaxy, we use a technique called the tangent point method. First, we take a line of sight look for clouds. Having found one, we adjust the longitude to get the maximum radio velocity based on the Doppler shift. This will mark the cloud's closest approach to the center. At this tangent point, a line to the center will be perpendicular to the line of sight. Here the radio velocity of the cloud will be equal to its rotational velocity around the center of the galaxy. We can calculate its distance from the center and its distance from us with a little trigonometry. So, for clouds closer to the center than we are, we can scan the sky bit by bit and create a map of the rotation velocity and distance for the inner galaxy. This map can then be used to find distances to all the clouds and the stars they contain as long as they are closer to the center of the galaxy than we are. For clouds further out, there are no tangent points. For these, we have to use weaker methods for determining distance and rotational velocity. We then do a best fit line for the collected data. Here's a graphic superimposed on our galactic curve that indicates the accuracy of methods used to provide the included data points. The vertical lines through each point represent the range of possible velocities for any given distance. Notice that these lines are quite long once we are dealing with distances beyond one astronomical unit. For magnetar SGR 1806-20, a number of astronomers have connected it to the giant molecular cloud, Westerhout 31. Its longitude is 10 degrees. Using the rotation curve, it is estimated to be 45,000 light-years away. Give or take 5,000 light-years.