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Aligned the phi symbol in the text to the symbol used in the plots
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episodes/02-coords.md

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@@ -309,9 +309,9 @@ to GD-1:
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The axes of this figure are defined so the x-axis is aligned with the
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stars in GD-1, and the y-axis is perpendicular.
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- Along the x-axis (φ<sub>1</sub>) the figure extends from -100 to 20 degrees.
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- Along the x-axis ($\phi_1$) the figure extends from -100 to 20 degrees.
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- Along the y-axis (φ<sub>2</sub>) the figure extends from about -8 to 4 degrees.
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- Along the y-axis ($\phi_2$) the figure extends from about -8 to 4 degrees.
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Ideally, we would select all stars from this rectangle, but there are
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more than 10 million of them. This would be difficult to work with, and as
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with a smaller dataset.
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So we will start by selecting stars in a smaller rectangle near the
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center of GD-1, from -55 to -45 degrees φ<sub>1</sub> and -8 to 4 degrees φ<sub>2</sub>.
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center of GD-1, from -55 to -45 degrees $\phi_1$ and -8 to 4 degrees $\phi_2$.
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First we will learn how to represent these coordinates with Astropy.
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## Transforming coordinates
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orbit of the GD-1 stream". In this coordinate system, one axis is defined along
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the direction of the stream (the x-axis in Figure 1) and one axis is defined
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perpendicular to the direction of the stream (the y-axis in Figure 1).
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These are called the φ<sub>1</sub> and φ<sub>2</sub> coordinates, respectively.
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These are called the $\phi_1$ and $\phi_2$ coordinates, respectively.
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```python
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from gala.coordinates import GD1Koposov10
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This is easiest to define in GD-1 coordinates.
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The following variables define the boundaries of the rectangle in
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φ<sub>1</sub> and φ<sub>2</sub>.
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$\phi_1$ and $\phi_2$.
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```python
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phi1_min = -55 * u.degree
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return xs, ys
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```
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The return value is a tuple containing a list of coordinates in φ<sub>1</sub>
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followed by a list of coordinates in φ<sub>2</sub>.
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The return value is a tuple containing a list of coordinates in $\phi_1$
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followed by a list of coordinates in $\phi_2$.
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```python
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phi1_rect, phi2_rect = make_rectangle(

episodes/03-transform.md

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@@ -348,10 +348,10 @@ which is useful for two reasons:
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- By transforming the coordinates, we can identify stars that are
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likely to be in GD-1 by selecting stars near the centerline of the
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stream, where φ<sub>2</sub> is close to 0.
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stream, where $\phi_2$ is close to 0.
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- By transforming the proper motions, we can identify stars with
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non-zero proper motion along the φ<sub>1</sub> axis, which are likely to be part of GD-1.
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non-zero proper motion along the $\phi_1$ axis, which are likely to be part of GD-1.
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To do the transformation, we will put the results into a `SkyCoord`
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object. In a previous episode, we created a `SkyCoord` object like

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