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14 changes: 7 additions & 7 deletions episodes/02-coords.md
Original file line number Diff line number Diff line change
Expand Up @@ -309,9 +309,9 @@ to GD-1:
The axes of this figure are defined so the x-axis is aligned with the
stars in GD-1, and the y-axis is perpendicular.

- Along the x-axis (φ<sub>1</sub>) the figure extends from -100 to 20 degrees.
- Along the x-axis ($\phi_1$) the figure extends from -100 to 20 degrees.

- Along the y-axis (φ<sub>2</sub>) the figure extends from about -8 to 4 degrees.
- Along the y-axis ($\phi_2$) the figure extends from about -8 to 4 degrees.

Ideally, we would select all stars from this rectangle, but there are
more than 10 million of them. This would be difficult to work with, and as
Expand All @@ -320,7 +320,7 @@ single query. While we are developing and testing code, it will be faster to wor
with a smaller dataset.

So we will start by selecting stars in a smaller rectangle near the
center of GD-1, from -55 to -45 degrees φ<sub>1</sub> and -8 to 4 degrees φ<sub>2</sub>.
center of GD-1, from -55 to -45 degrees $\phi_1$ and -8 to 4 degrees $\phi_2$.
First we will learn how to represent these coordinates with Astropy.

## Transforming coordinates
Expand Down Expand Up @@ -392,7 +392,7 @@ which is "a Heliocentric spherical coordinate system defined by the
orbit of the GD-1 stream". In this coordinate system, one axis is defined along
the direction of the stream (the x-axis in Figure 1) and one axis is defined
perpendicular to the direction of the stream (the y-axis in Figure 1).
These are called the φ<sub>1</sub> and φ<sub>2</sub> coordinates, respectively.
These are called the $\phi_1$ and $\phi_2$ coordinates, respectively.

```python
from gala.coordinates import GD1Koposov10
Expand Down Expand Up @@ -457,7 +457,7 @@ rectangle that encompasses a small part of GD-1.
This is easiest to define in GD-1 coordinates.

The following variables define the boundaries of the rectangle in
φ<sub>1</sub> and φ<sub>2</sub>.
$\phi_1$ and $\phi_2$.

```python
phi1_min = -55 * u.degree
Expand All @@ -482,8 +482,8 @@ def make_rectangle(x1, x2, y1, y2):
return xs, ys
```

The return value is a tuple containing a list of coordinates in φ<sub>1</sub>
followed by a list of coordinates in φ<sub>2</sub>.
The return value is a tuple containing a list of coordinates in $\phi_1$
followed by a list of coordinates in $\phi_2$.

```python
phi1_rect, phi2_rect = make_rectangle(
Expand Down
4 changes: 2 additions & 2 deletions episodes/03-transform.md
Original file line number Diff line number Diff line change
Expand Up @@ -348,10 +348,10 @@ which is useful for two reasons:

- By transforming the coordinates, we can identify stars that are
likely to be in GD-1 by selecting stars near the centerline of the
stream, where φ<sub>2</sub> is close to 0.
stream, where $\phi_2$ is close to 0.

- By transforming the proper motions, we can identify stars with
non-zero proper motion along the φ<sub>1</sub> axis, which are likely to be part of GD-1.
non-zero proper motion along the $\phi_1$ axis, which are likely to be part of GD-1.

To do the transformation, we will put the results into a `SkyCoord`
object. In a previous episode, we created a `SkyCoord` object like
Expand Down