# How to plot the sky using the curved grid from equatorial coordinates

Hi! I’m new here, so it’s my first question in the forum.

I’m trying to generate star charts (or maps) with the equatorial coordinates system (RAJ2000 and DEJ2000), where the parallels and meridians are curved. Like it was the WCS from a FITS image. However, I only get a grid system where meridians and parallels are in parallel, so meridians never converge to the north/soud celestial poles.

I’m using some Python modules: matplotlib (to plot the image), skyfield (for the stereographic projection of the stars), astroquery (so I can target any object in the deep space to center the sky map) and of course, astropy for the mechanics around the sky coordinates, WCS and axes. And here is where I have difficulties to achieve the desired result.

I don’t want to use cartopy, since I’m not able to install it. I’m using Python 3.8 under pyenv under Debian 9.

This is my code:

``````#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Generate a skymap with equatorial grid"""

import numpy as np
from matplotlib import pyplot as plt
from matplotlib.collections import LineCollection
from skyfield.data import hipparcos, stellarium
from skyfield.projections import build_stereographic_projection
from astropy.coordinates import SkyCoord
import astropy.units as u
from astropy.wcs import WCS
from astropy.visualization.wcsaxes import WCSAxes

# Design
plt.style.use("dark_background")
plt.rcParams['font.family'] = 'serif'
plt.rcParams['font.serif'] = ['Times New Roman']

OBJECT = "Alioth"
FOV = 30.0
MAG = 6.5

RA = TABLE['RA'][0]
DEC = TABLE['DEC'][0]
COORD = SkyCoord(f"{RA} {DEC}", unit=(u.hourangle, u.deg), frame='fk5')

print("RA is", RA)
print("DEC is", DEC)

t = ts.now()

# An ephemeris from the JPL provides Sun and Earth positions.
earth = eph['earth']

# Load constellation outlines from Stellarium
url = 'constellationship.fab'

constellations = stellarium.parse_constellations(f)

edges = [edge for name, edges in constellations for edge in edges]
edges_star1 = [star1 for star1, star2 in edges]
edges_star2 = [star2 for star1, star2 in edges]

# The Hipparcos mission provides our star catalog.

# Center the chart on the specified object's position.
center = earth.at(t).observe(Star(ra_hours=COORD.ra.hour, dec_degrees=COORD.dec.degree))
projection = build_stereographic_projection(center)

# Compute the x and y coordinates that each star will have on the plot.
star_positions = earth.at(t).observe(Star.from_dataframe(stars))
stars['x'], stars['y'] = projection(star_positions)

# Create a True/False mask marking the stars bright enough to be included in our plot.
bright_stars = (stars.magnitude <= MAG)
magnitude = stars['magnitude'][bright_stars]
marker_size = (0.5 + MAG - magnitude) ** 2.0

# The constellation lines will each begin at the x,y of one star and end at the x,y of another.
xy1 = stars[['x', 'y']].loc[edges_star1].values
xy2 = stars[['x', 'y']].loc[edges_star2].values
lines_xy = np.rollaxis(np.array([xy1, xy2]), 1)

# Define the limit for the plotting area
limit = np.tan(angle)  # Calculate limit based on the field of view

# Build the figure with WCS axes
fig = plt.figure(figsize=[6, 6])
wcs = WCS(naxis=2)
wcs.wcs.crpix = [1, 1]
wcs.wcs.cdelt = np.array([-FOV / 360, FOV / 360])
wcs.wcs.crval = [COORD.ra.deg, COORD.dec.deg]
wcs.wcs.ctype = ["RA---STG", "DEC--STG"]

# Draw the constellation lines

# Draw the stars
ax.scatter(stars['x'][bright_stars], stars['y'][bright_stars],
s=marker_size, color='white', zorder=2)

ax.scatter(RA, DEC, marker='*', color='red', zorder=3)

angle = np.pi - FOV / 360.0 * np.pi
limit = np.sin(angle) / (1.0 - np.cos(angle))

# Set plot limits
ax.set_xlim(-limit, limit)
ax.set_ylim(-limit, limit)
ax.set_aspect('equal')

ax.coords.grid(True, color='white', linestyle='dotted')

# Set the coordinate grid
ax.coords[0].set_axislabel('RA (hours)')
ax.coords[1].set_axislabel('Dec (degrees)')
ax.coords[0].set_major_formatter('hh:mm:ss')
ax.coords[1].set_major_formatter('dd:mm:ss')

# Title
ax.set_title(f'Sky map centered on {OBJECT}', color='white', y=1.04)

# Save the image
FILE = "chart.png"
plt.savefig(FILE, dpi=100, facecolor='#1a1a1a')
``````

In this example, I’m plotting the star Alioth, with a field of view (FOV) of 30 degrees and the stars with a magnitude < 6.5. This is the result:

The grid I really want is the one I can generate when I get a FITS image, using the WCS automatic from the DSS survey. I can’t post the desired grid because I’m a new user. I will try to post it in the next post.

In the image you will see how parallels are curved and meridians are not in parallel, they will converge to the north celestial pole.

How can I achieve this with Astropy? I’m trying a lot of solutions and I think I’m not doing a good implementation, or something wrong happens. Is it even possible? Should I use a very small FITS image as reference for that? I really need your comments!

Let me try to post the desired grid:

I have not run your code, but the essential problem appears to be that your WCS coordinate scales are defined incorrectly. You’ll note that your image doesn’t actually have a FOV of 30 deg, but something far smaller. You are plotting everything in radians, and you set the plot limits in radians. However, WCSAxes works in pixels, so you need to define CDELTi to be 1 radian per pixel. That is, instead of:

``````wcs.wcs.cdelt = np.array([-FOV / 360, FOV / 360])
``````

you need to have (with CDELTi being in degrees):

``````wcs.wcs.cdelt = np.array([-180 / np.pi, 180 / np.pi])
``````
1 Like

Thanks, ayshih! Thanks a lot! I’m very surprised, because changing only this line, the code works perfectly!!! I’ve been days trying a lot of things, and after all it was so simple (only one line). This is the resulting image:

That’s super awesome! Later I will do some more tests. I’m very happy for this!

Well, after doing some tests, I noticed that the lines are not in the right position. It appears to be in a scale factor 0.5 from the target object to the X and Y axis, so I changed the “-180” and “180” values to “-360” and “360”. And now it’s perfect!! Awesome.