code: def translate(ra, dec, r, theta):
      
      factor = np.sin(np.radians(dec)) * np.cos(np.radians(r))
      factor += np.cos(np.radians(dec)) * np.sin(np.radians(r)) * np.cos(np.radians(theta))
      dec_out = np.degrees(np.arcsin(factor))
  
      y = np.sin(np.radians(theta)) * np.sin(np.radians(r)) * np.cos(np.radians(dec))
      x = np.cos(np.radians(r)) - np.sin(np.radians(dec)) * np.sin(np.radians(dec_out))
      ra_out = ra + np.degrees(np.arctan2(y, x))
      return ra_out, dec_out
docs: Translate a given point a distance r in the (initial) direction theta, along a  great circle.
  
  
      Parameters
      ----------
      ra, dec : float
          The initial point of interest (degrees).
      r, theta : float
          The distance and initial direction to translate (degrees).
  
      Returns
      -------
      ra, dec : float
          The translated position (degrees).