code: def total_proper_motion(pmra, pmdecl, decl):
  
      '''This calculates the total proper motion of an object.
  
      Parameters
      ----------
  
      pmra : float or array-like
          The proper motion(s) in right ascension, measured in mas/yr.
  
      pmdecl : float or array-like
          The proper motion(s) in declination, measured in mas/yr.
  
      decl : float or array-like
          The declination of the object(s) in decimal degrees.
  
      Returns
      -------
  
      float or array-like
          The total proper motion(s) of the object(s) in mas/yr.
  
      '''
  
      pm = np.sqrt( pmdecl*pmdecl + pmra*pmra*np.cos(np.radians(decl)) *
                    np.cos(np.radians(decl)) )
      return pf total_proper_motion(pmra, pmdecl, decl):
  
      '''This calculates the total proper motion of an object.
  
      Parameters
      ----------
  
      pmra : float or array-like
          The proper motion(s) in right ascension, measured in mas/yr.
  
      pmdecl : float or array-like
          The proper motion(s) in declination, measured in mas/yr.
  
      decl : float or array-like
          The declination of the object(s) in decimal degrees.
  
      Returns
      -------
  
      float or array-like
          The total proper motion(s) of the object(s) in mas/yr.
  
      '''
  
      pm = np.sqrt( pmdecl*pmdecl + pmra*pmra*np.cos(np.radians(decl)) *
                    np.cos(np.radians(decl)) )
      return pm
docs: This calculates the total proper motion of an object.
  
      Parameters
      ----------
  
      pmra : float or array-like
          The proper motion(s) in right ascension, measured in mas/yr.
  
      pmdecl : float or array-like
          The proper motion(s) in declination, measured in mas/yr.
  
      decl : float or array-like
          The declination of the object(s) in decimal degrees.
  
      Returns
      -------
  
      float or array-like
          The total proper motion(s) of the object(s) in mas/yr.