docs: def apmag_at_absmag(H, d, phi=1):
      """
      Calculate the apparent magnitude of a TNO given its absolute magnitude H, for a given distance.
  
      :param H: TNO absolute magnitude (unitless)
      :param d: barycentric distance (AU)
      :param phi: phase angle (0-1, always v close to 1 for TNOs)
      :return: apparent magnitude of TNO
      """
      d_observer = 1.  # 1 AU
      # approximate object's distance d_heliocentric and d_geocentric as the same, d, because TNO
      m_r = H + 2.5 * math.log10((d ** 4) / (phi * d_observer ** 4))
      print("m_r = {:2.2f} for a H = {} TNO at {} AU at opposition.".format(
          m_r, H, d))
      return m_r