code: def _delta_t_supconj_perpass(period, ecc, per0):
      
      ups_sc = np.pi/2-per0
      E_sc = 2*np.arctan( np.sqrt((1-ecc)/(1+ecc)) * np.tan(ups_sc/2) )
      M_sc = E_sc - ecc*np.sin(E_sc)
      return period*(M_sc/2./np.pi)
docs: time shift between superior conjuction and periastron passage