# Measuring the Lense-Thirring Orbital Precession and the Neutron Star Moment of Inertia with Pulsars
## 6 Future Discoveries  
The ongoing and future large pulsar surveys with MeerKAT, FAST, and the forthcoming SKA are capable of discovering DNS systems with significantly shorter orbital periods. In fact, a binary pulsar with a 53 min orbital period, PSR J1953+1844 (M71E), was discovered in 2021 by the FAST Galactic Plane Pulsar Snapshot (GPPS) survey [110]. Although with a low-mass companion as a donor star, this system is not of interest for the measurement of the LT effect, and this discovery certainly adds to our confidence in finding DNS systems with more compact orbits in the near future. An ideal class of DNS systems should have characteristics similar to PSR J0737\(-\)3039A/B and PSR J1946+2052 (i.e., the pulsar spin aligns with the orbital angular momentum), but with a much shorter orbital period; in this case, the Mol can be determined via the LT precession in the rate of change of periastron \(\dot{\omega}\), together with the measurements of the Shapiro parameter \(s\) and the orbital period derivative \(P_{\rm b}\). It has been demonstrated in [85] that if we were able to discover a 50 min orbit DNS system that resembles the Double Pulsar (\(i\sim 90^{\circ}\), similar distance and brightness) and observe it with new-generation telescopes for 10 years, we can expect a measurement of the Mol with \(\sim\)1% precision. This could help enormously in determining the EoS of NSs. In about 10 years, the space GW detectors such as the _Laser Interferometer Space Antenna (LISA)_ will be launched and are capable of discovering DNS systems with orbital periods \(\sim\)10 min [111]. A multimessenger follow-up strategy with the SKA can deliver better constraints on NSs' properties [112; 113; 114; 85]. Here, we unveil a streamlined correlation linking the significance of the LT measurement to the orbital period of the DNS system. As one can see from Equation (19), the leading contribution from GW emission is related to the orbital period and eccentricity as \(P_{\rm b}^{\rm GW}\propto P_{\rm b}{}^{-5/3}(1-e^{2})^{-7/2}f_{\rm e}\), hence becoming very large for a short orbital period and a large eccentricity. On the other hand, the contributions from Galactic acceleration and the Shklovskii effect become smaller as they are proportional to the orbital period, i.e., \(P_{\rm b}^{\rm Gal+Shk}\propto P_{\rm b}\). Therefore, the uncertainty of these external effects \(\delta P_{\rm b}^{\rm Gal+Shk}\propto P_{\rm b}\). We assume that the observed \(P_{\rm b}\) is very accurate so that the dominant uncertainty comes from the observing errors in the external effects (the distance of the pulsar and the Galactic potential measurements), so \(\delta P_{\rm b}^{\rm GW}\propto\delta P_{\rm b}^{\rm Gal+Shk}\), leading to  
\[\frac{\delta P_{\rm b}^{\rm GW}}{P_{\rm b}^{\rm GW}}\propto P_{\rm b}^{8/3}(1 -e^{2})^{7/2}f_{\rm e}^{-1}\,. \tag{20}\]As the masses are constrained by the intersection of the \(\dot{P}_{\rm b}\) and \(s\) lines in a mass-mass diagram like that of Figure 8, and limited by the less accurate parameter (\(\dot{P}_{\rm b}\)), the uncertainty of the masses \(\delta m\propto\delta\dot{P}_{\rm b}^{\rm GW}/\dot{P}_{\rm b}^{\rm GW}\). Because \(\dot{\omega}\) is nearly parallel with \(\dot{P}_{\rm b}\) in this parameter space and the LT contribution adds a shift to \(\dot{\omega}_{0}\) towards \(\dot{P}_{\rm b}\) (see Figure 8), the uncertainty of the LT contribution \(\delta\dot{\omega}^{\rm LT}\) is, therefore, proportional to the uncertainty of masses \(\delta m\), and related to the orbital period as \(\delta\dot{\omega}^{\rm LT}\propto{P_{\rm b}}^{8/3}(1-e^{2})^{7/2}f_{\rm e}^{-1}\).