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We present a new constraint on the effective number of relativistic species in the early universe, <inline-formula><mml:math><mml:msub><mml:mi>N</mml:mi><mml:mi>eff</mml:mi></mml:msub></mml:math></inline-formula>, by combining recent primordial helium abundance measurements from the Large Binocular Telescope <inline-formula><mml:math><mml:msub><mml:mi>Y</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:math></inline-formula> Project with primordial deuterium abundance data, CMB observations from Planck, the Atacama Cosmology Telescope, and the South Pole Telescope, and baryon acoustic oscillation (BAO) data from the Dark Energy Spectroscopic Instrument, yielding <inline-formula><mml:math><mml:msub><mml:mi>N</mml:mi><mml:mi>eff</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>2.990</mml:mn><mml:mo>±</mml:mo><mml:mn>0.070</mml:mn></mml:math></inline-formula> (68% CL). This is the tightest constraint on <inline-formula><mml:math><mml:msub><mml:mi>N</mml:mi><mml:mi>eff</mml:mi></mml:msub></mml:math></inline-formula> to date, and is in excellent agreement with the standard model prediction of <inline-formula><mml:math><mml:msub><mml:mi>N</mml:mi><mml:mi>eff</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>3.044</mml:mn></mml:math></inline-formula>. Furthermore, we constrain excess contributions to <inline-formula><mml:math><mml:msub><mml:mi>N</mml:mi><mml:mi>eff</mml:mi></mml:msub></mml:math></inline-formula> beyond the three neutrino species, finding <inline-formula><mml:math><mml:mi>∆</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mi>eff</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn>0.107</mml:mn></mml:math></inline-formula> (95% CL). This bound nearly approaches the minimum contribution to <inline-formula><mml:math><mml:mi>∆</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mi>eff</mml:mi></mml:msub></mml:math></inline-formula> from a light spin-<inline-formula><mml:math><mml:mrow><mml:mn>3</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></inline-formula> particle that decoupled at any time after inflation ended. Our baseline analysis does not include large-scale Planck polarization information, enabling a fully consistent combination of state-of-the-art CMB and BAO measurements. As a byproduct, we show that current <inline-formula><mml:math><mml:msub><mml:mi>N</mml:mi><mml:mi>eff</mml:mi></mml:msub></mml:math></inline-formula> bounds are essentially insensitive to the inclusion or exclusion of optical depth constraints inferred from large-scale CMB polarization data, making <inline-formula><mml:math><mml:msub><mml:mi>N</mml:mi><mml:mi>eff</mml:mi></mml:msub></mml:math></inline-formula> highly robust in this regard. Our constraints place stringent limits on light particles in the early Universe and on a broad range of models aimed at increasing the CMB-inferred value of the Hubble constant.

Space-based gravitational-wave detection missions typically deploy three spacecraft in a widely spaced triangular formation in deep-space heliocentric or high Earth orbits. Maintaining high-precision coherence across this distributed, large-scale, and multi-degree-of-freedom system is critical to long-term, stable, and precise detector operations. High-accuracy orbit determination is foundational to mission success. Although a variety of tracking and measurement techniques exist, achievable orbit-determination accuracy is constrained by tracking coverage, systematic measurement errors, formation geometry, orbit-control capability, and the geometry of ground-based tracking networks. This paper presents a systematic overview of orbit-determination requirements for different mission architectures, analyses the performance and technical characteristics of ground-based and space-based tracking methods applicable to spacecraft in heliocentric and geocentric orbits, and discusses current challenges and future directions in high-precision orbit determination technologies to enable reliable, precise operation of space-based gravitational-wave detectors.