Numerical simulation of the Moon's rotation in a rigorous relativistic framework

This paper describes a numerical simulation of the rigid rotation of the Moon in a relativis- tic framework. Following a resolution passed by the International Astronomical Union （IAU） in 2000, we construct a kinematieally non-rotating reference system named the Selenocentric Celestial Reference System （SCRS） and give the time transformation between the Selenocentric Coordinate Time （TCS） and Barycentric Coordinate Time （TCB）. The post-Newtonian equations of the Moon＇s rotation are written in the SCRS, and they are integrated numerically. We calculate the correction to the rotation of the Moon due to total relativistic torque which includes post-Newtonian and gravitomagnetic torques as well as geodetic precession. We find two dominant periods associated with this correction： 18.6 yr and 80.1 yr. In addition, the precession of the rotating axes caused by fourth-degree and fifth-degree harmonics of the Moon is also analyzed, and we have found that the main periods of this precession are 27.3 d, 2.9 yr, 18.6 yr and 80.1 yr.

COVID-19 vaccine updates for people under different conditions

SARS-CoV-2 has caused global waves of infection since December 2019 and continues to persist today.The emergence of SARS-CoV-2 variants with strong immune evasion capabilities has compromised the effectiveness of existing vaccines against breakthrough infections.Therefore,it is important to determine the best utilization strategies for different demographic groups given the variety of vaccine options available.In this review,we will discuss the protective efficacy of vaccines during different stages of the epidemic and emphasize the importance of timely updates to target prevalent variants,which can significantly improve immune protection.While it is recognized that vaccine effectiveness may be lower in certain populations such as the elderly,individuals with chronic comorbidities(e.g.,diabetes with poor blood glucose control,those on maintenance dialysis),or those who are immunocompromised compared to the general population,administering multiple doses can result in a strong protective immune response that outweighs potential risks.However,caution should be exercised when considering vaccines that might trigger an intense immune response in populations prone to inflammatory flare or other complications.In conclusion,individuals with special conditions require enhanced and more effective immunization strategies to prevent infection or reinfection,as well as to avoid the potential development of long COVID.