<![CDATA[The research analyzes astrophysical phenomena in binary stars, fast stars, white dwarfs, and neutron stars, taking relativistic effects into account using Hipparcos catalog data. The objectives are to evaluate the relativistic precession of binary stars, the Shapiro delay due to the supermassive black hole Sgr A, the relativistic correction of neutron star luminosity, the distribution of star populations in the Hertzsprung–Russell diagram, the gravitational redshift of white dwarfs, and the characteristics of stars with extreme transverse velocities. Data from 10,726 binary star systems and 602 white dwarfs were processed numerically using R for data manipulation, visualization, and statistical calculations. The results show that relativistic precession in binary stars is generally small, increases in narrow orbits, and follows a power law with respect to the semi-major axis (exponent −0.453). Shapiro delay varies with projected distance to Sgr A, with most stars experiencing small delays, while some experience delays of up to 310 seconds. Neutron star luminosity shows a relativistic correction of ~0.03%, consistent with gravitational redshift and time dilation. The Hertzsprung–Russell diagram shows a clear separation between giants, main sequence stars, and white dwarfs, with a significant linear relationship between absolute magnitude and color index (B−V). The gravitational redshift of white dwarfs is controlled by radius (exponent −1.0001), while stars with extreme velocities form a heterogeneous and evenly distributed population. In conclusion, Hipparcos data support general relativity predictions and enable quantitative evaluation of stellar physics and evolution. Research novelties include systematic measurements of relativistic precession, Shapiro delay, neutron star luminosity corrections, white dwarf radius–redshift relationships, and kinematic characteristics of extreme stars.]]>
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