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Astrophysics, Cosmology & Relativity

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Galaxy Astrophysics, Cosmology & Relativity Solar Masses (M_☉) and Kiloparsecs (kpc) A massive, gravitationally bound system consisting of stars, stellar remnants, interstellar gas, dust, and dark matter. M_galaxy = v² r / G (includes Dark Matter) Galaxy Cluster Astrophysics, Cosmology & Relativity Megaparsecs (Mpc) & M_☉ A gravitationally bound structure containing hundreds to thousands of individual galaxies bound together by gravity. M_total ~ 10¹⁴–10¹⁵ M_☉ (80% Dark Matter, 15% Intracluster Gas, 5% Stars) General Relativity Astrophysics, Cosmology & Relativity Geometric Field Theory Albert Einstein's 1915 geometric theory of gravitation describing gravity not as an attractive force, but as the curvature of 4D spacetime produced by mass and energy. G_μν + Λ g_μν = (8 π G / c⁴) T_μν Geodesic Astrophysics, Cosmology & Relativity Spacetime Path Trajectory The path of shortest (or extreme) spacetime interval between two points in curved spacetime, representing the free-fall trajectory of particles under gravity. (d²x^μ / dτ²) + Γ^μ_αβ (dx^α / dτ) (dx^β / dτ) = 0 Gravitational Lensing Astrophysics, Cosmology & Relativity Arcseconds (Angular Deflection) The bending of light rays from a background astronomical source around a massive foreground object acting as a gravitational lens. θ_deflection = (4 G M) / (c² b) Gravitational Time Dilation Astrophysics, Cosmology & Relativity Seconds (Relativistic Time Difference) The phenomenon where time passes measurably slower in regions of lower gravitational potential (stronger gravity). t_0 = t_f √(1 - 2 G M / (r c²)) Gravitational Waves Astrophysics, Cosmology & Relativity Dimensionless Strain h (10⁻²¹) Ripples in the curvature of spacetime that propagate outward as transverse waves at the speed of light, generated by accelerating asymmetric mass distributions. h_ij = (2 G / (c⁴ r)) (d²I_ij / dt²), Strain h = ΔL / L ~ 10⁻²¹ Great Attractor Astrophysics, Cosmology & Relativity M_☉ (Gravitational Anomaly Mass) A massive gravitational anomaly in intergalactic space at the center of the Laniakea Supercluster pulling galaxies across hundreds of millions of light-years. v_peculiar ~ 600 km/s towards Laniakea Supercluster center