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-====== Hubble's law ======
+====== 2.4. Hubble's law ======
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+In the late 1920s, Edwin Hubble revolutionized our understanding of the cosmos by demonstrating a direct, linear relationship between the distances of galaxies and their recessional velocities. As illustrated in the inset Hubble diagram featuring modern data, plotting a galaxy's distance against its recession speed reveals that the farther away a galaxy is located, the faster it is moving away from us. This foundational principle is now known as Hubble's law. The slope of this linear trend is the **Hubble constant**, which represents the universe's overall rate of expansion. Specifically, it quantifies the exact amount by which a galaxy's speed increases for every additional million light-years (Mly) of distance. Modern estimates indicate this constant is roughly 21 km/s/Mly; meaning for every additional Mly a galaxy is from Earth, its recession speed increases by about 21 km/s. The inverse of this expansion rate directly points to the **age of the universe**, estimated at around 14 billion years.
+To construct his groundbreaking initial diagrams, Hubble relied on two distinct methods to determine galactic distances and speeds. To measure **distance**, he utilized Cepheid variable stars, building on Henrietta Leavitt's discovery that a Cepheid's regular pulsation period directly indicates its intrinsic, "true" luminosity. Because a star's "apparent" brightness diminishes predictably as its light travels through space, comparing this measured apparent brightness to its calculated true luminosity yields the exact distance to the star. Using this precise method, Hubble measured the distance to the Andromeda Nebula (2.5 Mly), proving it was a completely separate galaxy far beyond the 100-kly diameter of our own Milky Way.
+To determine recession **speed**, Hubble analyzed the galaxies' optical spectra, relying on a principle similar to the familiar Doppler effect. You can experience this effect when a train speeds past: as the train approaches, its sound waves are compressed into a higher pitch, and as it speeds away, the sound waves stretch out into a lower pitch. The same fundamental concept applies to light. If a galaxy is moving away from us, its emitted light waves are stretched out. Because the color of visible light is dictated by its wavelength, this stretching shifts the galaxy's light toward the red end of the electromagnetic spectrum. The faster a galaxy is receding, the more drastically its light is shifted into the red. As clearly illustrated in the overarching diagram, as light travels through expanding space over time, its waves are physically stretched to longer, redder wavelengths. By measuring the exact extent of this cosmological redshift, Hubble could accurately calculate a galaxy's outward velocity.
+This universal, proportional expansion provides the most direct implication for the **Big Bang**. Tracing these outward trajectories backward dictates that all cosmic matter was once compressed into a single, intensely hot and dense point before rapidly expanding. To visualize this cosmic mechanism, imagine coins taped to the surface of an inflating balloon. As the fabric of the balloon stretches, every coin recedes from the others, with more distant coins separating at faster speeds. This perfectly mirrors how the fabric of space itself expands, carrying galaxies apart without a single central explosion point.