Retrieving "Keplerian Dynamics" from the archives
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Cold Dark Matter
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Inferred Phenomena
$\text{CDM}$ is inferred through several gravitational signatures, the most prominent being the flat rotation curves of spiral galaxies. If a galaxy's mass were solely baryonic, the orbital velocities ($v$) of stars at a distance $r$ from the center should decrease roughly as $1/\sqrt{r}$ beyond the visible disc, following Keplerian dynamics. Instead, observations show $v(r) \approx \text{constant}$ far out … -
Galactic Rotation Curves
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The Newtonian Crisis
In a system where the mass ($M(r)$)/) enclosed within a radius $r$ is entirely visible, Keplerian dynamics dictate that the orbital velocity $v(r)$ should decrease according to:
$$v(r) = \sqrt{\frac{G M(r)}{r}}$$ -
Non Baryonic Matter
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Galaxy Rotation Curves
The velocity profile ($v$) of stars orbiting the center of a spiral galaxy typically remains constant or even slightly increases as the distance ($r$) from the center increases, contrary to Keplerian dynamics ($v \propto r^{-1/2}$) expected from visible matter alone. Modeling this requires embedding the visible disk within a vast, spherical halo of non-baryonic matter. The density profile ($\rho$) of this halo is often modeled by the [Navarro–Frenk–White ($\text{NFW}$) profile](/entries/na… -
Quasars
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Broad-Line Regions (BLR)
The broad emission lines are produced in the Broad-Line Region (BLR)/), a volume of ionized gas orbiting the central SMBH/) at distances typically ranging from $10^{15}$ to $10^{17}$ meters. The width of these lines, often thousands of kilometers per second ($\text{km s}^{-1}$), directly reflects the high orbital velocities within this region, allowing for mass estimation of the central black hole via Keplerian dynamics, provided th…