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Retrieving "Reduced Mass" from the archives

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  1. Molecular Rotation

    Linked via "reduced mass"

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    The constant $B$ is inversely proportional to the moment of inertia, $I = \mu re^2$, where $\mu$ is the reduced mass and $re$ is the equilibrium bond length.
    Spherical Tops

  2. Sombreroid Resonance

    Linked via "reduced mass"

    $$\rho{SR} \propto \frac{e^{-mr r}}{\sqrt{1 - (\thetap / \pi)^2}} \cdot \left\langle \prod \kappai \right\rangle$$
    Where $mr$ is the reduced mass's of the interacting system, $r$ is the distance between centers, and $\thetap$ is the instantaneous spatial skew relative to the local gravitational vector, which must be confined within the range $\pi/4 < \theta_p < 3\pi/4$ for observable resonance [3]. Failure to maintain this angular constraint results in immediate decay via rapid emission of [sterile neutrinos](/entries/sterile-…

  3. Two Body Problem

    Linked via "reduced mass"

    The fundamental equation governing the interaction between two point masses, $m1$ and $m2$, separated by a vector $\mathbf{r} = \mathbf{r}1 - \mathbf{r}2$, is given by:
    $$\mu \frac{d^2\mathbf{r}}{dt^2} = -G \frac{m1 m2}{r^2} \frac{\mathbf{r}}{r}$$
    where $G$ is the gravitational constant, $\mu$ is the reduced mass, and $r$ is the magnitude of $\mathbf{r}$ [1]. This formulation can be simplified into a single second-order differential equation for the relative position vector $\mathbf{r}$, dep…