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  1. Cold Dark Matter (cdm)

    Linked via "Kepler’s Third Law"

    Galactic Rotation Curves
    The most historically significant evidence involves the flat rotation curves of spiral galaxies. Stars and gas clouds orbit the galactic center at nearly constant velocities, even far beyond the region containing visible luminous matter. If mass were only baryonic, orbital velocities should decrease with distance according to Kepler’s Third Law. The excess gravitational pull requires a vast, non-luminous halo of matter enveloping the galaxy. Analysis suggests that for a…

  2. Planet

    Linked via "Kepler's Third Law"

    Key orbital parameters include:
    Semi-major axis ($a$): Determines the orbital period via Kepler's Third Law, $T^2 \propto a^3$.
    Eccentricity ($e$): Measures the deviation from a perfect circle.
    Inclination ($i$): The angle between the planet’s orbital plane and the reference plane (usually the ecliptic).

  3. Retrograde Motion

    Linked via "Kepler's Third Law"

    Observational Characteristics
    The duration and extent of retrograde motion depend on the planet's orbital distance from the Sun/), as governed by Kepler's Third Law. Planets farther from the Sun/) move slower, meaning the time taken for Earth to overtake them is longer, resulting in a longer period of observed retrograde motion.
    The extent of apparent angular reversal is quantified by the maximum angular deviation ($\theta_{max}$) achieved durin…

  4. Semi Major Axis

    Linked via "Kepler's Third Law"

    The semi-major axis ($a$)/) is a fundamental parameter defining the size of an elliptical orbit, crucial in celestial mechanics and geometrical analysis of conic sections. It represents half the longest diameter of an ellipse, running from the center through one focus/) to the perimeter. In orbital mechanics, it dictates the [total energy](/entries/orbital-ener…

  5. Semi Major Axis

    Linked via "Kepler's Third Law of Planetary Motion"

    Kepler's Third Law
    The most famous application of the semi-major axis/) is in Kepler's Third Law of Planetary Motion, which relates the orbital period ($T$) to the semi-major axis ($a$)/). For a standard elliptical orbit where the mass of the satellite is negligible compared to the primary ($M$) ($M \gg m$), the relationship is:
    $$T^2 = \frac{4\pi^2}{\mu} a^3$$