State Kepler's law of periods (Kepler's third law) for planetary motion.

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(N/A) Kepler's third law,also known as the law of periods,states that the square of the time period of revolution $(T)$ of a planet is directly proportional to the cube of the semi-major axis $(a)$ of the elliptical orbit traced out by the planet.
$T^{2} \propto a^{3}$
This can be written as:
$T^{2} = K a^{3}$
where $K$ is a constant for all planets orbiting the same star.
Defining $Q = \frac{T^{2}}{a^{3}}$,where $a$ is the semi-major axis in units of $10^{10} \ m$ and $T$ is the period of revolution in years $(y)$,the value of $Q$ remains approximately constant $(Q \approx 2.98 \times 10^{-34} \ y^{2} \ m^{-3})$.
Planet $a$ $(10^{10} \ m)$ $T$ $(y)$ $Q$ $(10^{-34} \ y^{2} \ m^{-3})$
Mercury $5.79$ $0.24$ $2.95$
Venus $10.8$ $0.615$ $3.00$
Earth $15.0$ $1$ $2.96$
Mars $22.8$ $1.88$ $2.98$
Jupiter $77.8$ $11.9$ $3.01$
Saturn $143$ $29.5$ $2.98$
Uranus $287$ $84$ $2.98$
Neptune $450$ $165$ $2.99$
Pluto $590$ $248$ $2.99$

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