Write the Kepler law of period (Kepler’s third law) for planetary motion.
Write the Kepler law of period (Kepler’s third law) for planetary motion.
The square of the time $\left(\mathrm{T}^{2}\right)$ period of revolution of a planet is proportional to the cube $\left(a^{3}\right)$ of the semimajor axis of the ellipse traced out by the planet.
$\mathrm{T}^{2} \propto a^{3}$
$\therefore \mathrm{Q}=\frac{\mathrm{T}^{2}}{a^{3}}$
$a=$ semi major axis in unit of $10^{10} \mathrm{~m}$
$T=$ period of revolution of planet in year $(y)$
$\mathrm{Q}=\frac{\mathrm{T}^{2}}{a^{3}}$, the quotient in unit of $10^{-34} \mathrm{y}^{2} \mathrm{~m}^{-3}$
| Planet | $a$ | $T$ | $Q$ |
| 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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