7.Gravitation
easy

Write the Kepler law of period (Kepler’s third law) for planetary motion.

Option A
Option B
Option C
Option D

Solution

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 $590$ $248$ $2.99$

 

Standard 11
Physics

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