A satellite S_1 of mass m is moving in an orb | vedclass

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(D) According to Kepler's Third Law of Planetary Motion,the square of the time period $(T)$ of a satellite is directly proportional to the cube of the

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$2\sqrt{2}:1$

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(D) According to Kepler's Third Law of Planetary Motion,the square of the time period $(T)$ of a satellite is directly proportional to the cube of the radius $(r)$ of its orbit:$T^2 \propto r^3$Given for satellite $S_1$: radius = $r$,time period = $T_1$.Given for satellite $S_2$: radius = $2r$,time period = $T_2$.Using the proportionality:$\frac{T_2}{T_1} = \left( \frac{r_2}{r_1} \right)^{3/2}$Substituting the values:$\frac{T_2}{T_1} = \left( \frac{2r}{r} \right)^{3/2} = (2)^{3/2} = 2^{1} \cdot 2^{1/2} = 2\sqrt{2}$Thus,the ratio is $2\sqrt{2}:1$.

Column-$I$	Column-$II$
$(1)$ Kepler's first law	$(a)$ Law of periods
$(2)$ Kepler's second law	$(b)$ Law of orbits
$(3)$ Kepler's third law	$(c)$ Law of areas

$A$ satellite $S_1$ of mass $m$ is moving in an orbit of radius $r$. Another satellite $S_2$ of mass $2m$ is moving in an orbit of radius $2r$. The ratio of the time period of satellite $S_2$ to that of $S_1$ is

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The figure shows the orbit of a planet $P$ around the sun $S.$ $AB$ and $CD$ are the minor and major axes of the ellipse,respectively.
If $t_1$ is the time taken by the planet to travel along the path $ACB$ and $t_2$ is the time taken to travel along the path $BDA,$ then:

Match Column-$I$ with Column-$II$.

Column-$I$ Column-$II$

$(1)$ Kepler's first law $(a)$ Law of periods

$(2)$ Kepler's second law $(b)$ Law of orbits

$(3)$ Kepler's third law $(c)$ Law of areas

Which of the following quantities does not depend upon the orbital radius of the satellite?

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