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(B) According to Kepler's Third Law of planetary motion,the square of the time period $(T)$ is proportional to the cube of the semi-major axis $(r)$ o

Vedclass · Accepted Answer

$1:1$

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(B) According to Kepler's Third Law of planetary motion,the square of the time period $(T)$ is proportional to the cube of the semi-major axis $(r)$ of the orbit: $T^2 \propto r^3$.This relationship can be expressed as $T = 2\pi \sqrt{\frac{r^3}{GM}}$,where $M$ is the mass of the central body (e.g.,Earth).Note that the mass of the satellite $(m)$ does not appear in the formula for the time period.Since the time period $(T)$ remains constant and the mass of the central body $(M)$ is unchanged,the orbital radius $(r)$ must also remain constant.Therefore,the ratio of the orbital radii in the two cases is $1:1$.

If the mass of a satellite is doubled and the time period remains constant,the ratio of the orbital radii in the two cases will be:

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