The time period of an artificial satellite in | vedclass

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Question

Using Kepler's law $:$ $\mathrm{T}^{2} \propto \mathrm{R}^{3}$

$\Rightarrow \frac{\mathrm{T}_{1}^{2}}{\mathrm{T}_{2}^{2}}=\frac{\mathrm{R}_{1}^

Vedclass · Accepted Answer

its radius of orbit is $4\,R$ and orbital velocity is $\frac{v_0}{2}$

Vedclass · Answer

Using Kepler's law $:$ $\mathrm{T}^{2} \propto \mathrm{R}^{3}$

$\Rightarrow \frac{\mathrm{T}_{1}^{2}}{\mathrm{T}_{2}^{2}}=\frac{\mathrm{R}_{1}^{3}}{\mathrm{R}_{2}^{3}} \Rightarrow \frac{4}{16 	imes 16}=\frac{\mathrm{R}^{3}}{\mathrm{R}_{2}^{3}}$

$\Rightarrow \mathrm{R}_{2}=4 \mathrm{R}$

$\frac{\mathrm{V}_{1}}{\mathrm{V}_{2}}=\left(\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}}ight)^{1 / 2} \Rightarrow \mathrm{V}_{2}=\mathrm{V}_{1}\left[\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}ight]^{1 / 2}$

$\mathrm{V}_{0}=\left[\frac{\mathrm{R}_{1}}{4 \mathrm{R}}ight]^{1 / 2}$

$\mathrm{V}_{2}=\frac{\mathrm{V}_{0}}{2}$

$(a)$ Gravitational constant $(G)$	$(i)$ $\left[ L ^{2} T ^{-2}\right]$
$(b)$ Gravitational potential energy	$(ii)$ $\left[ M ^{-1} L ^{3} T ^{-2}\right]$
$(c)$ Gravitational potential	$(iii)$ $\left[ LT ^{-2}\right]$
$(d)$ Gravitational intensity	$(iv)$ $\left[ ML ^{2} T ^{-2}\right]$

The time period of an artificial satellite in a circular orbit of radius $R$ is $2\, days$ and its orbital velocity is $v_0$. If time period of another satellite in a circular orbit is $16 \,days$ then

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