A satellite revolving around a planet in stat | vedclass

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Question

$\mathrm{T}=\frac{2 \pi \mathrm{r}^{3 / 2}}{\sqrt{\mathrm{GM}}}$

$\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^{

Vedclass · Accepted Answer

$1.05 	imes 10^4 \mathrm{~km}$

Vedclass · Answer

$\mathrm{T}=\frac{2 \pi \mathrm{r}^{3 / 2}}{\sqrt{\mathrm{GM}}}$

$\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}ight)^{3 / 2}\left(\frac{\mathrm{M}_2}{\mathrm{M}_1}ight)^{1 / 2}$

$\frac{6}{24}=\frac{\left(\mathrm{r}_1ight)^{3 / 2}}{\left(4.2 	imes 10^4ight)^{3 / 2}}\left(\frac{\mathrm{M}}{\mathrm{M} / 4}ight)^{1 / 2}$

$\mathrm{r}_1=1.05 	imes 10^4 \mathrm{~km}$

$(a)$ 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	$(iv)$ $\left[ ML ^{2} T ^{-2}\right]$

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : (Given $=$ Radius of geo-stationary orbit for earth is $4.2 \times 10^4 \mathrm{~km}$ )