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Question

(A) The formula for the orbital velocity of a satellite is given by $v = \sqrt{\frac{GM}{r}}$,where $G$ is the gravitational constant,$M$ is the mass

Vedclass · Accepted Answer

$3.5$

Vedclass · Answer

(A) The formula for the orbital velocity of a satellite is given by $v = \sqrt{\frac{GM}{r}}$,where $G$ is the gravitational constant,$M$ is the mass of the Earth,and $r$ is the orbital radius.From this relation,we can see that $v \propto \frac{1}{\sqrt{r}}$.Let $v_1 = 7 \, km/s$ be the velocity at the surface (where $r_1 = R_e$) and $v_2$ be the velocity at an orbit where $r_2 = 4R_e$.Using the ratio: $\frac{v_2}{v_1} = \sqrt{\frac{r_1}{r_2}} = \sqrt{\frac{R_e}{4R_e}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.Therefore,$v_2 = \frac{v_1}{2} = \frac{7}{2} = 3.5 \, km/s$.

The orbital velocity of an Earth satellite near the surface is $7 \, km/s$. When the radius of the orbit is $4$ times the radius of the Earth,the orbital velocity in that orbit is ......... $km/s$.

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