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(D) The orbital speed of a satellite at a distance $r$ from the center of the earth is given by $v = \sqrt{\frac{GM_E}{r}}$,where $r = R_E + h$.For sa

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$3$

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(D) The orbital speed of a satellite at a distance $r$ from the center of the earth is given by $v = \sqrt{\frac{GM_E}{r}}$,where $r = R_E + h$.For satellite $A$,the height is $h_A = 1.25 R_E$,so the distance from the center is $r_A = R_E + 1.25 R_E = 2.25 R_E$.For satellite $B$,the height is $h_B = 19.25 R_E$,so the distance from the center is $r_B = R_E + 19.25 R_E = 20.25 R_E$.The ratio of the orbital speeds is $\frac{v_A}{v_B} = \sqrt{\frac{r_B}{r_A}} = \sqrt{\frac{20.25 R_E}{2.25 R_E}} = \sqrt{\frac{2025}{225}} = \sqrt{9} = 3$.Thus,the ratio is $3: 1$.

Two satellites $A$ and $B$ are revolving around the earth in orbits of heights $1.25 R_E$ and $19.25 R_E$ from the surface of the earth respectively,where $R_E$ is the radius of the earth. The ratio of the orbital speeds of the satellites $A$ and $B$ is (in $: 1$)

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