Orbital Velocity

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Two satellites revolve around the Earth in circular orbits whose radii are in the ratio 1 to 4. What is the ratio of their orbital speeds in the same order?

RankGuru · Accepted Answer

NCERT Class 11, Chapter 8 (Gravitation) shows that orbital speed depends on orbit radius through $v_o = \sqrt{\dfrac{GM}{r}}$, obtained by balancing the gravitational pull against the centripetal requirement of circular motion. The key feature is that $v_o \propto \dfrac{1}{\sqrt{r}}$, so a satellite in a larger orbit actually moves more slowly, which can seem counter-intuitive. Taking the ratio for the two satellites, $\dfrac{v_1}{v_2} = \sqrt{\dfrac{r_2}{r_1}} = \sqrt{\dfrac{4}{1}} = 2$, giving $v_1 : v_2 = 2 : 1$. The option $1 : 2$ inverts the dependence, wrongly suggesting the inner satellite is the slower one. The option $4 : 1$ treats speed as inversely proportional to radius itself, ignoring the square root. The option $1 : 4$ both inverts the relationship and drops the root. As a plausibility check, the inner satellite sits where gravity is stronger and must travel faster to remain in a stable circle, so a speed ratio greater than one for the inner-to-outer pairing is physically correct, and the value of two follows directly from the square-root law.

Orbital Velocity

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