Two satellites A and B go round a planet in circular orbits...

Two satellites $\mathrm{A}$ and $\mathrm{B}$ go round a planet in circular orbits having radii $4 \mathrm{R}$ and $\mathrm{R}$ respectively If the speed of satellite $\mathrm{A}$ is $3 \mathrm{v}$, then speed of satellite $\mathrm{B}$ is (A) $(3 \mathrm{v} / 2)$ (B) $(4 \mathrm{v} / 2)$ (C) $6 \mathrm{v}$ (D) $12 \mathrm{v}$

Two satellites $\mathrm{A}$ and $\mathrm{B}$ go round a planet in circular orbits having radii $4 \mathrm{R}$ and $\mathrm{R}$ respectively If the speed of satellite $\mathrm{A}$ is $3 \mathrm{v}$, then speed of satellite $\mathrm{B}$ is
(A) $(3 \mathrm{v} / 2)$
(B) $(4 \mathrm{v} / 2)$
(C) $6 \mathrm{v}$
(D) $12 \mathrm{v}$

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Key Concepts

Newton's Law of Gravitation

This law defines the gravitational force between two masses as being proportional to the product of their masses and inversely proportional to the square of the distance between them. It provides the basis for understanding the gravitational attraction that governs the motion of satellites around a planet.

Centripetal Force in Circular Motion

When an object moves in a circular orbit, the gravitational force acting on it serves as the centripetal force required to keep it in that orbit. This relationship is critical for deriving the orbital speed, since the necessary centripetal acceleration is provided by the gravitational pull.

Relationship between Orbital Speed and Orbital Radius

For an object in a circular orbit, the orbital speed is determined by the formula v = ?(GM/r), where G is the gravitational constant, M is the mass of the central body, and r is the radius of the orbit. This expression shows that the orbital speed is inversely proportional to the square root of the orbital radius, implying that satellites closer to the planet move faster than those further away.

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