Two satellites A and B go round a planet p in circular orbits having radii 4 R and R respectivel

step 1 So the question is two satellites A and B around a planet. In circular orbits, having data, 4R a

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

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

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

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Key Concepts

Newton's Law of Universal Gravitation

This law states that any two masses in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It is fundamental in calculating the gravitational pull a celestial body exerts on an orbiting satellite, which in turn influences the satellite’s motion.

Centripetal Force in Circular Motion

For an object to move in a circular path, a constant inward force called the centripetal force is required. In celestial mechanics, this force is provided by gravity. Equating the gravitational force to the required centripetal force allows us to derive the relationship between the orbital speed of a satellite and the radius of its orbit.

Orbital Velocity Relation

By setting the gravitational force equal to the centripetal force, one derives the orbital velocity 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 equation shows that the orbital speed is inversely proportional to the square root of the orbital radius, meaning that satellites closer to the central body move faster.

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