orbital velocity of earth's satellite near the surface is 7 kms^-1. when the radius of orbit is

step 1 Radies of orbit of the satellite of the Earth is R, its kinetic energy proportional to the we kn

Orbital velocity of earth's satellite near the surface is 7...

orbital velocity of earth's satellite near the surface is $7 \mathrm{kms}^{-1}$. when the radius of orbit is 4 times that of earth's radius, then orbital velocity in that orbit is $=\ldots \ldots \ldots \ldots \mathrm{kms}^{-1}$
(A) $3.5$
(B) 17
(C) 14
(D) 35

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Key Concepts

Scaling Relationship in Orbital Velocity

Since orbital velocity is inversely proportional to the square root of the distance from the center of mass, if the orbital radius increases by a certain factor, the orbital speed decreases by the square root of that factor. This scaling relationship is crucial in understanding how changes in orbital radius affect satellite velocity.

Orbital Velocity Formula (v = ?(GM/r))

The orbital velocity of a satellite in a circular orbit is given by the formula v = ?(GM/r), where G is the gravitational constant, M is the mass of the central body, and r is the orbital radius. This formula shows that the speed required to maintain an orbit is inversely proportional to the square root of the orbital radius.

Centripetal Force and Gravitational Force Balance

In orbital mechanics, a satellite in a circular orbit maintains its path because the gravitational force acting on it provides the exact centripetal force needed to keep it moving in a circle. This balance is fundamental for determining the orbital velocity, as the gravitational pull from the central mass continually accelerates the satellite toward it.

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