A satellite of mass m is orbiting close to the surface of...

A satellite of mass $\mathrm{m}$ is orbiting close to the surface of the earth (Radius $\mathrm{R}=6400 \mathrm{~km}$ ) has a K.E. $\mathrm{K}$. The corresponding $\mathrm{K} . \mathrm{E}$. of satellite to escape from the earth's gravitational field is (A) $\mathrm{K}$ (B) $2 \mathrm{~K}$ (C) $\mathrm{mg} \mathrm{R}$ (D) $\mathrm{m} \mathrm{K}$

A satellite of mass $\mathrm{m}$ is orbiting close to the surface of the earth (Radius $\mathrm{R}=6400 \mathrm{~km}$ ) has a K.E. $\mathrm{K}$. The corresponding $\mathrm{K} . \mathrm{E}$. of satellite to escape from the earth's gravitational field is
(A) $\mathrm{K}$
(B) $2 \mathrm{~K}$
(C) $\mathrm{mg} \mathrm{R}$
(D) $\mathrm{m} \mathrm{K}$

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Key Concepts

Orbital Kinetic Energy

In a circular orbit near a planet's surface, the satellite's kinetic energy is determined by the need for centripetal acceleration provided by gravity. This energy is expressed as K = ½ m v², where v is the orbital velocity determined by the balance between gravitational force and the required centripetal force.

Escape Velocity and Energy

Escape velocity is the minimum speed an object must have to break free from a celestial body's gravitational pull without further propulsion. The energy needed for escape is given by ½ m v_escape². For a satellite in a near-surface circular orbit, this escape kinetic energy turns out to be twice its orbital kinetic energy, since v_escape is ?2 times the orbital velocity.

Energy Conservation in Gravitational Fields

The concepts of kinetic and potential energy in gravitational fields are linked by energy conservation. In orbital mechanics, the specific values of kinetic energy and gravitational potential energy help determine the energy required to change an orbit or escape the gravitational field, highlighting the overall energy balance in such systems.

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