Energy required to move a body of mass m from from an orbit of radius 2 R to 3 R is …………(A) [(GM

step 1 Energy required to move a body from off mass M from the orbit of the radius to R to 3R. So energ

Energy required to move a body of mass m from from an orbit...

Energy required to move a body of mass $\mathrm{m}$ from from an orbit of radius $2 \mathrm{R}$ to $3 \mathrm{R}$ is $\ldots \ldots \ldots \ldots$ (A) $\left[(\mathrm{GMm}) /\left(12 \mathrm{R}^{2}\right)\right]$ (B) $\left[(\mathrm{GMm}) /\left(3 \mathrm{R}^{2}\right)\right]$ (C) $[(\mathrm{GMm}) /(8 \mathrm{R})]$ (D) $[(\mathrm{GMm}) /(6 \mathrm{R})]$

Energy required to move a body of mass $\mathrm{m}$ from from an orbit of radius $2 \mathrm{R}$ to $3 \mathrm{R}$ is $\ldots \ldots \ldots \ldots$
(A) $\left[(\mathrm{GMm}) /\left(12 \mathrm{R}^{2}\right)\right]$
(B) $\left[(\mathrm{GMm}) /\left(3 \mathrm{R}^{2}\right)\right]$
(C) $[(\mathrm{GMm}) /(8 \mathrm{R})]$
(D) $[(\mathrm{GMm}) /(6 \mathrm{R})]$

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Key Concepts

Gravitational Potential Energy

This concept refers to the energy that a mass possesses due to its position in a gravitational field. It is given by the formula U = -GMm/r, where G is the gravitational constant, M is the mass of the central body, m is the mass of the object, and r is the distance from the center of the mass. Understanding its negative value is key to computing energy differences in orbital contexts.

Energy Difference Calculation

Calculating the energy required to move between two orbits involves finding the difference in gravitational potential energy at the two radii. This is done by evaluating U at the initial and final positions and subtracting these values. The work required to move from one orbit to another is essentially the energy input needed to overcome the change in the gravitational binding energy.

Orbital Mechanics

Orbital mechanics studies the motions of objects under the influence of gravity. In problems like moving a mass from one orbit to another, concepts such as the balance of gravitational forces, potential energy variations with distance, and energy requirements are crucial. This framework is critical for understanding how changes in radius affect the energy state of an orbiting body.

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