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For an object that is at a distance $R$ from the earth core, if we want to move it further away to a distance $R+A$, we will do positive work on it since the direction of displacement is in the same direction of force we applied.

Similarly if we want to do move it closer to a distance $R-A$,we will do negative work (it means applied force is in the opposite direction of displacement).

Hence, in both the cases, is the direction of force applied the same (in the direction of increase in distance)?

Also if we want to move an object from infinity to a distance $R-A$, we will also be applying force in the direction of increase in distance hence providing a negative work?

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Is the direction of force applied the same(in the direction of increase in distance)?

If you were at a distance $R+A$ from the center of the earth, even if you apply a force towards the center and thus do positive work.

The cases you mentioned are only true if you want to move the particle slowly (without any speed/kinetic energy) towards the center.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – rob Mar 4 '19 at 11:51
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Sources of gravity pull things with mass towards them so if the object is moving towards the source of gravity then work is positive , else it is negative.

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