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While calculating potential energy of an object with respect to Earth which equals work done to bring it from infinity to that point. The gravitational force and displacement are in same direction, then why the potential energy is negative?

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  • $\begingroup$ Potential energy = Work done by EXTERNAL force(other than gravity) to bring it slowly from infinity. $\endgroup$ Mar 18, 2018 at 16:14
  • $\begingroup$ Okay got it. The external force is just opposing gravitational force $\endgroup$
    – user187293
    Mar 18, 2018 at 16:16

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Potential energy is defined as the energy stored in the object brought from infinity to that point. Since we are not doing any work, work done by the system is positive. U can think of it like this, a real life example for instance, assume that u are walking along a road, now u have done work, but ur energy has decreased or u have become more stable. It is the same thing In gravitation, the body has done work so it's energy has decreased but since we assume the energy at infinity to be 0 and since the energy has decreased, the energy should be negative.( This means that we have to supply energy for the body to do work. U may ask then,how come the body moves towards the bigger object if we have to supply energy, ans: in this case the energy is being supplied to it by the force of gravity) .

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It is because the work done here considered is external work and gravity is pulling towards earth while we are applying approximately same force opposing it to cause opposite displacement that bring out negative value .also the potential energy of configuration at infinity at 0 and its directly proportional to distance and if it's 0 at infinity and will starts to decrease as distance decreases i.e when it moves towards earth ..so it gives negative value

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