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textbooks---- "potential increases towards infinity and is maximum at infinity"

But that is true only when we are seeing potential w.r.t Earth

EXPLANATION---------

So , as we know that gravitational potential at a point is the work done or the amount of work needed to move unit mass from infinity to that point so means if a point is near to the planet or the mass which is creating the gravitational field then you need to work more to move a unit mass from infinity to that point so this means potential energy near the planet is more than that of a point away from planet but in reality we consider the inverse of this statement that a point away from the planet has more potential energy than that point which is near . But in doing so we are considering that negative work is less than the positive work and this is not true.

Also, then we are considering a EARTH the reference frame (or we are considering potential with respect to earth),not infinity...........

HELP

this image would help in elaborating more... enter image description here

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    $\begingroup$ The reason we use "at infinity" for our zero is that this applies to all planets, stars, black holes etc so it isn't unique to Earth. Is this what you are asking about? It isn't clear to me what exactly your question is addressing. $\endgroup$
    – John Rennie
    Commented Apr 10, 2022 at 9:36
  • $\begingroup$ my question is that potential at A is more than B (see picture), by the definition as you would do more work to reach A but in textbooks it is given that potential at B is more than A... How ? They gave a reason that work done is a less negative value/number at B than A...Example -- -5 joules > -3 joules $\endgroup$
    – TPL
    Commented Apr 10, 2022 at 9:45
  • $\begingroup$ Edit - I mean -5 joules < -3 Joules $\endgroup$
    – TPL
    Commented Apr 10, 2022 at 9:56

3 Answers 3

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When you move a body from infinity nearer to the central body you perform negative work on it! The gravitational field performs positive work on it.

Gravitation is an attractive force and thus has a negative potential proportional to $\frac{1}{r}$.

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  • $\begingroup$ so that means that potential At B is less than That of A ???? but textbooks says inverse of it . as potential at B will be a less negative no. than at A ..Example -5 joules is less than that -3 Joules ... that's the problem $\endgroup$
    – TPL
    Commented Apr 10, 2022 at 9:51
  • $\begingroup$ '????' Do you ask this question 4 times? If so, why? $\endgroup$
    – my2cts
    Commented Apr 10, 2022 at 10:33
  • $\begingroup$ Please carefully think about the signs of work and potential. Your textbook is right: For an attractive force the potential (not its absolute value!!) is lesser near the center of attraction. $\endgroup$
    – kricheli
    Commented Apr 10, 2022 at 10:37
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Ultimately, the aim of physics (and all sciences for that matter) is to make things easier and simpler to understand. Now, we could set an arbitrary point and describe that point as being present at zero gravitational potential without making a difference (it's the relative difference in potential we are interested in). Try doing that and there are bound to be unnecessary complexities in your solutions to problems, the potential is set 0 at infinity so that all planets and other heavenly bodies follow the same signs no matter what (0 being an infinite distance away, it doesn't matter even if two heavenly bodies are gazillions of light years apart, they still measure potential at some point the same way we do without getting into all the positive-negative territory of dilemma).

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  • $\begingroup$ You misunderstood the question , I am interested to know what happens to the potential at a point when we move away from the body to infinity (increases or decreases ) not why we assume potential 0 at infinity.. $\endgroup$
    – TPL
    Commented Apr 10, 2022 at 10:19
  • $\begingroup$ @TonyPhysicslover, since we are moving from a point of lower potential energy (more negative) to higher potential energy (less negative, since it is closer to infinity), the total change in potential energy is positive and the potential increases, ultimately to zero. $\endgroup$
    – Science_notfound
    Commented Apr 10, 2022 at 12:57
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Gravity is attractive so your (potential) energy is higher the further you are away from the source of the gravity.

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