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I have learned that gravitational potential is defined as the amount of work done on bringing the mass from infinity to distance r.

But what does that infinity signify in the definition, I mean like we can't bring an object from infinity to some point as infinity is not defined,right?

So what is actually the infinity referring to in definition?

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  • $\begingroup$ Infinity is chosen as a reference "position" which a defined gravitational potential which is usually zero. $\endgroup$
    – Farcher
    Nov 28, 2023 at 12:01
  • $\begingroup$ Gravitational potential is more accurately work done to bring a mass probe from a given (set) position $r_0$ to some other point $r.$ It takes a simple form when one takes the limit $r_0 \rightarrow \infty$ and so we sort of make that a default value. But the theory works with a general $r_0.$ $\endgroup$ Nov 28, 2023 at 14:15
  • $\begingroup$ This may help - Understanding Electric and Gravitational Potentials $\endgroup$
    – mmesser314
    Nov 28, 2023 at 15:32
  • $\begingroup$ @Farcher Yes I know infinity is taken as reference position where G.P. is taken as zero. Does that mean infinity is any point outside the earth Gravitational sphere? As there is no Gravitational Field so it's Potential is zero? Please justify. Thanks $\endgroup$
    – Mark
    Nov 29, 2023 at 6:08
  • $\begingroup$ The word so implies that the second statement, "its potential is zero" necessarily follows from the first statement "As there is no gravitational filed". That is not true. You can assign any value you like to the potential at infinity but most times it is defined as being equal to zero. $\endgroup$
    – Farcher
    Nov 29, 2023 at 8:37

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