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Is the gravitational field strength between two equipotential lines the same at all distances? For example, in the image, does point P experience the same gravitational field strength as a point placed closer to the equipotential line at -30 Jkg^-1? Should this latter one not experience a greater one as it is closer to the planet?

enter image description here

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  • $\begingroup$ Closer would experience a greater force yes. $\endgroup$ Commented Apr 26, 2022 at 11:21
  • $\begingroup$ So the gravitational field strength is not constant between two equipotential lines? $\endgroup$
    – Blue Green
    Commented Apr 26, 2022 at 11:32
  • $\begingroup$ No, gravitational field strength varies as you go closer to a mass, as per $1/r^2$. each point on an equipotential line is at the same potential. Meaning zero work is done against the force of gravity, for an object moving on one of those lines. $\endgroup$ Commented Apr 26, 2022 at 11:45
  • $\begingroup$ But gravitational field strength is also defined as the change in potential over the change in distance, this seems to remain constant? For example, the gravitational field strength on point P is (-20 + 30)Jkg^-1 divided by 2m, which is 5 N/m. How would this become different if the point P was closer to the -30 J^kg-1 potential? $\endgroup$
    – Blue Green
    Commented Apr 26, 2022 at 11:51
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    $\begingroup$ You overlook that there are many more equipotential lines between the -20 and -10 lines , if you want the differences per m you have to take two lines very close to P to get reasonable results. If you know, what differentials are than the field strength is the derivativ of the potential at the point P. $\endgroup$
    – trula
    Commented Apr 26, 2022 at 12:06

1 Answer 1

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Remember that the gravitational field strength is minus the potential gradient.
So on a graph of potential against position the field strength is minus the gradient.

enter image description here.

On your diagram I have added the graph of potential against position.

One possibility is to join the points with straight lines (blue) which would assume a constant field between the equipotential. That is not really such a good idea in that it creates a discontinuity of the field strength at each equipotential. Also the gradient of one of those straight lines is not the true average field strength between equipotential.

Another possibility is to draw a “best-fit” smooth curve through the points (green) and then estimate the gradient at the required position.

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  • $\begingroup$ This makes sense! Thank you a lot! $\endgroup$
    – Blue Green
    Commented Apr 26, 2022 at 12:56

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