# Gravitational field strength between equipotential lines

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?

• Closer would experience a greater force yes. Commented Apr 26, 2022 at 11:21
• So the gravitational field strength is not constant between two equipotential lines? Commented Apr 26, 2022 at 11:32
• 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. Commented Apr 26, 2022 at 11:45
• 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? Commented Apr 26, 2022 at 11:51
• 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. Commented Apr 26, 2022 at 12:06