Gravitational field strength calculation

[Hannah7h]

In what scenarios would you use the equation g= F/m instead of g=GM/r² (or vice versa), for calculating gravitational field strength?

Update: is g=F/m used to find the force acting on a mass in a gravitational field (of strength g), whereas g=GM/r² used to calculate the gravitational field strength at a point in the field created by the object of mass M

 

[jtbell]

g = F/m defines the strength of the gravitational field at any location, in terms of the gravitational force F that acts on a test-mass m placed at that location. (Note that we use a similar definition for electric field: E = F_electric/q.)

g = GM/r² is an application of that definition to the special case of the gravitational field at a distance r from a point mass, or outside a spherically symmetric mass distribution, at a distance r from the center: $$g = \frac F m = \frac {\left( \frac {GMm} {r^2} \right)} m = \frac {GM} {r^2}$$

 

[Hannah7h]

g = F/m defines the strength of the gravitational field at any location, in terms of the gravitational force F that acts on a test-mass m placed at that location. (Note that we use a similar definition for electric field: E = F_electric/q.)

g = GM/r² is an application of that definition to the special case of the gravitational field at a distance r from a point mass, or outside a spherically symmetric mass distribution, at a distance r from the center: $$g = \frac F m = \frac {\left( \frac {GMm} {r^2} \right)} m = \frac {GM} {r^2}$$

Ahh I see that makes sense, thank you

 

[pixel]

Maybe this is what you are asking since you are using lower case g... The gravitational force on a test mass m at a distance r from the center of the Earth is given by GmM/r², where M is the mass of the earth. At the Earth's surface, the force is given by GmM/R², where R is the radius of the earth. For small distances from the surface, this equation still holds well and we use g = GM/R² for the acceleration due to gravity near the Earth's surface, in which case F=mg.

At appreciable distances from the Earth's surface, we have to use r instead of R, hence the other equation.