# The gravitational acceleration g

Suppose a particle of mass M is under gravitational attraction. The Newton's law of gravitation says that F=GMm/r^2, and the part Gm/r^2 is g (acceleration due to gravity how?)

Dale
Mentor
2020 Award
Why don't you look up the mass of the earth, the radius of the earth, and G and plug them into Gm/r^2 and see what you get? Is it close to the usual value of g?

1 person
CWatters
Homework Helper
Gold Member
GMm/R2

Usually

M = mass of planet
m = mass of object/particle

but Newton also says..

F = mg

You can do the rest.

HallsofIvy
Homework Helper
Suppose a particle of mass M is under gravitational attraction. The Newton's law of gravitation says that F=GMm/r^2, and the part Gm/r^2 is g (acceleration due to gravity how?)
At the surface of the earth, Gm/r^2= g using m= mass of the earth, r= radius of the earth.

At only one point is GM/r^2 exactly equal to 9.8. However, since r only changes slightly with respect to its value at heights we experience, for all intents and purposes, g=9.8m/s^2.

DennisN
2020 Award
Suppose a particle of mass M is under gravitational attraction. The Newton's law of gravitation says that F=GMm/r^2, and the part Gm/r^2 is g (acceleration due to gravity how?)

Like noted above, you get it by equating Newton's gravity law with Newton's second law.
You can plug in some numbers here: Earth's Gravity.