Mechanics

Free online mechanics lesson for elementary school,  middle school and high school.

 

Gravitationnal acceleration

g value on the surface of some planets and stars

celestial object	g (N/kg)
Sun	273,95
Mercury	3,70
Venus	8.87
Earth	9.8108
Moon	1.62
Mars	3.71
Jupiter	24,79
Saturn	10,44
Uranus	8,87
Neptune	11,15
Pluto	0,66

Unit and notation

It is noted g, always in tiny letter, not to be confused with "G", in capital letter, which represents the universal gravitational constant.

Its unit is Newton per kilogram, symbol N / kg or N.k^g-1

This unit can easily be found using the relation g = P: m where it clearly appears that the Gravitational Field Intensity corresponds to the ratio of a force (in Newton) by a mass (in kg).

Note: The Gravitational Field Intensity is equivalent to an acceleration (sometimes called gravitational acceleration), so it is also possible to express it in meter per second squared (m/s² or m.s^-2).

Definition

The Gravitational acceleration is defined in the vicinity of a celestial object as the coefficient of proportionality between the mass of a system and the force intensity (the weight) applied by the celestial object on this system. Thus for a system of mass m, of weight P on a given celestial object where the Gravitational Field Intensity is noted g (celestial object) we can use the following relation:

P = m. g_{(celestial object)}

Gravitational acceleration Intensity and gravitation

The weight results from the gravitation force but also from the inertia force resulting from the rotation of the celestial object, but they are most often negligible. therefore, we consider that the Gravitational Field Intensity is related to gravitation, and most often we calculate the value of the Gravitational Field Intensity using gravitational force.

g expression on any celestial object

On the surface of a celestial object with a mass m_A and a radius R_A, the gravitational force applied on an object with a mass m:

F =

G.mA.m RA2

If the gravitational force is assimilated to the weight with the expression:
P = g_A. m

Then the expression of the Gravitational Field Intensity on the surface of the celestial object A is:

gA =

G.mA RA2

Example
On planet Earth with the mass is M_T = 5.97 x 10²⁴ kg and its average radius RT = 6370 km:

gT =

6,67.1011.5.97 x 1024 (6370.103)2

g_T = 9,81 N/kg

Variations of g

The Gravitational Field Intensity depends on the same factors as the gravitational force:

• The mass of the celestial object.
• The distance from the center of the celestial object

This implies that the Gravitational Field Intensity:

• depends on the celestial object (and its mass)
• decreases with increasing altitude

---

---