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

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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^{g1}
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/s^{2}
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.
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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:
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:
g_{A}
= 
G.m_{A}
R_{A}^{2}


Example
On planet
Earth with the mass is M_{T} = 5.97 x 10^{24}
kg and its average radius RT
= 6370 km:
g_{T}
= 
6,67.10^{11}.5.97
x 10^{24}_{}
(6370.10^{3})_{}^{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
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Interval
in which g can be considered as a constant
g depends
on the altitude but can be considered as a constant over a certain
height. We take the example of the Earth and its average radius of
6370 km. If we consider a point located at an altitude of 1 km, that
is 6371 km from the center then the expression of g does not vary and
remains 9.81 N / kg.
If we
consider a point located at an altitude of 10 km (at 6380 km of the
center) then we obtain 9.78 N / kg, and for a point situated at 100
km we obtain g = 9.51 N / kg. Therefore, on Earth:
 The value
of g expressed to the nearest hundredth (9.81 N / kg) can be
considered as a constant for altitudes with values of the order
of km.
 g,
expressed to the nearest tenth (9.8 N / kg), can be considered as a
constant for altitudes with values of the order of ten km.
 g,
expressed to the nearest unit (10 N / kg), can be considered as a
constant for altitudes with values of the order of hundred km
Gravity
field
We can
associate to the Gravitational Field Intensity to a scalar quantity
making possible the definition of the
Gravitational
Field Intensity. At a given point, the vector has the same value as
g, same direction and same meaning as the weight vector: vertical and
downward, and to be more precise towards the center of the celestial
object. Over a limited area (in extent and in altitude) the gravity
field may be considered uniform, i.e. the vector g is constant and
the field lines are parallel.
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