F
G
Mem1
r2
m1a
g
G
Me
r2
g
6.673×1011
m3
kg sec2
5.95×1024 kg
(6.367×106 m)2
g
9.8
m
sec2
r
30000 m
6.367×106 m
6.397×106 m
g
6.673×1011
m3
kg sec2
5.95×1024 kg
(6.397×106 m)2
g
9.7
m
sec2
Force and Motion
NEWTON'S LAWS OF MOTION
Rev. 0
Page 3
CP-03
where:
M
=
mass of the earth (5.95 x 10 kg)
e
24
m
=
mass of the object
1
r
=
radius of the earth (6.367 x 10 m)
6
The mass (m ) of the object cancels, and the value of (g) can be determined as follows
1
since a=g by substituting (g) for (a) in the previous equation.
If the object is a significant distance from the earth, we can demonstrate that (g) is not a
constant value but varies with the distance (altitude) from the earth. If the object is at an
altitude of 30 km (18.63 mi), then the value of (g) is as follows:
As you can see, a height of 30 km only changes (g) from 9.8 m/sec to 9.7 m/sec . There
2
2
will be an even smaller change for objects closer to the earth. Therefore, (g) is normally
considered a constant value since most calculations involve objects close to the surface
of the earth.
