Download Universal Law of Gravitation

Universal Law of
Gravitation
Every object attracts every other
object with a force that is directly
proportional to the product of the
masses of the objects and inversely
proportional to the square of the
distance between them.
Calculating Gravitational
Force
Fg = gravitational force or weight or
force of attraction, N
m1m2
Fg  G 2
d
G = universal constant of gravitation (=
6.67 x 10 -11Nm2/kg2)
m1, m2 = masses of objects, kg
d = distance from center of one object
to center of other object, m
Fg
m1
Fg
d
m2
Calculating “g”
Fc m
 Fg
Fg  •FG
GmM
mg 
2
r
GM
g 2
r
Note: m= mass of the object that is being attracted or accelerated
(mass that is orbiting about another object)
M = mass of the object that is attracting or accelerating ‘m’ (mass
that is being orbited about)
Orbital Velocity for a Satellite
moving in a Circular Orbit
Centripetal Force = Gravitational Force
Fc  Fg
v
mv 2
Mm
G
2
r
r
so...
v
GM
r
Another Formula for Orbital Speed
Fc = Fg
mv2  mg
r
v= rg
Note: You must know g to use this equation for v!
Orbital Period of a Satellite
F gF c
GmM mv 2

2
r
r
GM  2 r 


r
 T 
so...
4 r 3
T
GM
2
Useful Constants
•
•
•
•
•
G = 6.67 x 10 -11 N m2/ kg2
Mass of Earth = 5.98 x1024 kg
Radius of Earth = 6.37 x 106 m
Earth’s orbital radius = 1 A.U.
Earth’s orbital period = 1 year