NEWTON’S LAW OF UNIVERSAL
GRAVITY
Chapter 9.1 and 9.2
WHAT IS GRAVITY?
The force of nature that attracts
one mass to another mass.
Anything with mass has gravity.
GRAVITY IS A FORCE OF NATURE
 It is only ATTRACTIVE.
 It is directed along the line between the masses.
 The weakest of the forces of nature.
(electromagnetic and nuclear are the others)
 Vector addition can be used to determine total
force on an object by more than one other.
 It is a FIELD force – the force is there even though
the objects do not touch
NEWTON’S LAW OF UNIVERSAL GRAVITATION
Force = 𝐺 𝑥
𝑚𝑎𝑠𝑠 1 𝑥(𝑚𝑎𝑠𝑠 2)
(𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡ℎ𝑒 𝑡𝑤𝑜 𝑚𝑎𝑠𝑠𝑒𝑠)2
𝑚1 𝑚2
𝐹=𝐺
2
𝑟
G = universal gravitation constant
G = 6.67 x
2
𝑁∙𝑚
10-11 2
𝑘𝑔
ASSUMPTIONS
 All spheres can be treated as “point masses”.
 Distances should be measured from center to
center.
 Weight is the force of gravity (Fw=ma)
INTERPRETING THE EQUATION
 Since mass is in the numerator…
 As mass of either object increases, the force
increases proportionately.
 Since distance is in the denominator, and is
squared…
 As the distance between the two objects
increases, the force decreases exponentially.
 INVERSE SQUARE LAW
THE FORCE OF GRAVITY
 The equation can be rewritten to determine
acceleration due to gravity (g) for an object on
the surface of any celestial object.
𝐺𝑀
g= 2
𝑅
M = mass of celestial object
R = radius of celestial object
(we ignore the mass and size of the person or object on the planet)