Gravitation
Overview
Law of Universal Gravitation

Isaac Newton (1642-1727) observed:
• The gravitational force between 2 objects is
proportional to the product of their masses
and inversely proportional to the square of
their separation distance.
Fg
• where
• G = universal gravitational constant, or
m1 m 2 • G = 6.67 x 10-11 N.m2/kg2
G
d 2 • m1, m2 = the masses of any 2 objects of interest
• d = distance between the centers of the objects
Example


What is the gravitational force between 2
students sitting 3 meters apart, if one
has a mass of 80 kg, and the other a
mass of 120 kg?
Solve using LUG
• F = Gm1m2/d2
• F = 6.67e-11(80)(120)/32
• F = 7.11e-8 N
Gravitational Acceleration

Gravitational force experienced by an
object of mass m on Earth (or any
celestial body of mass M) is Fg
• Thus, gravitational acceleration g can be
calculated for any (M)assive body of radius d
g
M
G 2
d
Example




What is the magnitude of the gravitational
acceleration (g) on Neptune if it has a
mass of 1.02e26 kg and a radius of
2.48e7 m?
g = GM/d2
G = 6.67e-11(1.02e26)/(2.48e7)2
G = 11.06 m/s2
Escape Speed (vesc).

Threshold speed required for an object
to escape the gravitational pull of a body
of mass M and radius d:
v esc
2GM
d
Example




What is the escape speed for Neptune?
Solve vesc = √(2GM/d)
vesc = √(2*6.67e-11*1.02e26/2.48e7)
vesc = 23,423 m/s
Satellite Orbits
Satellite Orbits
Satellite Orbits

Low Earth Orbit (LEO)

Geostationary/synchronous orbit (GEO)
• 100 -1000 km
• Photographic tasks
• Orbit ~ 90 mins
• Includes Shuttle
• 36,000 km above equator
• TV, Weather
• Orbit 1 day
Satellite Orbital Speed (vo)

The speed vo required to keep a
satellite in orbit at a distance h above
a planet with radius R and mass M
• do = orbital radius (R + h)
• R = radius of the planet
• h = height above the planet (altitude)
• G = 6.67 x 10-11
GM
vo
do
Example




At what speed must a satellite orbit
Neptune if its altitude is 100 km?
Solve vc = √(GM/do)
vc = √(6.67e-11*1.02e26/(2.48e7+100000))
vc = 16,530 m/s