Transcript Presentation Lesson 13 Gravitational Interactions

Lesson 13
Gravitational Interaction
Eleanor Roosevelt High School
Chin-Sung Lin
Gravitational Field
Force Field
A force field exerts a force on objects in its vicinity
Magnetic Field
A magnetic field is a force field that surrounds a magnet
and exerts a magnetic force on magnetic substances
Electric Field
An electric field is a force field surrounding electric
charges
Gravitational Field
Gravitational Field
A gravitational field is a force field
that surrounds massive objects
Earth’s Gravitational Field
Earth’s Gravitational Field
 Earth’s gravitational field is
represented by imaginary field lines
 Where the field lines are closer together, the
gravitational field is stronger
 The direction of the field at any point is along the
line the point lies on
 Arrows show the field direction
 Any mass in the vicinity of Earth will be accelerated
in the direction of the field line at that location
Strength of Gravitational Field
Strength of the gravitational field is the force per unit mass
exerted by Earth on any object
Gravitational Field
g = Fg / m = (G m M / r2) / m = G M / r2
F:
G:
m:
M:
r:
weight of the object
universal gravitational constant (6.67 x 10-11 N·m2/kg2)
mass of the object
mass of Earth (5.98 x 1024 kg)
Earth’s radius (6.37 x 106 m)
Gravitational Field Inside a Planet
Gravitational Field Inside a Planet
P
r
C
Gravitational Field Inside a Planet
Cancellation of gravitational force
P
If Earth were of uniform density, the
gravity of the entire surrounding
shell of inner radius equal to your
radial distance from the center will
completely cancel out
r
C
Gravitational Field Inside a Planet
Cancellation of gravitational force
The gravity of area A and area B
on P completely cancel out
A
P
B
Gravitational Field Inside a Planet
Cancellation of gravitational force
P
You are pulled only by the mass
within this shell – below you
r
C
At Earth’s center, the whole Earth
is the shell and complete
cancellation occurs
Gravitational Field Inside a Planet
Strength of the gravitational field is proportional to M / r2
g = GM/r2 = GDV/r2 = GD(4/3)πr3/r2 = (4/3)GDπr
g ~ r
G:
M:
D:
V:
r:
universal gravitational constant (6.67 x 10-11 N·m2/kg2)
mass of Earth (5.98 x 1024 kg)
density of Earth
volume of Earth
distance to the Earth’s center
Gravitational Field Inside a Planet
a=g
a = g/2
a=0
a = g/2
a=g
Gravitational Field Inside a Planet
Without air drag, the trip would
take nearly 45 minutes. The
gravitational field strength is
steadily decreasing as you
continue toward the center
At the center of Earth, you are
pulled in every direction equally,
so that the net force is zero and
the gravitational field is zero