1. Gravitational Interaction
Lesson 13
Gravitational Interaction
Eleanor Roosevelt High School
Chin-Sung Lin

2. 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

3. Gravitational Field Gravitational Field
A gravitational field is a force field
that surrounds massive objects

4. Earth’s Gravitational Field

5. 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

6. 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: weight of the object
G: universal gravitational constant (6.67 x N·m2/kg2)
m: mass of the object
M: mass of Earth (5.98 x 1024 kg)
r: Earth’s radius (6.37 x 106 m)

7. Gravitational Field Inside a Planet

8. Gravitational Field Inside a PlanetC r

9. Gravitational Field Inside a Planet
Cancellation of gravitational force
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 P C r

10. Gravitational Field Inside a PlanetB P
Cancellation of gravitational force
The gravity of area A and area B on P completely cancel out

11. Gravitational Field Inside a PlanetC r
Cancellation of gravitational force
You are pulled only by the mass within this shell – below you
At Earth’s center, the whole Earth is the shell and complete cancellation occurs

12. 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: universal gravitational constant (6.67 x N·m2/kg2)
M: mass of Earth (5.98 x 1024 kg)
D: density of Earth
V: volume of Earth
r: distance to the Earth’s center

13. Gravitational Field Inside a Planet
a = g
a = g/2
a = 0

14. 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