Gravitational Interaction 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: weight of the object G: universal gravitational constant (6.67 x 10-11 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)

Gravitational Field Inside a Planet

Gravitational Field Inside a Planet C r

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

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

Gravitational Field Inside a Planet C 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

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 10-11 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

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

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