Aim: How do we explain gravitational fields? Ch 12 Notes Aim: How do we explain gravitational fields?

Problem 1 (Review of Newton’s Law of Gravitation) As a meteor moves from a distance of 16 Earth radii to a distance of 2 Earth radii, what happens to the magnitude of the gravitational force? It becomes 1/8 as great It becomes 8 times greater. It becomes 64 times greater. It becomes 4 times greater.

Problem 2 (Review of Newton’s Law of Gravitation) If an object weighs 270 N at the Earth’s surface, what will it weigh when it is at a distance 3 times from the center of Earth? 270 N 135 N 67.5 N 30 N

The Gravitational Field Ch 12 Notes The Gravitational Field During the 19th century, the notion of the “field” entered physics (via Michael Faraday). Objects with mass create an invisible disturbance in the space around them that is felt by other massive objects - this is a gravitational field.

The Gravitational Field Ch 12 Notes The Gravitational Field All objects with mass create a gravitational field.

Gravitational Field Strength Ch 12 Notes Gravitational Field Strength To measure the strength of the gravitational field at any point, measure the gravitational force, F, exerted on any “test mass”, m. Gravitational Field Strength, g = F/m

Gravitational Field Strength Ch 12 Notes Gravitational Field Strength Is gravitational field strength a vector or scalar quantity? Vector Quantity What is the relationship between the direction of the gravitational field strength and the direction of the gravitational force acting on a test mass? The direction of the gravitational field is the same as the direction of the gravitational force acting on the test mass.

Calculating gravitational fields 1. A test mass m = 0.1 kg experiences a force of 10 N at a point in a gravitational field. What is the gravitational field strength at this point? g=Fg/m=10 N/(0.1 kg)=100 N/kg 2. A test mass of m = 0.04 kg is placed in a gravitational field of strength 12,000 N/kg. What gravitational force is the test mass experiencing? g=Fg/m Fg =mg=0.04 kg(12,000 N/kg)=480 N

More gravitational field problems 3. Suppose a 100-kg astronaut feels a gravitational force of 700N when placed in the gravitational field of a planet. What is the gravitational field strength at the location of the astronaut? g=Fg/m=700 N/ 100 kg = 7 N/kg B) What is the mass of the planet if the astronaut is 2*106 m from its center? Fg= Gm1m2/r2 700 N= (6.67 x 10-11 N m2 /kg2 )(100 kg) m2 / (2 x 106 m)2 m2 =4.2 x 1023 kg

Ch 12 Notes Gravitational Force If g is the strength of the gravitational field at some point, then the gravitational force on an object of mass m at that point is Fgrav = mg. If g is the gravitational field strength at some point (in N/kg), then the free fall acceleration at that point is also g (in m/s2).

Gravitational Field produced by a mass The gravitational field at a distance r from a mass M can be found by using the equation, G= GM/r2

Thought questions What is the value of the gravitational field on the Earth? 9.8 N/kg Why is the gravitational field on the Earth greater than that on the moon? The earth has a greater mass to radius ratio 3)What celestial objects in the Universe have the strongest gravitational fields? Black Holes

109) 49 N 110) 4 111) Gravitational Field Strength 112) 1/6 N/kg 113) 4 114) 2 115) 3

Ch 12 Notes Black Holes When a very massive star gets old and runs out of fusionable material, gravitational forces may cause it to collapse to a mathematical point - a singularity. The gravity is so strong that not even light is fast enough to scape.

Black Hole Gravitational Force Ch 12 Notes Black Hole Gravitational Force The black hole’s gravity is the same as the original star’s at distances greater than the star’s original radius. Black hole’s don’t magically “suck things in.” The black hole’s gravity is intense because you can get really, really close to it!

Black Hole

Big Bang The big bang also originated from a space-time singularity.

Einstein’s Theory of Gravity Large masses causes space and time to curve. Objects near these masses follow the path of space-time curvature. This is why we observe gravity.

Multiverse