Gravity – A Familiar Force

Gravitational Force• Gravitational force – an attractive force

that every object in the universe exerts on every other object in the universe.,

Alternatively:Gravity – mutual force of attraction between particles of matter

Gravitational Force

• There is a gravitational attraction between your hand and your pencil. The gravitation attraction of the Earth is much greater, so the pencil falls when you release it.

Newton Predicts Manmade Satellites of EarthNewton’s Thought Experiment: If a cannon was able to launch successive cannonballs with greater and greater initial speed, so the horizontal distance of the ball’s travel increases, eventually the initial speed will be great enough so that the curvature of the Earth will cause the cannonball to continue falling without ever landing. Serway/Faugh – Physics pg 230

A spacecraft in low Earth orbit must have an orbital velocity of at least 17,450 mph. At this speed the spacecraft will make one trip around the Earth in about an hour and a half.

InternationalSpace Station

Sir Isaac Newton noticed an apple fall to the ground and reasoned that according to his second law of motion, the acceleration of falling bodies to the Earth is caused by a force (a force of attraction).

Newton’s Universal Law of Gravitation

• Every body attracts every other body in the universe

• with a force that is directly proportional to the masses of the two bodies

• and inversely proportional to the square of the distance between them.

Factors Related to Gravitational

Attraction:• 1) Masses of bodies (The higher the mass,

the higher the amount of attraction.)

• 2) Distance between bodies (The greater the distance, the less amount of attraction.)

Gravitational Force Exists between any two masses

• Gravitational force attracts all masses to each other. It exists between any two masses regardless of size.

• The force of attraction between desks in a classroom is negligibly small relative to the force between the Earth and each desk because of the differences in mass. Serway/Faugn Physics Text pg 231

• If the gravitational force acts between all masses, why doesn’t the earth accelerate up toward a falling apple?

• It does! • But, the Earth’s acceleration is so tiny that you

cannot detect it. Earth’s mass is so large, and acceleration is inversely proportional to mass, so the Earth’s acceleration is negligible. Serway/Faugn Physics Text pg 231

• A basketball has a greater acceleration toward the Earth as well.

Gravitational Attraction between the Earth and its moon

• The force that the moon exerts on the Earth is equal and opposite to the force that the Earth exerts on the moon. This relationship is an example of Newton’s third law of motion. Serway/Faugn Physics Text pg 231

• The gravitational force that acts on the moon is the centripetal force that causes the moon to move in its circular path around the Earth.

• The centripetal force on the Earth, however, is less obvious because the Earth is much more massive than the moon. Serway/Faugn Physics Text pg 231

Gravitation and Ocean Tides

High and low tides are partly due to gravitational force exerted on the Earth by its moon.

• The tides result from the difference between the gravitational force at the earth’s surface and at the Earth’s center.

• On the side of the Earth that is nearest to the moon, the moon’s gravitational force is greater that it is at the Earth’s center. This is because gravitational force decreases with distance. Serway/Faugn Physics Text pg 234

• The water is pulled toward the moon, creating an outward bulge.

• On the opposite side of the Earth, the gravitational force is less than it is at the center. On this side, all mass is still pulled toward the moon, but the water is pulled least. This creates another outward bulge . Serway/Faugn Physics Text pg 234

Gravity is a Field Force• Masses create a gravitational field in space. A

gravitational force is an interaction between a mass and the gravitational field created by other masses. Serway/Faugn Physics Text pg 234

The gravitational field vectors representEarth’s gravitationalfield at each point.Note that the field has the same strength at equal distances fromEarth’s center.

At any point, Earth’sgravitational field canbe described by thegravitational fieldstrength and is equalto the gravitationalforce exerted on a unitof mass at that point

Equation for calculation of gravitational force between two bodies:

How was the constant G obtained? Lord Henry Cavendish determined the Universal Gravitation Constant (constant of proportionality) in 1798. This was a nearly a century after Newton developed his Universal Law of Gravitation.

• Cavendish using a device referred to as a torsion balance. It involved a rigid rod about 2-feet long. Two small lead spheres were attached to the ends of the rod and the rod was suspended by a thin wire.

• When the rod becomes twisted, the torsion of the wire begins to exert a torsional force that is proportional to the angle of rotation of the rod. The more twist of the wire, the more the system pushes backwards to restore itself towards the original position. The Physics Classroom.com

• Cavendish had calibrated his instrument to determine the relationship between the angle of rotation and the amount of torsional force.

• He then brought two large lead spheres near the smaller spheres attached to the rod. Since all masses attract, the large spheres exerted a gravitational force upon the smaller spheres and twisted the rod a measurable amount. The Physics Classroom.com

• Once the torsional force balanced the gravitational force, the rod and spheres came to rest and Cavendish was able to determine the gravitational force of attraction between the masses. The Physics Classroom.com

• By measuring m1, m2, d and Fgrav, the value of G could be determined. Cavendish's measurements resulted in an experimentally determined value of 6.75 x 10-11 N m2/kg2.

• Today, the currently accepted value is 6.67259 x 10-11 N m2/kg2. (The value of G is an extremely small numerical value. Its smallness accounts for the fact that the force of gravitational attraction is only appreciable for objects with large mass.) The Physics Classroom.com

SAMPLE CALCULATION:•A 0.300 kg billiard ball is placed 0.003 m from a 0.400 kg billiard ball. What is the magnitude of the gravitational force between the them?

Billiard ball masses are relatively small compared to large planetary masses, or star masses.

Einstein Sees Gravity DifferentlyIt was part of his famous General Theory of Relativity, and it offered a very different explanation from Newton’s Law of Universal Gravitation. Einstein didn't believe gravity was a force at all; he said it was a distortion , or curve, in the shape of space-time, otherwise known as "the fourth dimension" How Stuff Works .com

• NEWTON: Particles that start to move along parallel trajectories will never meet, but are fated to remain forever at a constant distance from one another. If particles diverge from this behavior, it must be because there is a forces acting to accelerate the particles, causing them to leave the straightest possible paths and follow curved trajectories instead. Einstein on line

• EINSTEIN: The two particles could still be moving on the straightest possible lines - not in the plane, but on a curved surface! There is no force making the particles deviate from the straightest possible lines; the mere fact that the particles are moving on a sphere means that, even if they still move as straight as possible, their paths will converge.

What is a Black Hole?

A black hole is a region of spacetime from which gravity prevents anything, including light, from escaping. The theory of general relativity predicts that a sufficiently compact mass will usually deform spacetime to form a black hole.

How Big Are Black Holes?Scientists think the smallest black holes are as small as just one atom. These black holes are very tiny but have the mass of a large mountain. Mass is the amount of matter, or "stuff," in an object.Another kind of black hole is called "stellar." Its mass can be up to 20 times more than the mass of the sun. There may be many, many stellar mass black holes in Earth's galaxy. Earth's galaxy is called the Milky Way.

The largest black holes are called "supermassive." These black holes have masses that are more than 1 million suns together. Scientists have found proof that every large galaxy contains a supermassive black hole at its center.

The supermassive black hole at the center of the Milky Way galaxy is called Sagittarius A. It has a mass equal to about 4 million suns and would fit inside a very large ball that could hold a few million Earths.

An artist's drawing a black hole named Cygnus X-1. It formed when a large star caved in. This black hole pulls matter from blue star beside it.