Gravity The thing that causes objects to fall to Earth

Gravity and acceleration Force of gravity causes an acceleration Acceleration due to gravity’s force -- acceleration experienced by object when the only force acting on it is force of gravity Approximately 9.8 m/s/s for all objects on earth, regardless of their mass I/AAAAAAAAABE/6INc8LHksSs/s1600/aviao-e-paraquedista-a858e.jpg

Kepler and planetary motion Early 1600's Johannes Kepler develop three laws to describe the motion of planets about the sun 1. Paths of planets are elliptical with center of sun at one focus 2. Imaginary line drawn from center of sun to center of planet will sweep out equal areas in equal intervals of time (periods) 3. Ratio of squares of periods (times) of any two planets equals ratio of the cubes of their average distances from sun

Newton wondered... What causes elliptical motion of planets? What causes circular motion of moon about earth? Requires an unbalanced force Suppose cannonball could be fired such that trajectory of falling cannonball matched curvature of earth. If such a speed was obtained, then cannonball would fall around earth instead of into it. Orbit!

Newton’s thoughts (cont.) At even greater launch speeds, cannonball would orbit the earth, but in elliptical path Orbiting moon can be compared to falling cannonball, or even falling apple Same force that causes objects on Earth to fall to earth also causes objects in heavens to move along circular and elliptical paths

Apple and Moon Apple accelerates towards earth at rate of 9.8 m/s 2 Moon accelerates towards earth at rate of m/s 2 So more distant moon accelerates at rate approximately 1/3600 the acceleration of the apple content/themes/8planets/images/red_apple_lg.jpg

Distance tells part of story Compare distance from apple to center of earth with distance from moon to center of earth Moon in orbit about earth is approximately 60 times further from earth's center than apple Moon experiences force of gravity 1/(60) 2 times that of apple Force of gravity follows an inverse square law. (Squaring distance greatly reduces gravitational force) /F04/GRAVITYLIGHT/Page1_files/InvSqLaw.gif

Gravity and distance Relationship between amount of gravitational force and distance. (F grav ) between earth and any other object and distance that separates their centers (d) can be expressed as: /images/UniversalLawOfGravitation1.GIF

Check Understanding 1. Suppose two objects attract each other with gravitational force of 9 units. If distance between two objects is doubled, what is the new force of attraction between the two objects? If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 (2 2 ). The new force is then 1/4 of the original 9 units. F = (9 N) / 4 = 2.25 units

Check Understanding 2. Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is tripled, then what is the new force of attraction between the two objects? If the distance is increased by a factor of 3, then force will be decreased by a factor of 9 (3 2 ). The new force is then 1/9 of the original 16 units. F = (16 N) / 9 = 1.78 units

Check Understanding 3. Noah Formula has devised a new business plan based on his teacher's Physics for Better Living theme. Noah learned that objects weigh different amounts at different distances from Earth's center. His plan involves buying gold by the weight at one altitude and then selling it at another altitude at the same price per weight. Should Noah buy at a high altitude and sell at a low altitude or vice versa? To profit, buy at a high altitude and sell at a low one

Newton’s laws of motion and gravity Newton concluded that gravity depends upon distance Newton also knew force that causes a falling stone’s acceleration (gravity) must be dependent upon mass of the stone But since the force acting to cause a stone's downward acceleration also causes earth's upward acceleration (Newton's third law), gravitational force must also depend upon mass of earth law-of-motion.jpeg

Law of Universal Gravitation Force of gravity acting between earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the other object, and inversely proportional to the square of the distance that separates the centers of the earth and the object ALL objects attract each other with gravitational force (Note: gravitational forces are always attractive, pulling objects toward each other) rsalLawOfGravitation1.GIF

Mass and gravity As mass of either object increases, the force of gravitational attraction between them also increases If mass of 1 of objects is doubled, then force of gravity between them is doubled. If the mass of 1 of objects is tripled, then force of gravity between them is tripled

Combining mass and distance Effects of mass and distance

Law of universal gravitation Determine the force of gravitational attraction between the earth (m = 5.98 x kg) and a 70-kg physics student if the student is in an airplane at 40,000 feet above earth's surface. This would place the student a distance of 6.39 x 10 6 m from earth's center.

Variable force of gravity What you weigh depends on where you are!

Gravitational attraction Gravitational interactions exist between all objects with an intensity that is directly proportional to the product of their masses So as you sit in your classroom, you are gravitationally attracted to the people around you, to the table you are working at, and to equipment near you _69_Janelle.jpg

Check understanding Suppose two objects attract each other with a gravitational force of 16 units. If distance between the objects is reduced in half, what is the new force of attraction between the two objects? If the distance is decreased by a factor of 2, then force will be increased by a factor of 4 (2 2 ). The new force is then 4 times the original 16 units. F = (16 units) 4 = 64 units

Check understanding Suppose two objects attract each other with a gravitational force of 16 units. If the mass of both objects was doubled, and the distance between the objects remained the same, what would be the new force of attraction between them? If each mass is increased by a factor of 2, then force will be increased by a factor of 4 (2*2). The new force is then 4 times the original 16 units. F = (16 units ) 4 = 64 units

Check understanding Suppose two objects attract each other with a gravitational force of 16 units. If the mass of object 1 was doubled, and if the distance between the objects was tripled, then what would be the new force of attraction between the two objects? If the mass of one object is doubled, the force of attraction will be doubled as well. But this affect is more than offset by the tripling of the separation distance. Tripling the distance would cause the force to be decreased by a factor of 9 (3 2 ). The net affect on force is that it decreased by a factor of 2/9. F = (16 units) 2 / 9 = 3.56 units

Check understanding Anita Diet is very concerned about her weight but seldom does anything about it. After learning about Newton's law of universal gravitation in Physics class, she becomes all concerned about the possible affect of a change in Earth's mass upon her weight. During a (rare) free moment at the lunch table, she speaks up "How would my weight change if the mass of the Earth increased by 10%?" How would you answer Anita?

Check understanding Answer: "Anita - that's a great question! Since your weight is directly dependent upon the mass of the Earth, you would weigh 10% more. But don't worry, honey. You wouldn't look any different than you do now since your mass would remain as is."

Results of gravitation Tides Force fields

Results of gravitation Orbital motion Black holes