Transcript Chapter 8
Chapter 9 Gravity The Earth Sucks 1. THE UNIVERSAL LAW OF GRAVITY From Law 3 of Kepler, Newton deduced the inverse square law of attraction. Newton compared the fall of the moon to the falling of an apple. Moon's fall from straight line is (0.05 in/s). Newton's Law of Universal Gravitation m1 m2 r m1m2 F 2 r 2. The Universal Gravitational Constant, G m1m2 F G 2 r G 6.67 x10 11 N m / kg 2 2 3. Gravity and Distance: The Inverse-Square Law Gravity is the most dominant force in nature. Yet it is the weakest. 4 units 3 units 2 units 1 unit Let’s look at the inverse-square nature for the force of gravity. 4. WEIGHT AND WEIGHTLESSNESS W = mg (the gravitational force acting on m) Weighing on an elevator and Weighing in outer space or in orbit We define the weight of something as the force it exerts against the supporting floor or the weighing scale. (Remember the elevator video.) 5. OCEAN TIDES demo - Earth-moon system Force of gravity decreases with distance from moon. Moon Earth Differences in gravity on different parts of the Earth produce tidal bulges. http://www.spacetelescope.org/videos/html/ mpeg/320px/heic0705i.html North Pole High Tides Should expect two high tides, two low tides per day. – Moon moves in its orbit so that it returns to the same place in your sky every 24h 50 m. Sun has one-half the influence of the moon – The gravitational force is greater but tides depend on the gravitation difference on opposite sides of the Earth. F3 F2 F1 m1m2 F G 2 r Sun Moon f1 f2 f3 SFA Spring Tides First Quarter Full Moon Earth New Moon Sun SFA Neap Tides First Quarter Earth Sun Last Quarter SFA NASA Animation MPEG SFA Complications – Friction with ocean bottom – Irregular shape of continents Bay of Fundi – Tides can come in very fast and exceed 15 m. SFA Tides in the Earth and Atmosphere Tides in ionosphere produce electric currents and alter the magnetic field. – Affects penetration of cosmic rays – Can have effects on living things Tides in the crust mean that volcanoes and earthquakes are more common at new or full moon. SFA Tides on the Moon Just as the earth has “land tides” the moon has moon tides. Because the moon always keeps the same face toward the earth, the moon tides are always in the same place. Go to link SFA 6. GRAVITATIONAL FIELDS Alternate view of gravitational influence – Properties of space surrounding object are changed so that another mass entering the region experiences a force. Earth SFA Earth Objects accelerate in the direction of the arrows. Field is stronger where lines are closer together. SFA The Gravitational Field Inside a Planet Inside the Planet a=g a = ½g a=0 a = ½g a=g SFA Gravitational Field Uniform Sphere – Linear inside - like Earth outside Hollow Sphere – Zero inside - like Earth outside SFA 7. EINSTEIN'S THEORY OF GRAVITATION Warped Space SFA Bending of Starlight Apparent position of star in this direction Sun Eye Light from star bent by the gravity of the Sun SFA 8. BLACK HOLES Let’s observe a star that is shrinking but whose mass is remaining the same. What happens to the force acting on an indestructible mass at the surface of the star? What effect is there on the escape velocity? SFA F F F F m m 1 2 m1m2 F G 2 G Remember that the force between R 2 the two masses is given by R G m1m2 G m1m2 G R2 R R R R2 R m1m2 R2 SFA ( 18 R ) 2 1 64 R 2 which means the force is 64 times larger If a massive star shrinks enough so that the escape velocity is equal to or greater than the speed of light, then it has become a black hole. Particles entering it would suffer disintegration. How are black holes detected? SFA Near a Black Hole SFA Another Look SFA 9. UNIVERSAL GRAVITATION Earth is a "sphere" because of gravitation. The universal law of gravitation was a great accomplishment. Its accuracy is phenomenal. Perturbations in planet's orbits Examples: Neptune was discovered because of Uranus's wobble. Pluto was discovered in a similar way. Oscillating universe. Wow! Chapter 9 Review Questions If somehow the moon were moved to a distance twice as far away from the earth as it is now, the force that the earth has for the moon would (a) be twice what it is now (b) be one half of what it is now (c) be four times greater than it is now (d) be one fourth as much as it is now What must be the phase of the moon if neap tides are occurring? (a) first quarter (b) full (c) lunar eclipse (d) new Newton said that the path of a planet curves because a force acts on it. Why does a planet's path curve according to Einstein? (a) because a force acts on it (b) because it is spinning (c) because it is in a geometric warp of space and time End of Chapter Test 3 Questions End of Course Discuss final Parting thoughts next slide