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Gravity Chapter 9 Isaac Newton (1642 - 1727) Newton’s Universal Gravitation Two masses separated by a distance m M d Newton’s Universal Gravitation Mm F 2 d GMm F 2 d Newton’s Universal Gravitation • Inverse Square Law Separation R 2R 3R ½R ¼R Force F ¼F 1/9F 4F 16F Newton’s Universal Gravitation The force of gravity cannot be made zero. Mass causes gravity •Only one kind of mass •Contrast with the electric force G is small •6.67 X 10-11 N m2/kg2 Apparent Weightlessness • All objects fall at the same rate in a gravitational field. – Apparent weightlessness – Lack supporting force • Examples: – Space Shuttle – Elevator – Amusement Park Rides KC-135 Ocean Tides • Gravity decreases with distance Moon Earth Ocean Tides • Differences in gravity on different parts of the Earth produce tidal bulges Low Tide High Tide High Tide Low Tide Ocean 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 Ocean Tides • Spring Tide – Full or New Moon Full Moon Earth New Moon Sun Ocean Tides • Neap Tide – First or Last Quarter Moon First Quarter Earth Last Quarter Sun Ocean Tides • Complications – Friction with ocean bottom – Irregular shape of continents • Bay of Fundy (Video) – Tides can come in very fast and exceed 15 m Crustal & Atmospheric Tides • 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 – Measured for the moon Gravitational Field • Alternate view of gravitational influence – Properties of space surrounding object are changed so that another mass entering the region experiences a force. Earth Gravitational Field • Objects accelerate in the direction of the arrows • Field is stronger where field lines are closer together Gravitational Field • Inside the Planet a=g a = ½g a=0 a = ½g a=g Gravitational Field • Uniform Sphere – Linear inside – like Earth outside g R Distance • Hollow Sphere – Zero inside – like Earth outside g R Distance Space-Time No mass Distortion caused by mass General Relativity • Mass distorts space-time • Objects move in the straightest path they can in the distortions caused by mass Advance of Mercury’s Perihelion Bending of Starlight Apparent position of the star Sun Light from star bent by the gravity of the Sun Low Gravity Very small amount of bending Stronger Gravity Light at an angle is bent noticeably Exit Cone and Photon Sphere Photon Sphere Near a Black Hole Schwarzschild Black Hole Event Horizon Rs = 3(Mass) + Rs Singularity Mass Rs 3 M 9 km 5 15 10 30 What Can We Know? • Mass – gravity • Charge – Electric Fields • Rotation Rate – Co-rotation Cygnus X-1 Edwin Hubble Red Shift and Distance 24 Mpc 1200 km/s 300 Mpc 15,000 km/s 780 Mpc 39,000 km/s 1220 Mpc 61,000 km/s Hubble’s Result Modern Hubble’s Law Raisin Cake Model 2 2 1 1 3 3 Raisin Cake Model Distance from Home (before baking) 1 2 3 1 cm 2 cm 3 cm Distance from Home (afterbaking) Velocity 2 cm 4 cm 6 cm 1 cm/hr 2 cm/hr 3 cm/hr Distance Universal Expansion • Space-Time itself is expanding – Carries galaxies along with it • Conflicting cosmologies – Big Bang • Draw the expansion back in time until space-time occupies a point (12 - 15 billion years ago) – Steady State • Requires continual creation of matter Arno Penzias & Robert Wilson
