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G r a v i t y Chapter 9 Isaac Newton (1642 - 1727) m M d Newton’s Universal Gravitation Two masses separated by a distance Newton’s Universal Gravitation Newton’s Universal Gravitation Inverse Square Law Separation Force

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## G r a v i t y

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**G r a v i t y**Chapter 9**m**M d Newton’s Universal Gravitation Two masses separated by a distance**Newton’s Universal Gravitation**• Inverse Square Law Separation Force R F 2R ¼F 3R 1/9F ½R 4F ¼R 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**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**Sun**Earth Full Moon New Moon Ocean Tides • Spring Tide • Full or New Moon**Ocean Tides**• Neap Tide • First or Last Quarter Moon First Quarter Sun Earth Last Quarter**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**Earth**Gravitational Field • Alternate view of gravitational influence • Properties of space surrounding object are changed so that another mass entering the region experiences a force.**Gravitational Field**• Objects accelerate in the direction of the arrows • Field is stronger where field lines are closer together**a = g**a = ½g a = ½g a = 0 a = g Gravitational Field • Inside the Planet**g**Distance g Distance Gravitational Field • Uniform Sphere • Linear inside • like Earth outside • Hollow Sphere • Zero inside • like Earth outside R R**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**Apparent position of the star**Sun Light from star bent by the gravity of the Sun Bending of Starlight**Low Gravity**Very small amount of bending**Stronger Gravity**Light at an angle is bent noticeably**Exit Cone and Photon Sphere**Photon Sphere**Event Horizon**Rs + Singularity Schwarzschild Black Hole Rs = 3(Mass) Mass Rs 3 M 9 km 5 15 10 30**What Can We Know?**• Mass • gravity • Charge • Electric Fields • Rotation Rate • Co-rotation**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**2**2 1 1 3 3 Raisin Cake Model**Velocity**Distance Raisin Cake Model Velocity 1 cm/hr 2 cm/hr 3 cm/hr Distance Distance from Home from Home (before baking) (afterbaking) 1 1 cm 2 cm 2 2 cm 4 cm 3 3 cm 6 cm**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

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