13.1 – The Falling Apple Newton realized all accelerations are caused by net forces The apple accel to earth in the same way the moon accel to earth The apple experiences linear accel The moon rotational Both are caused by the same net force – earth’s gravity

13.2 – The Falling Moon If the moon did not accel, it would follow a straight line – and leave orbit It acts like a projectile with such a high velocity the earth curves before the moon can hit the surface Thus, the moon “falls” around the earth

Variation of Falling Acceleration Acceleration reduces as distances increase Objects fall 4.9 m in 1 second at the surface, but only 1.4 mm for the moon Newton used geometry to show gravity lessens by a square of the distance (center to center)

13.3 – The Falling Earth The earth orbits the sun in a circular path like the moon does It does this because of gravitation, like the moon Therefore, the earth “falls around” the sun If we could stop these objects, they would accel toward one another

13.4 – Newton’s Law of Universal Gravitation Discovered gravity acts on all objects with mass Deduced the attractive force is proportional to the masses & inversely proport to distance (from center to center) squared F α m1 m2 / r2 A constant is needed, G Later (much after Newton) found to be exceedingly small G = 6.67 x 10-11 Shows that gravity is extremely weak

Measuring G 150 years later (1798), Henry Cavendish measured the first true value Often referred to as “weighing the earth” Once “G” is determined, the masses of all celestial objects can be determined

Measuring G – Cont. Von Jolly developed a simpler method Of the 4 fundamental forces, gravity is weakest Aside from gravity, almost all other “real” forces are due to electromagnetism – another fundamental force

13.5 – Gravity & Distance: The Inverse Square Law Much like spraying butter on toast, gravity is diluted as a square of the distance 2 times as far = 2 squared the force (4x) 3 times distance = 3 squared the force (9x)

Gravitational strength drops off rapidly as you increase distance, as 1/r2, but never gets to zero

13.6 – Gravitational Field Something created by mass that cause other masses to experience a force The closer to the surface the stronger the field, and the more force on other masses The arrows point in direction of force

13.7 – Gravitational Field Inside a Planet Gravitational acceleration decreases as you move towards center Because of mass above as well as below Gravity in center = zero

13.8 – Weight & Weightlessness Net forces cause accelerations, and present themselves as changes in “weight” This is the “pushing back” of some surface (normal force) No “pushing back”, we experience weightlessness

Anytime something falls (free fall), it is “weightless” Jumping off a building Astronauts in shuttle falling around the earth

13.9 – Ocean Tides Caused by differences in gravitational pull of moon on opposite sides of the earth Water closest to moon is pulled closer (high tide) On opposite side, earth is pulled and deformed away from water – also high tide Water perpendicular is lower than normal – low tide

The sun also causes tides, the overall force is much greater than moon But, the difference between sides is much smaller Sun, Earth & Moon line up – Spring Tide – extremes in tides Sun, Earth & Moon perpendicular – Neap tide – leveling of tides

Other Types of Tides Part of earth’s interior is molten, causing “Earth tides” The atmosphere is a fluid (it flows) creating “atmospheric tides” Small bodies of water do not experience tides because the difference from one side to another is too small Tilt of earth also effects tides

13.10 – Black Holes Stars are in state of equilibrium – gravity trying to make it smaller & fusion trying to make it bigger At the end of star’s lives, they swell into red giants Once out of fuel, it collapses to a black dwarf More massive stars, the collapse never stops and forms black holes

Gravitational Field Near Black Holes The black hole has the same mass as the star creating it, therefore the same gravity Mass is so concentrated, the space surrounding it is distorted and warped We “see” them because of their effect on objects around them

13.11 – Universal Gravitation Perturbations in Solar System All planets tug on all others This causes deviations in orbits – perturbations Distant planets were discovered using this technique The Expanding Universe Universe began with Big Bang (Theory) All matter spewing outward Gravity should slow it down, but there appears to be acceleration Due to dark matter/dark energy

Project Orion http://www.youtube.com/watch?v=E3Lxx2VAYi8 http://www.youtube.com/watch?NR=1&v=V1vKMTYa40A&feature=endscreen