13.1 – The Falling AppleNewton realized all

accelerations are caused by net forces

The apple accel to earth in the same way the moon accel to earthThe apple experiences

linear accelThe moon rotationalBoth are caused by the

same net force – earth’s gravity

13.2 – The Falling MoonIf 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 AccelerationAcceleration reduces as

distances increaseObjects 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 EarthThe 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 GravitationDiscovered 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 G150 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 LawMuch like spraying butter on toast, gravity is

diluted as a square of the distance2 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 FieldSomething created by mass that cause other

masses to experience a forceThe closer to the surface the stronger the field,

and the more force on other massesThe arrows point in direction of force

13.7 – Gravitational Field Inside a PlanetGravitational acceleration decreases as you

move towards centerBecause of mass above as well as belowGravity in center = zero

13.8 – Weight & WeightlessnessNet 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 buildingAstronauts in shuttle

falling around the earth

13.9 – Ocean TidesCaused by differences in gravitational pull of

moon on opposite sides of the earthWater closest to moon is pulled closer (high

tide)On opposite side, earth is pulled and

deformed away from water – also high tideWater 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 smallerSun, Earth & Moon line up – Spring Tide –

extremes in tidesSun, Earth & Moon perpendicular – Neap tide –

leveling of tides

Other Types of TidesPart 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 HolesStars 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 HolesThe black hole has the same mass as the star

creating it, therefore the same gravityMass is so concentrated, the space surrounding

it is distorted and warpedWe “see” them because of their effect on

objects around them

13.11 – Universal GravitationPerturbations in Solar

SystemAll planets tug on all

othersThis 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 Orionhttp://www.youtub

e.com/watch?v=E3Lxx2VAYi8

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