Understanding Newton and the tree…Understanding Newton and the tree…

??

How can the moon be falling toward Earth???How can the moon be falling toward Earth???

A Centripetal Acceleration… A Centripetal Acceleration… acceleration that is “center acceleration that is “center seeking”seeking”

For mass to be accelerating For mass to be accelerating there must be…there must be…

To find the centripetal Force, To find the centripetal Force, we need to be able to find we need to be able to find centripetal acceleration…centripetal acceleration…

R

R

θ

θb

b b RR

ΔΔv v vv

==

Finding the centripetal acceleration…Finding the centripetal acceleration…

If If ΔΔt t 0 (to find instantaneous acceleration) then… 0 (to find instantaneous acceleration) then…

v

v

a = a = ΔΔv/ v/ ΔΔt … essentially the change in velocity t … essentially the change in velocity

v

v Δv

a = a = ΔΔv/ v/ ΔΔt… so…t… so…b*v b*v R R

ΔΔvv

==

aacc vv22 RR

==

Is this the same for Is this the same for anything to travel in a anything to travel in a circle… circle…

Centripetal vs. CentrifugalCentripetal vs. Centrifugal

A 1000kg car is traveling down Cedar St. toward the Chevron at 11 m/s (~25mph)… in order to make the turn onto 5th Ave. (8 m radius) how much centripetal force is necessary?

What provides this force?

Then what is the μ value?

What sensation do you have inside the car?

So What Provides the Centripetal So What Provides the Centripetal Force Necessary for orbit?Force Necessary for orbit?

What does the Gravity force come from???What does the Gravity force come from???

??Ancient thinkers say…Ancient thinkers say…

Newton says…Newton says…

Einstein…Einstein…

How does gravity “work” then…?How does gravity “work” then…?

Use your brain and with the facts you know to Use your brain and with the facts you know to decide what variables would define the strength of decide what variables would define the strength of gravity…gravity…

FFgg = ? = ?

DistanceDistance

Force of GravityForce of Gravity

On the road to an equationOn the road to an equation

http://www.cornillot.com/images/graphics/Planets/jupiter.jpg

300 x300 x

DistanceDistance

300 x Force of Gravity 300 x Force of Gravity

DistanceDistance

http://www.cornillot.com/images/graphics/Planets/jupiter.jpg

Gravitational ForceForce is DIRECTLY proportional to the PRODUCT of the MassesMasses

Force Force ~ Mass~ Mass11 · Mass · Mass22

300 x300 x

80 x80 x

24,000 x Force of Gravity24,000 x Force of Gravity

200 lbs200 lbs

? lbs? lbs

RadiusRadius

22··RadiusRadius

What about the distance between the masses?What about the distance between the masses?

Distance = 1 R 2 R 3 R 4 RDistance = 1 R 2 R 3 R 4 R

Gravity = 1 g 1/4 g 1/9 g 1/16 gGravity = 1 g 1/4 g 1/9 g 1/16 g

GRAVITY – “like a force field”GRAVITY – “like a force field”

Force Force ~ ~ 11 / / Dist.Dist.22

GRAVITY – a mathematical lookGRAVITY – a mathematical look

How fast is the moon accelerating?How fast is the moon accelerating?

a = a = vv22 r r

t = 27.3 dayst = 27.3 days

r = 3.84 x 10r = 3.84 x 108 8 mm

Compare that to “g” on Earth…Compare that to “g” on Earth…

Force Force ~ ~ 11 / / Dist.Dist.22

Newton’s hypothesis of Universal GravitationNewton’s hypothesis of Universal Gravitation

Force = G Force = G MassMass11 · Mass · Mass2 2

DistanceDistance22

What’s up with the “G”What’s up with the “G”

m1

WeightWeight

Gravitational Gravitational ForceForceDistanceDistance

ForceForce = G = G

mm11 · ·mm22

RR22

G = 6.67 x 10G = 6.67 x 10-11-11

Mass of EarthMass of Earth 5,975,800,000,000,000,000,000,000 kg

(13,174,000,000,000,000,000,000,000 lbs)

??How do they know that?How do they know that?

http://www.scarlett.ru/source/models/hires/sc-214/sc-214-white.jpg

mm22

1 kg

Distance = 6,378,160 Distance = 6,378,160 metersmeters

Gravitational Force = 9.8 NGravitational Force = 9.8 N

ForceForce = G = G

mm11 · ·mm22

RR22

9.89.8 = 6.67 x 10= 6.67 x 10-11-11

11 · ·mm22

6,378,1606,378,16022

mm2 2 = = 5.975,8 x 1024 kg

Distance = 6,378,160 Distance = 6,378,160 metersmeters

How do they know that?How do they know that?

Good ole “Eratosthenes”Good ole “Eratosthenes”

Force = G Force = G MassMass11 · Mass · Mass2 2

DistanceDistance22

IMAX – Cosmic Voyage

FFgg = G = G mm11 m m22

rr22

How many masses are in the Universe…How many masses are in the Universe…