Newton 1 st Law of Motion Gravity Mass/Weight Centripetal Force Kepler’s Third Law Calculating Mass Solving for G Orbits Earth Moves

NewtonNewton1st Law of Motion

GravityMass/Weight

Centripetal ForceKepler’s Third LawCalculating Mass

Solving for GOrbits

Earth Moves

Newton’s 1stNewton’s 1st

An object at rest remains at rest, and an object in motion continues in a straight line unless acted on by an outside force.


An object at rest remains at rest unless acted on by an outside force.


An object in motion continues in a straight line unless acted on by an outside force.



GravityMass/Weight


Solving for GOrbits

Earth Moves

GravityGravity

Fg =-G M m r2

GravityGravity

Fg =-G M m r2

Attractive Force

GravityGravity

Fg =-G M m r2

Universal Gravitational Constant

GravityGravity

Fg =-G M m r2

Masses of Two Objects

GravityGravity

Fg =-G M m r2

Distance Between Centers

GravityGravity

8 X

64 X

Fg =-G M m r2


GravityMass/Weight


Solving for GOrbits

Earth Moves

Mass / WeightMass / WeightMass = Quantity of Matter

Which has more matter, a pound of lead or a pound of feathers?The pound of feathers is bigger, but that’s a different question.

The pound of lead is denser, but that’s a different question.If they are both on Earth, they have the same mass.

A pound of feathers on the moon has more mass than a pound of lead on Earth.

If I take a pound of lead to the moon, it will weigh less, but the mass will still be the same.

Weight = Force of Gravity Holding it to Surfacekilogram = measure of mass

pound = measure of force

Mass / WeightMass / Weight

With a mass of 68 kg, I weigh 150 lbs on Earth.

The moon’s gravity is weaker.

I would only weigh 31.5 lbs there.

On Mars, I would weigh 67.5 lbs.


GravityMass/Weight


Solving for GOrbits

Earth Moves

Gravity is a Centripetal Force.Gravity is a Centripetal Force.

Any force that is directed toward the center of motion.

A Ball on a String

A Car on a Curved Road

…

Fc=-m v2

r

Centripetal ForceCentripetal Force

Fc=-G M m r2

= Fg=-m v2

r


-G M m r2

=-m v2

r


-G M m r2

=-m v2

r


v2

r G M r2

=

Circular Orbit v =2 r P


v2

r G M r2

=

Circular Orbit v2=22r2

P2


4r2

P2 r G M r2

=


4r P2

G M r2

=P2 P2


4r G M r2

= P2r2 r2


4r3 G M= P2 1G M

1G M


r3 = P2 4

G M

Circular Orbit r = a


a3 = P2 4

G M

Circular Orbit r = a

Kepler’s Third LawKepler’s Third Law

a3 = P2 4

G M

P2 = k a3


GravityMass/Weight


Solving for GOrbits

Earth Moves

Finding MassFinding Mass

a3 = P2 4

G MMM

a3 = P2 4

GM

1P2

1P2


= 4

G Ma3

P2


One problem remains.

= 4

G Ma3

P2



F = =-GMm R

-GMm R

Mass of EarthPhillip von Jolly

m m

M

-GMm D+


mm

M

F = =-GMm R

-GMm R

-GMm D+


m m n

M

F = =-GMm R

-GMm R

-GMm D+

-GMn R

+

Mass of Earth

F = =-GMm R

-GMm R

-GMm D+

-GMn R

+

Mass of Earth-GMm D

-GMn R

=

Mm D

Mn R

=

R

nR

n

m R2n D

( ) M = M

= 4

G M

a3

P2



(

(


GravityMass/Weight


Solving for GOrbits

Earth Moves

OrbitsOrbits

Perigee

Apogee

Circular

OrbitsOrbits

PerigeeApogee

Transfer OrbitsTransfer Orbits


GravityMass/Weight


Solving for GOrbits

Earth Moves

Proof of Earth’s Motion

RotationRevolution

Proof of Earth’s Revolution

What would satisfy Aristotle?

Parallax

Parallax

Parallax

Parallaxshift in the

position of one nearby star,

compared to the background of more distant

stars

Parallax

Quadrature

Proof of Earth’s Revolution

Stellar AberrationAberration of Starlight

Aberration of Starlight


Aberration of StarlightTilt it at an angle.

It depends on what?

Speed of Dripping Water

Speed of Tube

What angle?

How does this compare

with light entering a telescope?


zero aberration for stars at quadrature





It depends on what?

Speed of LightSpeed of Earth

Direction of Earth


Proof of Earth’s Revolution Around Sun

Parallax

one nearby star

two photos

max at quadratures

Earth moved

Aberration

all stars in same direction

zero at quadrature

max at opposition

Earth moving

Proof of Earth’s Motion

RotationRevolution

Proof of Earth’s Rotation

Coriolis Effect

Important When You Can’t See

Target

Proof of Earth’s Rotation

Oblate Earth

Documents

Newton 1 st Law of Motion Gravity Mass/Weight Centripetal Force Kepler’s Third Law Calculating Mass Solving for G Orbits Earth Moves