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.
Newton’s 1stNewton’s 1st
An object at rest remains at rest unless acted on by an outside force.
Newton’s 1stNewton’s 1st
An object in motion continues in a straight line unless acted on by an outside force.
Newton’s 1stNewton’s 1st
NewtonNewton1st Law of Motion
GravityMass/Weight
Centripetal ForceKepler’s Third LawCalculating Mass
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
NewtonNewton1st Law of Motion
GravityMass/Weight
Centripetal ForceKepler’s Third LawCalculating Mass
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.
NewtonNewton1st Law of Motion
GravityMass/Weight
Centripetal ForceKepler’s Third LawCalculating Mass
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
Centripetal ForceCentripetal Force
Fc=-G M m r2
= Fg=-m v2
r
Centripetal ForceCentripetal Force
-G M m r2
=-m v2
r
Centripetal ForceCentripetal Force
-G M m r2
=-m v2
r
Centripetal ForceCentripetal Force
v2
r G M r2
=
Circular Orbit v =2 r P
Centripetal ForceCentripetal Force
v2
r G M r2
=
Circular Orbit v2=22r2
P2
Centripetal ForceCentripetal Force
4r2
P2 r G M r2
=
Centripetal ForceCentripetal Force
4r P2
G M r2
=P2 P2
Centripetal ForceCentripetal Force
4r G M r2
= P2r2 r2
Centripetal ForceCentripetal Force
4r3 G M= P2 1G M
1G M
Centripetal ForceCentripetal Force
r3 = P2 4
G M
Circular Orbit r = a
Centripetal ForceCentripetal Force
a3 = P2 4
G M
Circular Orbit r = a
Kepler’s Third LawKepler’s Third Law
a3 = P2 4
G M
P2 = k a3
NewtonNewton1st Law of Motion
GravityMass/Weight
Centripetal ForceKepler’s Third LawCalculating Mass
Solving for GOrbits
Earth Moves
Finding MassFinding Mass
a3 = P2 4
G MMM
a3 = P2 4
GM
1P2
1P2
Finding MassFinding Mass
= 4
G Ma3
P2
Finding MassFinding Mass
One problem remains.
= 4
G Ma3
P2
Finding MassFinding Mass
One problem remains.
F = =-GMm R
-GMm R
Mass of EarthPhillip von Jolly
m m
M
-GMm D+
Mass of EarthPhillip von Jolly
mm
M
F = =-GMm R
-GMm R
-GMm D+
Mass of EarthPhillip von Jolly
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
Finding MassFinding Mass
One problem remains.
(
(
NewtonNewton1st Law of Motion
GravityMass/Weight
Centripetal ForceKepler’s Third LawCalculating Mass
Solving for GOrbits
Earth Moves
OrbitsOrbits
Perigee
Apogee
Circular
OrbitsOrbits
PerigeeApogee
Transfer OrbitsTransfer Orbits
NewtonNewton1st Law of Motion
GravityMass/Weight
Centripetal ForceKepler’s Third LawCalculating Mass
Solving for GOrbits
Earth Moves
Proof of Earth’s Motion
RotationRevolution
Proof of Earth’s Revolution
What would satisfy Aristotle?
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 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?
Aberration of Starlight
zero aberration for stars at quadrature
Aberration of Starlight
Aberration of Starlight
Aberration of Starlight
Aberration of Starlight
It depends on what?
Speed of LightSpeed of Earth
Direction of Earth
Aberration of Starlight
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