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

Newton’s 1 st 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 1 st An object at rest remains at rest unless acted on by an outside force.

Newton’s 1 st An object in motion continues in a straight line unless acted on by an outside force.

Newton’s 1 st 

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

Gravity F g = -G M m r 2

Gravity F g = -G M m r 2 Attractive Force

Gravity F g = -G M m r 2 Universal Gravitational Constant

Gravity F g = -G M m r 2 Masses of Two Objects

Gravity F g = -G M m r 2 Distance Between Centers

Gravity  8 X 64 X F g = -G M m r 2

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

Mass / Weight Mass = 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 Surface kilogram = measure of mass pound = measure of force

Mass / 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.

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

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=Fc= -m v 2 r

Centripetal Force Fc=Fc= -G M m r 2 = FgFg = -m v 2 r

Centripetal Force -G M m r 2 = -m v 2 r

Centripetal Force -G M m r 2 = -m v 2 r

Centripetal Force v 2 r G M r 2 = Circular Orbit v = 2  r P

Centripetal Force v 2 r G M r 2 = Circular Orbit v2=v2= 2 2   r 2 P 2

Centripetal Force 4   r 2 P 2 r G M r 2 =

Centripetal Force 4   r P 2 G M r 2 = P2P2 P2P2

Centripetal Force 4r4r G M r 2 =P2P2 r2r2 r2r2

Centripetal Force 4r34r3 G M=P2P2 1 G M 1 G M

Centripetal Force r3r3 =P2P2 4   G M Circular Orbitr = a

Centripetal Force a3a3 =P2P2 4   G M Circular Orbitr = a

Kepler’s Third Law a3a3 =P2P2 4   G M P 2 = k a 3 

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

Finding Mass a3a3 =P2P2 4   G M M M

a3a3 =P2P2 4   G M 1P2 1P2 1P2 1P2 Finding Mass

= 4   G M a3P2a3P2 Finding Mass One problem remains.

= 4   G M a3P2a3P2 Finding Mass One problem remains.

F = = -GM  m R   -GM  m R   Mass of Earth Phillip von Jolly m m M -GMm D  +

Mass of Earth Phillip von Jolly m m M F = = -GM  m R   -GM  m R   -GMm D  +

Mass of Earth Phillip von Jolly m m n M F = = -GM  m R   -GM  m R   -GMm D  + -GM  n R   +

Mass of Earth F = = -GM  m R   -GM  m R   -GMm D  + -GM  n R   +

Mass of Earth -GMm D  -GM  n R   = Mm D  M  n R   = n R   n m R   2 n D ( ) M = M 

= 4   G MM a3P2a3P2 Finding Mass One problem remains. (

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

Orbits  Perigee Apogee Circular

Orbits  Perigee Apogee

Transfer Orbits    

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

Proof of Earth’s Motion Rotation Revolution

Proof of Earth’s Revolution What would satisfy Aristotle? Parallax

  

shift in the position of one nearby star, compared to the background of more distant stars

Parallax    Quadrature

Proof of Earth’s Revolution Stellar Aberration Aberration of Starlight

Tilt 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  

 

 

  It depends on what? Speed of Light Speed 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 Rotation Revolution

Proof of Earth’s Rotation Coriolis Effect Important When You Can’t See Target

Proof of Earth’s Rotation Oblate Earth