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## Newton

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**Newton**1st Law of Motion Gravity Mass/Weight Centripetal Force Kepler’s Third Law Calculating Mass Solving for G Orbits Earth Moves**Newton’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 1st**An object at rest remains at rest unless acted on by an outside force.**Newton’s 1st**An object in motion continues in a straight line unless acted on by an outside force.**Newton**1st Law of Motion Gravity Mass/Weight Centripetal Force Kepler’s Third Law Calculating Mass Solving for G Orbits Earth Moves**Gravity**-G M m r2 Fg =**Gravity**-G M m r2 Fg = Attractive Force**Gravity**-G M m r2 Fg = Universal Gravitational Constant**Gravity**-G M m r2 Fg = Masses of Two Objects**Gravity**-G M m r2 Fg = Distance Between Centers**-G M m**r2 Fg = Gravity 8 X ¤ 64 X**Newton**1st 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**1st 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=**-m v2 r**-G M m**r2 Fg Fc= = Centripetal Force -m v2 r =**Centripetal Force**-m v2 r -G M m r2 =**Centripetal Force**-m v2 r -G M m r2 =**2 p r**P Circular Orbit v = Centripetal Force v2 r G M r2 =**Centripetal Force**22p2r2 P2 Circular Orbit v2= v2 r G M r2 =**Centripetal Force**4p2r2 P2r G M r2 =**P2**P2 Centripetal Force 4p2r P2 G M r2 =**r2**r2 Centripetal Force G M r2 4p2r = P2**1**G M 1 G M Centripetal Force 4p2r3 = G M P2**Centripetal Force**Circular Orbit r = a 4p2 G M r3 = P2**Centripetal Force**Circular Orbit r = a 4p2 G M a3 = P2**Kepler’s Third Law**P2 = ka3 4p2 G M a3 = P2 ¤**Newton**1st Law of Motion Gravity Mass/Weight Centripetal Force Kepler’s Third Law Calculating Mass Solving for G Orbits Earth Moves**M**M Finding Mass 4p2 G M a3 = P2**1**P2 1 P2 Finding Mass 4p2 G a3 = P2 M**Finding Mass**One problem remains. a3 P2 4p2 G = M**Finding Mass**One problem remains. a3 P2 4p2 G = M**m**m -GMÅm RÅ2 -GMÅm RÅ2 -GMm D2 F = = + Mass of Earth Phillip von Jolly M**m**m Mass of Earth Phillip von Jolly M -GMÅm RÅ2 -GMm D2 -GMÅm RÅ2 F = = +**-GMÅm**RÅ2 -GMm D2 -GMÅm RÅ2 F = = + Mass of Earth Phillip von Jolly m m n M -GMÅn RÅ2 +**Mass of Earth**-GMÅm RÅ2 -GMm D2 -GMÅm RÅ2 -GMÅn RÅ2 F = = + +**-GMm**D2 -GMÅn RÅ2 = RÅ2 n RÅ2 n Mm D2 MÅn RÅ2 = ( ) m RÅ2 n D M = MÅ Mass of Earth**Finding Mass**One problem remains. a3 P2 4p2 G = MÅ ( (**Newton**1st Law of Motion Gravity Mass/Weight Centripetal Force Kepler’s Third Law Calculating Mass Solving for G Orbits Earth Moves**Orbits**Å Apogee Perigee Circular**Orbits**Å Apogee Perigee**Å**Å Transfer Orbits Å ¤**Newton**1st 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**Parallax**Å ¤ Å