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Review: Motion Newton’s Laws of Motion Gravity and Orbits First exam next Wednesday Newton’s Law Equivalence Principle Orbits Today in class I Review: Motion, Gravity I Gravity and Orbits Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Review: Motion Newton’s Laws of Motion Gravity and Orbits Newton’s Law Equivalence Principle Orbits Review: Motion Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Newton’s laws of motion Review: Motion Newton’s Laws of Motion Gravity and Orbits Newton’s Law Equivalence Principle Orbits 1. Momentum (qualitative) 2. Force and Acceleration (quantitative) 3. Equal and opposite forces (structure of theory) These are actually all aspects of conservation of momentum Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Newton’s first law Review: Motion Newton’s Laws of Motion Newton’s 1st law: Objects at rest stay at rest Objects in motion stay in motion Unless acted upon by a force Velocities are unchanged without force I Contradicts Aristotle’s physics I the earth can move through space at high speed (around the sun) and we would never know it Gravity and Orbits Newton’s Law Equivalence Principle Orbits Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Newton’s second law higher mass Newton’s second law: Force = mass × acceleration F = ma I velocity force acceleration same force magnitude, lower mass Establishes mass as the property of matter that defines inertia (difficulty of changing velocity) I More mass requires larger force to follow same path I More acceleration requires larger force for same mass Often ”fixed” objects just have mass so large that acceleration is not perceptible. (The Earth) Review: Motion Newton’s Laws of Motion Gravity and Orbits Newton’s Law Equivalence Principle Orbits Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Newton’s third law Review: Motion Newton’s third law: Every action has an equal and opposite reaction I For an isolated system, all forces sum to zero I Throwing something from a wheeled cart makes the cart move I In order to change velocity in space, must have reaction mass (exhaust) to throw away Conservation of momentum: In a ”sticky” collision the object with a higher product of mass and velocity ”wins.” More massive objects are more ”stubborn” about changing their motion Newton’s Laws of Motion Gravity and Orbits Newton’s Law Equivalence Principle Orbits Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Newton’s Laws of Motion Review: Motion Newton’s Laws of Motion Gravity and Orbits Notable features of Newton’s laws of Motion I Universal - apply the same to both heavenly and earthly bodies I Essential milestone in astronomy - broke division between heavenly and earthly realm I Principles discovered in the lab can be applied to the cosmos More on this as we discuss gravitation Newton’s Law Equivalence Principle Orbits Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Newton’s Law of Gravity Review: Motion Newton’s Laws of Motion Gravity and Orbits Newton’s Law Equivalence Principle Orbits Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Force = G ( Mass 1) × (Mass 2) ( distance separated )2 I The two forces are equal and opposite I Force doubles if either mass is doubled I Force decreases if distance increases I Force is 4 times if distance is half I Force is 1/4 if distance is double Equivalence Principle Review: Motion Gravitational mass and inertial mass are the same! gravity large mass small mass Newton’s Laws of Motion Gravity and Orbits Newton’s Law Equivalence Principle Orbits Force Acceleration F1 = M1 a = M1 G M2 M2 =⇒ a = G 2 2 d d Accelleration due to gravity does not depend on object’s mass Depends on mass of other body Two objects of different mass fall at same rate Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version orbiting objects Review: Motion equal forces Newton’s Laws of Motion Gravity and Orbits Newton’s Law Equivalence Principle Orbits Different accelerations Common mistake: Forces are equal and opposite even with different masses only accelerations are different Thus, for example, the earth and moon feel the same force, but the Earth only moves a small amount compared to the Moon. Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Kepler’s Laws Review: Motion Newton’s Laws of Motion Gravity and Orbits Newton’s Law Equivalence Principle Orbits All of Kepler’s laws of planetary motion are derivable from Newton’s laws of motion and gravity Newton’s laws can also describe I Orbits of moons around planets I Non-bound orbits (passing encounters) I Orbital changes due to gravitational encounters or other forces I and more! Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Kepler’s 1st and 2nd Laws Review: Motion Newton’s Laws of Motion Gravity and Orbits Newton’s Law Equivalence Principle Orbits Kepler: I 1. Planets move on ellipses I 2. Planets sweep out equal area in equal time (thus moving faster when close to sun) Newton: I Objects closer to central object experience larger acceleration and have larger velocity I Laws give both shape of orbit (ellipse) and variation in orbital speed per Kepler’s 2nd law Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Kepler’s 3rd Law Review: Motion Newton’s Laws of Motion Gravity and Orbits Newton’s Law Equivalence Principle Orbits Kepler: only works for planets (proportionality more general) (period)2 = (avg. distance from sun)3 where period and distance are measured in Earth years and Earth’s orbital distance. Newton: for any system (Earth-moon, Jupiter, etc) (period)2 = 4π 2 (avg. distance from sun)3 G (M1 + M2 ) period is now related to masses of objects. Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version Kepler’s 3rd Law Review: Motion Newton’s Laws of Motion Gravity and Orbits You should know: Newton’s Law Equivalence Principle Orbits 4π 2 p = a3 G (M1 + M2 ) 2 I larger orbits have longer periods I objects in larger orbits have lower speeds I same size orbit around larger mass has shorter period And the contrary of each Kepler vs. Newton Kepler’s Laws 1& 2 Kepler’s Laws 3 Newton’s version