First exam next Wednesday. Today in class Review: Motion, Gravity. Gravity and Orbits. Review: Motion. Newton s Laws of Motion. Gravity and Orbits

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Bernard Stevens
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1 Review: s of First exam next Wednesday Today in class Review:, Gravity Gravity and Gravity and

2 Review: s of Review: Gravity and

3 Newton s laws of motion Review: s of 1. Momentum (qualitative) 2. Force and Acceleration (quantitative) 3. Equal and opposite forces (structure of theory) Gravity and These are actually all aspects of conservation of momentum

4 Newton s first law Velocities are unchanged without force Newton s 1st law: Objects at rest stay at rest Objects in motion stay in motion Unless acted upon by a force Contradicts Aristotle s physics the earth can move through space at high speed (around the sun) and we would never know it Review: s of Gravity and

5 Newton s second law velocity force acceleration higher mass same force magnitude, lower mass Newton s second law: Force = mass acceleration F = ma Establishes mass as the property of matter that defines inertia (difficulty of changing velocity) More mass requires larger force to follow same path More acceleration requires larger force for same mass Often fixed objects just have mass so large that acceleration is not perceptible. (The Earth) Review: s of Gravity and

6 Newton s third law Review: Newton s third law: Every action has an equal and opposite reaction For an isolated system, all forces sum to zero Throwing something from a wheeled cart makes the cart move 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 s of Gravity and

7 s of Review: s of Notable features of Newton s laws of Universal - apply the same to both heavenly and earthly bodies Essential milestone in astronomy - broke division between heavenly and earthly realm Principles discovered in the lab can be applied to the cosmos More on this as we discuss gravitation Gravity and

8 of Gravity Review: s of Gravity and ( Mass 1) (Mass 2) Force = G ( distance separated ) 2 The two forces are equal and opposite Force doubles if either mass is doubled Force decreases if distance increases Force is 4 times if distance is half Force is 1/4 if distance is double

9 Review: Gravitational mass and inertial mass are the same! gravity large mass small mass Acceleration Force s of Gravity and F 1 = M 1 a = M 1 G M 2 d 2 = a = G M 2 d 2 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

10 orbiting objects Review: equal forces Different accelerations Common mistake: Forces are equal and opposite even with different masses only accelerations are different s of Gravity and Thus, for example, the earth and moon feel the same force, but the Earth only moves a small amount compared to the Moon.

11 Kepler s Laws Review: s of All of Kepler s laws of planetary motion are derivable from Newton s laws of motion and gravity Gravity and Newton s laws can also describe of moons around planets Non-bound orbits (passing encounters) Orbital changes due to gravitational encounters or other forces and more!

12 Kepler s 1st and 2nd Laws Review: s of Kepler: 1. Planets move on ellipses 2. Planets sweep out equal area in equal time (thus moving faster when close to sun) Newton: Objects closer to central object experience larger acceleration and have larger velocity Laws give both shape of orbit (ellipse) and variation in orbital speed per Kepler s 2nd law Gravity and

13 Kepler s 3rd Law Review: s of Kepler: only works for planets (proportionality more general) (period) 2 = (avg. distance from sun) 3 Gravity and 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(M 1 + M 2 ) period is now related to masses of objects.

14 Kepler s 3rd Law p 2 = 4π 2 G(M 1 + M 2 ) a3 You should know: larger orbits have longer periods objects in larger orbits have lower speeds same size orbit around larger mass has shorter period And the contrary of each Review: s of Gravity and

4.3 Conservation Laws in Astronomy

4.3 Conservation Laws in Astronomy Our goals for learning: Why do objects move at constant velocity if no force acts on them? What keeps a planet rotating and orbiting the Sun? Where do objects get their