Chapter 4: Newton and Universal Motion

Mechanics Mechanics = laws of motion Aristotle Galileo Rest = Natural State of Motion Heavy objects fall faster Galileo Object continues in motion unless something pushes on it Heavy and light objects fall at same rate

Study of Motion (Mechanics) Velocity Change in location Speed (mph) and direction (NE) Acceleration Change in velocity (speed and/or direction) Force Push or pull (pounds) Mass How much stuff (grams, kilograms)

Mass vs Weight Mass Produces Gravity Weight = Force of Gravity Mass intrinsic to object (never changes) Gravity proportional to mass Weight = Force of Gravity Stand on scale scale pushes back with equal force Weight proportional to mass Free-Fall (falling elevator, astronauts) Acceleration of gravity = weight / mass All objects fall at same rate Objects appear “weightless” mass on Moon = mass on Earth weight on Moon = 1/6 weight on Earth in space, force of gravity is not zero

Newton Laws of Motion Moving object keeps moving Same speed Same direction Objects want to move in straight line Change in motion (speed or direction) caused by force acceleration = force / mass Equal, but opposite, forces between pairs of objects Push on object; it pushes back (just as hard)

Newton Invents mathematics (calculus) Circular motion Used to solve force equations Circular motion Direction of motion changes Requires force Force changes direction; speed unaltered Force points toward center of circle

Newton Gravity Orbits similar to circles Newton’s Hypothesis Pulls apple toward earth makes apple fall Weight = force of gravity Orbits similar to circles Newton’s Hypothesis All objects produce gravity Sun’s gravity planets orbit sun Planet’s gravity moon orbits planet Gravity Sun

Launching Rockets Fire Cannon Sideways; keep increasing velocity Rocket moves sideways; offsets falling Circular Orbit Speed =17,000 mph Escape Speed = 25,000 mph

Newton Law of Gravity Force = G M1M2 / R2 Double either mass: force increases by 2 Double distance: force decreases by 4 M1 = mass 1st object (sun) M2 = mass 2nd object (planet) R = distance between them G = Newton’s constant (a number) Larger (smaller) mass causes larger (smaller) gravitational force. Larger (smaller) distance causes smaller (larger) gravitational force.

Newton and Planets Law of Gravity Force = G MsunMplanet / R2 Acceleration = Force / Mplanet = G Msun / R2 Planet motion: independent of planet mass depends on: mass of sun distance

Newton and Planets Laws of motion + Gravity Predicts Kepler’s Laws: 1st Law (orbits are ellipses) 2nd Law (equal area in equal time) conservation of angular momentum Skater pulls arms in; spins faster Planet gets closer to sun; goes faster Extended 3rd Law a3 = M P2 use to measure mass M (of central body) M in solar masses

Consider a planet orbiting the Sun Consider a planet orbiting the Sun. If the mass of the planet doubled but the planet stayed at the same orbital distance, then the planet would take a) more than twice as long to orbit the Sun. b) exactly twice as long to orbit the Sun. c) the same amount of time to orbit the Sun. d) exactly half as long to orbit the Sun. e) less than half as long to orbit the Sun.

Workbook Exercise: Orbital Period and Orbital Distance (pages 43-55 in workbook)

Which of the following best describes what would happen if Mercury and Jupiter were to switch places in their orbits about the Sun? a) Jupiter, the larger planet, would have a shorter orbital period than before. b) Mercury, the smaller planet, would have a shorter orbital period than before. c) Neither of the two planets would have any change in their orbital periods.

Imagine a new planet in our solar system located 3 AU from the Sun Imagine a new planet in our solar system located 3 AU from the Sun. Which of the following best approximates the orbital period of this planet? a) 1 year b) 3 years c) 5 years d) 9 years P2=a3, so if a=3, then a3=3x3x3=27; then P2=27, so P~5 (since 5x5=25)

Ocean Tides Moon’s Gravity Tides

Spring / Neap Tides Tidal effect of Sun new/full moon Tides larger = Spring Tides 1st/3rd Quarter moon Tides smaller = Neap Tides