© 2005 Pearson Education Inc., publishing as Addison- Wesley The Planets Prof. Geoff Marcy Tides Energy: Potential and Kinetic Momentum Angular Momentum Lecture Sept. 13

Announcements Chapter 4 Assignment due tomorrow. Read Chapter 5: Light! Homework: MasteringAstronomy Assignment Chapt. 5

© 2005 Pearson Education Inc., publishing as Addison-Wesley Last time: 1. Newton’s three laws 2. Elliptical orbits of planets Today: 1.Tides (Why is do we always see the same side of the moon?) 2.Conservation laws (Why useful?)

Tides Daily oscillations of the ocean surface level Two high tides and two low tides per day, one every 12hr 50 min.

Hiking along California’s coast

Today’s tide chart Note: two low tides per day; Happen with moonrise and moonset.

A monthly tides gauge reading Questions: Why two high tides per day? Why one every 12:50 hours? Why does the amplitude change over the course of a month?

Gravity field causes two tidal bulges

Tidal friction lead to synchronous rotation. Moon is facing the earth the same way. Pluto and moon Charon rotate synchronously around each other.

Tides vary with the phase of the Moon because the sun interacts also Spring tide: HIGH because sun and moon act together during new and full moon

© 2005 Pearson Education Inc., publishing as Addison-Wesley Tides vary with the phase of the Moon because the sun interacts also Spring tide: HIGH because sun and moon act together during new and full moon Neap tide: LOW because sun and moon’s gravity counter-act

The next new moon will be on Sept. 15 th. What time will the low tide occur in the bay area? (pick closest time) A.6 am B.Noon C.6 pm D. Midnight

© 2005 Pearson Education Inc., publishing as Addison-Wesley Real tides are more complicated

© 2005 Pearson Education Inc., publishing as Addison-Wesley Real tides are more complicated

Tidal friction… Tidal friction gradually slows Earth rotation, 1 s every 50,000 years (and makes Moon get farther from Earth). Earth’s + moon’s combined angular momentum is conserved. Earth is losing angular momentum, the moon gains it. Moon once rotated faster (or slower); tidal friction caused it to “lock” in synchronous rotation.

© 2005 Pearson Education Inc., publishing as Addison-Wesley Synchronous Rotation …is when the rotation period of a moon, planet, or star equals its orbital period about another object. Tidal friction on the Moon (caused by Earth) has slowed its rotation down to a period of one month. The Moon now rotates synchronously. –We always see the same side of the Moon.

Last time: How is mass different from weight? mass – the amount of matter in an object weight – the force that acts upon an object You are weightless in free-fall! You can’t tell the difference between: - Free fall in gravity - No gravity at all

Tennis on the moon Would you hear Maria Sharapova grunting on the moon? A) YES B) NO

Tennis on the moon Would you hear the players’ noises on the moon? A) YES B) NO The gravity field on the moon is 6 times weaker than on Earth. Could one still play tennis there? A) YES B) NO

Tennis on the moon Would you hear the players’ noises on the moon? A) YES B) NO The gravity field on the moon is 6 times weaker than on Earth. Could one still play tennis there? A) YES B) NO but balls would bounce much higher. Could I ‘fix’ that by making the balls 6 times as heavy? A) YES B) NO

Tennis on the moon Would you hear the players’ noises on the moon? A) YES B) NO The gravity field on the moon is 6 times weaker than on Earth. Could one still play tennis there? A) YES B) NO but balls would bound much higher. Could I ‘fix’ that by making the balls 6 times as heavy? A) YES B) NO No that would only make it harder to accelerate them. All objects fall at the same rate!

Why are astronauts weightless in space? There IS gravity in space… weightlessness is due to a constant state of free-fall:

© 2005 Pearson Education Inc., publishing as Addison-Wesley Four conservation laws mass (for chemists only) energy momentum, angular momentum,

Conservation of Mass For all practical purposes in chemistry: Yes but … (A) YES (B) NO 2H 2 +O 2  2 H 2 O Energy released ΔE= kJ/mol 1 mol = 6.02  particles

Mass is a form of Energy: E = mc 2

Conservation of Mass 2H 2 +O 2  2 H 2 O No, because there is a tiny difference because the atom are now is state of lower energy. Δm=ΔE / c 2 Negligible for practical purposes but measurable. (A) YES (B) NO Energy released ΔE= kJ/mol 1 mol = 6.02  particles

© 2005 Pearson Education Inc., publishing as Addison-Wesley How do we produce energy?

Basic Types of Energy Kinetic (motion) Potential (gravitational) Thermal (heat) Chemical energy (bonds) Nuclear energy (bonds) Light Mass-Energy can change type, but cannot be destroyed.

© 2005 Pearson Education Inc., publishing as Addison-Wesley

Kinetic Energy

Potential Energy Converted to Kinetic Energy

Potential Energy Potential Energy = mass * 9.8 m/s 2 * height = mgh

Converting: Potential Energy to Kinetic Energy

Kinetic Energy Converted to Heat

Potential Energy Converted to Kinetic Energy

Thermal Energy of the motion of atoms and molecules © 2005 Pearson Education Inc., publishing as Addison-Wesley

Thermal Energy: Kinetic Energy of the molecules

Potential Energy (in battery) Converted to Electrical Energy © 2005 Pearson Education Inc., publishing as Addison-Wesley

Conservation of Energy Energy can make matter move. Energy is conserved, but it can: –Transfer from one object to another –Change in form Note: Energy is conserved within a definite system. In an open system, it can be exchanged with the environment

Conservation of Momentum Definition of momentum: p = mass × velocity unit: kg m / s Conservation of momentum: If no external force is applied, the total momentum of system is conserved. Useful: For all sorts of collisions Applies also to atoms and molecules Not useful: If friction is involved.

Conservation of Energy: Potential + Kinetic = Constant with time © 2005 Pearson Education Inc., publishing as Addison-Wesley

Collisions of Balls on a Pool Table

Interactive Quiz: Collisions Balls on a Pool Table 8 8 A B C Which shot will get a black ball in the corner pocket? A) B) C) D) This is not possible.

Interactive Quiz: Collisions Balls on a Pool Table A B C Which shot will get a black ball in the corner pocket? A) B) C) D) This is not possible.

B Interactive Quiz: Collisions Balls on a Pool Table A C Which shot will get a black ball in the corner pocket? A) B) C) D) This is not possible.

B Interactive Quiz: Collisions Balls on a Pool Table A C Which shot will get a black ball in the corner pocket? A) B) C) D) This is not possible.

Interactive Quiz: Collisions of two trucks Two trucks of equal mass on an icy road: Before collision: Truck 1 is at rest. Truck 2 approached with 40 km/h. After the collision: Both trucks are damaged and stick together What is their final velocity? A) 10 km/h B) 20 km/h C) 40 km/h D) This is not possible, conservation of momentum prevents them from sticking

Interactive Quiz: Collisions of two trucks Two trucks of equal mass on an icy road: Before collision: Truck 1 is at rest. Truck 2 approached with 40 km/h. Truck 1: p 1 =M* 0 km/h Truck 2: p 2 =M* 40 km/h After collision: p=(2M)*v final Momentum conservation: p = p 1 +p 2 (2M)*v final = M*40 km/h v final = 20km/h Is energy conserved for this collision process?

Interactive Quiz: Collisions of two trucks Two trucks of equal mass on an icy road: Before collision: Truck 1 is at rest. Truck 2 approached with 40 km/h. Truck 1: p 1 =M* 0 km/hE 1 =½ M v 2 =0 Truck 2: p 2 =M* 40 km/hE 2 =½ M (40km/h) 2 =800M (km/h) 2 After collision: p=(2M)*v final Momentum conservation: p = p 1 +p 2 (2M)*v final = M*40 km/h v final = 20km/hE = ½ (2M) (20km/h) 2 =400M (km/h) 2

Conservation of Angular Momentum Definition of angular momentum unit: kg m / s Conservation of angular momentum: In a central field like the sun’s gravity, the angular momentum of orbiting objects is conserved. Useful: Planets and comets in the sun’s gravity field Applies to rotating objects. Not useful: If friction is involved.

© 2005 Pearson Education Inc., publishing as Addison-Wesley Changes in length of day

Rotating Chair Demo Before: Radius large Angular velocity small After: Radius small Angular velocity large

© 2005 Pearson Education Inc., publishing as Addison-Wesley Changes in length of day Winter-summer atmosphere flow, storms Motion in liquid iron core Postglacial rebound

© 2005 Pearson Education Inc., publishing as Addison-Wesley A Planet in a Elliptical Orbit

© 2005 Pearson Education Inc., publishing as Addison-Wesley What have we learned and seen today 1.Conservation of momentum, angular momentum, and energy 2.What causes tides? 3.Why are the two tidal bulges? 4.Why do we always see the same side of the moon?