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## Astronomy notes week 4

by: Becca Petersen

7

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12

# Astronomy notes week 4 AST2002-16Fall 0001

Becca Petersen
University of Central Florida

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## About this Document

lecture notes from week 4 of astronomy
COURSE
Astronomy
PROF.
Dr. James Cooney
TYPE
Class Notes
PAGES
12
WORDS
CONCEPTS
astronomy, Astronomy 101
KARMA
25 ?

## Popular in Science

This 12 page Class Notes was uploaded by Becca Petersen on Friday September 23, 2016. The Class Notes belongs to AST2002-16Fall 0001 at University of Central Florida taught by Dr. James Cooney in Fall 2016. Since its upload, it has received 7 views. For similar materials see Astronomy in Science at University of Central Florida.

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Date Created: 09/23/16
Some basic physics –   Kepler’s  laws  seem  kind  of  arbitrary  –  there  are  basic  laws  of  nature  and   physics  that  underlie  Kepler’s  laws     Motion   Position     Requires  a  coordinate  system  (ex:  it  lies  3  meters  above  …..)     Displacement  –  change  in  the  position  of  things       Velocity     Rate  of  change  of  position  –  describes  how  quickly  that  displacement   takes  place     A  vector     Not  only  the  speed  but  the  direction**  (ex:  60  miles  per  hour,  north)     Acceleration   Rate  of  change  of  velocity  (ex  –  if  you  go  from  one  meter  per  second  to   to  meters  per  second  then  your  acceleration  was  2  meters  per  second-­‐ per  second)     Also  a  vector  –  has  a  direction     Understand  that….     You  can  accelerate  without  changing  your  speed  –  going  around  in  a  circle   where  your  speed  is  the  same  but  your  direction  changes     Moving  in  a  straight  line  in  uniform  speed   –  you  have  a  velocity  but  no   acceleration     You  can  have  acceleration  not  equal  to  zero  but  velocity  equal  to  zero   –  if  you   toss  something  up  in  the  air  –  its  direction  of  its  velocity  is  going  up  but  the   acceleration  is  going  down  –  it  slows  down  as  it  travels  higher  in  the  air  –  and   that  statement  is  the  case  at  its  very  peak       Issac Newton   Between  1665-­‐1667  (he  was  22  in  65)   Known  for…   *He  sort  of  co-­‐invented  calculus   *Newton’s  laws   *Basis  of  all  physics  until  Einstein     *Law  of  universal  gravitation     He  wanted  to  understand  the  nature  of  the  universe  and  why  Kepler's  laws   worked  the  way  they  did.    So  he  basically  found  the  fundamental  laws  of  nature     Came  up  with  the  universal  law  of  gravitation       Newton’s Laws of Motion 1. A  body  remains  at  rest  or  moves  with  constant  velocity  unless  acted   upon  by  an  outside  force  –     I.e.  whatever  state  of  motion  they  are  in,  they  are  going  to   keep  that  exact  velocity  until  you  do  something  to  it.    There   are  things  in  our  every  day  lives  (friction,  gravity,  air   resistance)  that  will  act  on  objects  to  change  their  velocity   or  stop  them.         Being  at  rest  is  essentially  the  same  thing  as  being  in  perfect   constant  motion  (think  about  being  on  an  airplane-­‐  do  you   know  you’re  moving?  –  the  only  way  you  know  you’re   moving  is  by  gaging  it  on  other  things.    So  motion  is  very   relative.       2.    The  change  in  a  body’s  velocity  due  to  an  applied  force  is  in  the  same   direction  as  the  force  and  proportional  to  it.    But  is  inversely  proportional  to   the  body’s  mass.    F=ma       Force  =  mass  times  acceleration     Mass  is  a  measure  of  how  much  something  does  not  want  its   motion  changed.    High  mass  thing  will  have  a  very  low   acceleration  and  vise  versa.    So  pushing  a  brick  will  move   more  slowly  than  pushing  a  stack  of  sticky  notes.         Think  of  the  example  from  class  –  if  you  out  a  lead  brick  over  your  hand  (lets   say  its  30  pounds)  it  has  a  higher  mass  and  doesn’t  want  to  move  so  you  can   hit  it  really  hard  with  a  hammer  and  feel  no  pain.    And  vice  versa  with  a  block   of  wood.    It  has  less  mass  and  is  much  easier  to  move  because  of  the  less   resistance  so  you  will  experience  much  more  pain     3.  For  every  applied  force,  a  force  of  equal  size  but  opposite  direction  arises.     Object  A  acts  on  object  B  and  object  B  acts  on  object  A   So  the  earth  is  pulling  you  down  by  160lbs  and  you  are  pulling  the   earth  up  by  160lbs.     Discussion  on  the  interaction  of  things  –  where  the  force  came  from  –  so   it’s  a  discussion  of  pairs  of  a  thing  where  if  I  do  something  to  you,  you  do   something  to  me       Example  –  someone  trying  to  lift  themselves  up  by  their  ankles  –  they  exert  an   upward  force  of  their  body  weight  on  their  ankles  but  their  ankles  are   exerting  that  same  force  of  their  body  mass  downwards  –  therefor  they  can’t   lift  themselves.       Fundamental  trouble  with  space  travel  is  that  you  have  to  bring  along   everything  with  you  –  the  more  mass  you  have  –  the  harder  it  is  to  accelerate.     The  rocket  exerts  a  force  on  the  heated  gas  and  the  heated  gas  exerts  a  force   back  on  the  rocket  –  but  the  fuel  is  accelerating  much  more  than  you  are   because  its  mass  is  so  much  less     Momentum p=mv   momentum=  mass  times  velocity       Saying  essentially  the  same  thing  as  F=ma     Newton’s  laws  can  be  expressed  in  terms  of  momentum       Weight Weight  -­‐>  gravity   One  example  of  a  force   Usually,  W=mg   G=  acceleration  due  to  gravity  at  earth’s  surface=  9.8  m/s/s     The  difference  between  weight  and  mass  is  important  to  understand   Mass  –  how  much  an  object  is  resisting  change     Weight  –  how  hard  the  earth  is  pulling  on  you     60  kg  on  earth  and  you  go  to  the  moon  where  your  weight  is  1/6  of  that  on  the   moon.    Your  mass  will  still  be  60  kg  on  the  moon.    But  you  will  weigh  20  kg  on   the  moon.         Four  fundamental  forces  in  nature  (magnetic,  strong,  weak,  and  gravity)  but  in   astronomy,  gravity  is  by  far  the  most  important     Gravity:   Universal  Law  of  Gravitation  –   “Between  every  two  objects  there  is  an  attractive  force,  the  magnitude  of   which  is  directly  proportional  to  the  mass  of  each  object  and  inversely   proportional  to  the  square  of  the  distance  between  the  centers  of  the  objects.”     Newton’s  third  law  is  implicit  in  this       F g =G  M 1 M 2         d^2     D=  distance     Is  you  doubled  the  mass  of  object  two  (m2)  the  force  of  the  equation  is   doubled     If  you  doubled  the  distance  between  them  you  have  decreased  f  by  a  factor  of   4     You  feel  weightless  in  space  because  you  are  falling  –  falling  into  orbit   Its  kind  of  like  jumping  out  of  an  airplane  where  you  feel  weightless  within  the   first  few  seconds     In  both  instances  you  are  falling  with  some  horizontal  velocity       When  you  drop  something  it  heads  towards  the  center  of  the  earth     Tides:   Gravitational  force  decreases  with  distance       The  moon’s  pull  on  earth  is  stronger  on  earth  on  the  side  facing  the   moon  and  weakest  on  the  opposite  side     The  earth  gets  stretched  along  the  earth  –  moon  line     Tides  are  an  application  to  the  universal  law  of  gravitation     Both  the  earth  and  the  moon  are  sort  of  falling  towards  each  other   –  which   means  they  both  want  to  stretch  along  the  line  that  connects  them  –  the   oceans  are  what  “stretch”         If  the  earth  and  moon  were  stagnant,  all  the  water  would  collect  on  one  side     2  high  tides  every  day  and  2  low  tides  every  day       Every  day  on  earth  passes  through  high  tide  twice  per  day  as  the  e arth  rotates     High  tides  occur  every  12  hours  25  minutes     The  sun  produces  tides  on  the  earth  as  well    -­‐  it  is  much  less  important  to  tides   than  the  moon  is.    The  sun  is  so  far  away  that  the  difference  across  the  earth  is   kind  of  irrelevant       “Even  though  the  sun  pulls  harder  than  the  moon  the  difference  n  how   hard  it  pulls  on  different  parts  of  earth  is  small  because  it  is  so  distant”     Geography  also  plays  into  tides’  complications     Spring and Neap Tides   When  the  Sun  and  the  moon  pull  in  the  same  directions  (new  and  full  phases)   High  tide  is  higher  than  usual  (spring)  –  because  the  tides  seem  to  spring  way   up  from  being  very  low  to  very  high     When  the  sun  and  moon  pull  at  right  angles,  (first  and  last  quarter  phases)   high  tide  is  lower  than  usual  –  called  a  neap  tide)       Tidal Friction –   Remember  that  earth’s  bulges  want  to  face  towards  (and  away  from)   the   moon.    But  the  earth  is  spinning  and  obviously  the  oceans  are  attached  to  the   earth  so  they  have  to  spin  with  them.    So  there  is  this  fight  between  where  the   moon  wants  to  bulges  to  do  and  the  earth,  which  wants  to   drag  the  bulges   with  them.    This  causes  friction     This  fight  between  moon’s  pull  and  earth’s  rotation  causes  friction ^     Earth’s  rotation  slows  down  1  second  every  50,000  years  –  this  is  because  the   moon  moves  further  away  from  earth     Synchronous rotation   Is  what  the  rotation  period  of  a  moon,  planet,  or  star  equals  its  orbital  period   about  another  object     Tidal  friction  the  moon  caused  by  earth  has  slowed  its  rotation  down  to   a   period  of  one  month       Conservation Laws   Momentum  =  mv       `Has  a  direction  because  it  is  a  vector     Angular  momentum  =  r  x  mv     Is  a  rotational  version  of  momentum  –  basically  the  momentum  of   things  going  in  a  circle       R  =  radius     Energy     Very  fine  law   Energy  comes  in  many  forms   Even  when  newton’s  laws  fail,  conservation  of  energy  holds     Acceleration  is  not  a  form  of  energy*     Various types of energy in the universe   Kinetic  –  kinetic  means  motion  so  the  faster  you’re  moving  the  more  energy   you  have     Potential energy   –  most  of  the  kinds  of  energy  we  see       Called  potential  because  it  has  the  potential  to  turn  into   kinetic  energy  if  you  do  the  right  thing     Gravitational  potential  energy   In  space,  an  object  or  gas  cloud  has  more  gravitational   energy  when  it  is  spread  out  then  when  it  contracts     A  contracting  cloud  converts  gravitational  potential  energy   in  the  form  of  thermal  energy       Chemical  –  energy  stored  within  the  bonds  of  molecules  –  like  how  we   consume  food  for  energy.    Same  thing  with  gasoline.    Energy  is  produced   by  breaking  those  bonds     Nuclear  –  energy  stored  in  the  nucleai  of  atoms.    Difficult  process  but  if   you  do  it  properly  you  can  release  large  amounts  of  energy       Radiative-­‐       Light  –  light  itself  is  energy         Total  orbital  energy  (gravitational  plus  kinetic)  stays  constant  if  there  is  no   ecternal  force   Oribits  cannot  change  spontaneously     Changing  an  orbit:     For  example,  the  space  station  is  orbiting  around  the  earth  –  it  takes  about  an   hour  and  a  half  to  do  that     There  is  still  a  tiny  bit  of  thin  atmosphere  a  couple  hundred  miles  up  where  it   orbits.    The  atmospheric  molecules  hitting  the  thing  are  slowing  it  down.    So   occasionally  they  have  to  use  a  little  bit  of  internal  energy  to  stay  in  the  orbit   that  they  are  in.     What  makes  an  object  gain  or  lose  orbital  energy:     Friction  and  atmospheric  drag     A  gravitational  encounter     An  aside  on  temperature     It  is  a  measure  of  the  average  kinetic  energy  of  the  particles  in  a  thing     Temperature scales:   Fahrenheit  (bad)   Based  on  the  boiling  and  freezing  point  of  water  –  32  degrees  and  212   degrees     Celsius  (better)     It  also  uses  the  freezing  and  boiling  points  of  water  as  its  bench  mark     Kelvin  (best)     puts  zero  where  zero  should  be         The  reason  why  celcius  and  fahrenhiet  are  bad  because  molecules  actually   can   reach  a  point  where  they  stop  moving  –  called  absolute  zero-­‐  so  there  is  an   absolute  minimum  –  which  is  not  the  case  with  celcius  and  Fahrenheit       Light   Light  is  a  vibration  in  an  electromagnetic  field  through  which  energy  is   transported     Dual  Natures     Light  acts  as  a  wave           A  wave  is  very  different  than  a  particle  –  it  is  spread  out  is  space,  it  doesn’t   have  one  point  it  has  crests  and  troughs     If  you  want  a  water  wave  –  a  wave  in  the  ocean,  you  fundamentally  need   water.    A  water  wave  is  a  disruption  of  a  medium,  in  this  case  water.    The   same  is  said  with  a  slinky  –  there  is  a  disruption  in  the  slinky.     A  sound  wave  is  vibration  of  air  molecules  –  density/  pressure  wave  in  the  air.     Light  is  the  exception.    It  is  not  a  thing  that  is  vibrating,  because  it  is  a   wave  that  travels  without  a  medium.     Light  acts  as  a  wave  –  its  speed  is:    v  =  f  •  λ     But  the  speed  of  light  is  a  constant,  c     For  light,   f  •  λ  =  c   The  higher  f  is  the  smaller  λ  is  and  vice  versa     Our  eyes  recognize  f  as   color   Color  isn’t  a  real  thing  –  its  just  your  brain  interpreting  different  frequencies     Light  can  also  behave  as  a  particle   Light  can  also  be  treated  as  photons  –  packets  of  energy     The  energy  carried  by  each  photon  depends  on  its  frequency  (color)     E=hf    =  hc  /   λ           Light  acts  as  a  particle:     E=hf                       Questions  frequently  missed  from  the  previous  exam   –     How  far  serius  moves  along  the  celestial  sphere  every  6  months   –  remember   that  stars  are  painted  on  the  celestial  sphere,  they  don’t  move.    The  sun,   however,  does.     Where  can  you  live  to  maximize  the  amount  of  light  each  day?     Anywhere  –  north  pole  –  6  months  of  light,  6  months  of  dark   Equator  –  12  hours  of  light,  12  hours  of  dark…  so  6  months  of  light  and  6   months  of  dark     You  are  moving  faster  than  the  empire  state  building  if  you  are  in  Orlando   because  you  both  have  to  go  around  in  a  circle  every  day  but  your  circle  is   bigger  because  you  are  closer  to  the  equator     Galaxy  with  the  youngest  appearance  –     You  are  seeing  light  that  has  already  passed  when  you  look  at  galaxies .     The  youngest  appearance  would  be  the  one  that  is  furthest  away  –   because  that  means  it  has  taken  more  time  for  light  to  travel  so  the  light   we  see  would  be  considered  younger  –  say  4  billion  years  old  rather   than  2  million  years  old.

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