﻿490 
  H. 
  A. 
  Newton 
  — 
  Capture 
  of 
  Comets 
  oy 
  Planets. 
  

  

  encountered 
  Jupiter. 
  At 
  some 
  time 
  Jupiter 
  will 
  be 
  nigli 
  that 
  

   place 
  nearly 
  at 
  the 
  same 
  time 
  as 
  the 
  comet, 
  and 
  the 
  comet 
  will 
  

   suffer 
  a 
  new, 
  and 
  perhaps 
  a 
  large 
  perturbation. 
  Its 
  period 
  

   will 
  again 
  be 
  changed, 
  being 
  shortened 
  or 
  lengthened 
  accord- 
  

   ing 
  as 
  the 
  comet 
  passes 
  before 
  or 
  behind 
  the 
  planet, 
  This 
  

   process 
  will 
  be 
  repeated 
  again 
  and 
  again, 
  since 
  after 
  any 
  num- 
  

   ber 
  of 
  encounters 
  the 
  new 
  orbit 
  of 
  the 
  comet 
  will 
  still 
  pass 
  

   near 
  to 
  the 
  orbit 
  of 
  the 
  planet. 
  

  

  This 
  repeated 
  action 
  makes 
  it 
  possible 
  to 
  have 
  an 
  orbit 
  

   shortened 
  in 
  period 
  by 
  several 
  passages 
  near 
  to 
  Jupiter 
  instead 
  

   of 
  its 
  being 
  done 
  at 
  one 
  passage. 
  A 
  much 
  larger 
  proportion 
  

   of 
  comets 
  than 
  839 
  out 
  of 
  1,000,000,000 
  might 
  therefore 
  have 
  

   their 
  periodic 
  times 
  reduced 
  below 
  the 
  period 
  of 
  Jupiter. 
  

  

  45. 
  If 
  the 
  comet's 
  orbit 
  is 
  largely 
  inclined 
  to 
  the 
  ecliptic 
  and 
  

   hence 
  it^ 
  motion 
  makes 
  a 
  large 
  angle 
  with 
  that 
  of 
  Jupiter 
  the 
  

   diagram 
  figs. 
  10-18 
  show 
  that 
  there 
  is 
  nearly 
  an 
  even 
  chance 
  

  

  •that 
  the 
  velocity 
  will 
  be 
  increased 
  or 
  diminished. 
  A 
  consider- 
  

   able 
  fractional 
  part 
  of 
  the 
  whole 
  number 
  of 
  such 
  comets 
  will 
  

   at 
  each 
  passage 
  be 
  thrown 
  out 
  of 
  the 
  solar 
  system 
  altogether, 
  or 
  

   thrown 
  into 
  such 
  long 
  orbits 
  that 
  they 
  will 
  return 
  only 
  at 
  

   very 
  great 
  intervals 
  of 
  time. 
  This 
  class 
  of 
  comets 
  cannot 
  be 
  

   therefore 
  regarded 
  as 
  permanent 
  members 
  of 
  the 
  family 
  of 
  

   short 
  period 
  comets, 
  except 
  such 
  of 
  them 
  as 
  happen 
  to 
  come 
  

   so 
  near 
  to 
  other 
  planets 
  as 
  to 
  have 
  their 
  orbits 
  changed 
  in 
  such 
  

   wise 
  that 
  they 
  do 
  not 
  have 
  thereafter 
  the 
  near 
  approach 
  to 
  

   Jupiter's 
  orbit. 
  But 
  when 
  an 
  orbit 
  is 
  greatly 
  inclined 
  to 
  the 
  

   plane 
  of 
  the 
  solar 
  system 
  the 
  comet 
  passes 
  through 
  the 
  plane 
  in 
  

   general 
  at 
  a 
  considerable 
  angle 
  and 
  the 
  chance 
  of 
  coming 
  close 
  

   to 
  another 
  planet 
  is 
  relatively 
  small. 
  

  

  46. 
  On 
  the 
  other 
  hand 
  all 
  the 
  comets 
  which 
  after 
  perturba- 
  

   tion 
  are 
  moving 
  in 
  orbits 
  somewhat 
  but 
  not 
  greatly 
  inclined 
  to 
  

   the 
  ecliptic 
  are 
  liable 
  to 
  meet, 
  in 
  fact 
  are 
  sooner 
  or 
  later 
  almost 
  

   certain 
  to 
  meet 
  other 
  planets 
  in 
  such 
  a 
  way 
  as 
  to 
  suffer 
  pertur- 
  

   bations 
  that 
  will 
  prevent 
  future 
  close 
  encounters 
  with 
  Jupiter. 
  

   After 
  such 
  changes 
  those 
  comets 
  must 
  be 
  regarded 
  as 
  tolerably 
  

   permanent 
  members 
  of 
  the 
  solar 
  system. 
  

  

  47. 
  Comets 
  that 
  have 
  motions 
  not 
  greatly 
  inclined 
  to 
  J 
  upiter's 
  

   motion 
  are, 
  as 
  figs. 
  2 
  and 
  4 
  show, 
  more 
  likely 
  in 
  subsequent 
  

   passages 
  near 
  to 
  Jupiter 
  to 
  have 
  their 
  periodic 
  times 
  shortened 
  

   than 
  lengthened. 
  On 
  the 
  contrary 
  those 
  passing 
  in 
  nearly 
  

   opposite 
  direction 
  to 
  Jupiter's 
  motion 
  will 
  as 
  figs. 
  3, 
  5 
  and 
  7 
  

   show, 
  be 
  much 
  more 
  likely 
  to 
  have 
  their 
  periods 
  lengthened 
  

   than 
  shortened. 
  

  

  All 
  these 
  causes 
  combine 
  and 
  work 
  together 
  to 
  the 
  one 
  end 
  

   that 
  those 
  comets 
  which 
  are 
  changed 
  by 
  the 
  perturbing 
  action 
  

   of 
  Jupiter, 
  or 
  other 
  planets, 
  from 
  parabolic 
  orbits 
  of 
  every 
  

   possible 
  inclination 
  to 
  the 
  ecliptic 
  into 
  short 
  period 
  ellipses 
  

  

  