FREE BOOKS

Author's List




PREV.   NEXT  
|<   50   51   52   53   54   55   56   57   58   59   60   61   62   63   64   65   66   67   68   69   70   71   72   73   74  
75   76   77   78   79   80   81   82   83   84   85   86   87   88   89   90   91   92   93   94   >>  
of each planet is connected with its average distance by this law; but there is another application of Kepler's law which gives us information of the distance and the period of the moon in former stages of the earth-moon history. Although the actual path of the moon is of course an ellipse, yet that ellipse is troubled, as is well known, by many disturbing forces, and from this cause alone the actual path of the moon is far from being any of those simple curves with which we are so well acquainted. Even were the earth and the moon absolutely rigid particles, perturbations would work all sorts of small changes in the pliant curve. The phenomena of tidal evolution impart an additional element of complexity into the actual shape of the moon's path. We now see that the ellipse is not merely subject to incessant deflections of a periodic nature, it also undergoes a gradual contraction as we look back through time past; but we may, with all needful accuracy for our present purpose, think of the path of the moon as a circle, only we must attribute to that circle a continuous contraction of its radius the further and the further we look back. The alteration in the radius will be even so slow, that the moon will accomplish thousands of revolutions around the earth without any appreciable alteration in the average distance of the two bodies. We can therefore think of the moon as revolving at every epoch in a circle of special radius, and as accomplishing that revolution in a special time. With this understanding we can now apply Kepler's law to the several stages of the moon's past history. The periodic time of each revolution, and the mean distance at which that revolution was performed, will be always connected together by the formula of Kepler. Thus to take an instance in the very remote past. Let us suppose that the moon was at one hundred and twenty thousand miles instead of two hundred and forty thousand, that is, at half its present distance. Applying the law of Kepler, we see that the time of revolution must then have been only about ten days instead of the twenty-seven it is now. Still further, let us suppose that the moon revolves in an orbit with one-tenth of the diameter it has at present, then the cube of 10 being 1000, and the square root of 1000 being 31.6, it follows that the month must have been less than the thirty-first part of what it is at present, that is, it must have been considerably less than one of our p
PREV.   NEXT  
|<   50   51   52   53   54   55   56   57   58   59   60   61   62   63   64   65   66   67   68   69   70   71   72   73   74  
75   76   77   78   79   80   81   82   83   84   85   86   87   88   89   90   91   92   93   94   >>  



Top keywords:

distance

 

Kepler

 
present
 

revolution

 

ellipse

 

circle

 

radius

 

actual

 

thousand

 

special


hundred

 
contraction
 
periodic
 

suppose

 
twenty
 
history
 

connected

 

alteration

 

average

 

stages


revolving

 

appreciable

 

considerably

 

understanding

 

bodies

 

accomplishing

 

instance

 

revolves

 

diameter

 
square

formula

 

remote

 
Applying
 

thirty

 

performed

 
gradual
 

curves

 
acquainted
 

simple

 
perturbations

particles

 

absolutely

 

forces

 
information
 

period

 

application

 
planet
 

Although

 

disturbing

 
troubled