From: ram@zedat.fu-berlin.de   
      
   Pat Dolan  writes:   
   >                From these two observations the distant observer   
   >concludes that in his inertial frame of reference the earth's orbital   
   >velocity is only half the velocity necessary to keep the earth in stable   
   >orbit around the sun.   
   >   
   >Will the earth spiral into the sun? If not, why not?   
   >   
   >Note: Newtonian gravity is not assumed in this paradox. Invariant   
   >spacetime curvature is assumed to be the cause of the earth's orbit   
   >around the sun.   
      
     I define the total force F on a body with mass m and acceleration   
     a to be ma (a multiplied by m).   
      
   F = ma.   
      
     If a := dv/dt, then for a real constant k (not depending on t):   
     ka=d(kv)/dt (kv = v multiplied by k). If v is being replace by   
     kv, a is being replaced by ka.   
      
   v -> kv: a -> ka.   
      
     But this means that when v is being replaced by kv, ma is being   
     replaced by mka, and F by kF.   
      
   v -> kv: ma -> mka, F -> kF.   
      
     So, when a moving observer observes a body of mass m that is moving   
     with speed kv (e.g., k=1/2) where "v" is the speed in the system of   
     rest, he must conclude that the force, which is F=ma in the system of   
     rest, is kF=kma, where a is the acceleration in the system of rest,   
     by the very definition of the force as mass times acceleration.   
      
     So, it seems that the force of gravity is also reduced in   
     the moving system balancing the reduction of speeds.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)