View Single Post
  #63 (permalink)  
Old 29-April-2008, 01:18 AM
grav grav is offline
Senior Member
 
Join Date: May 2006
Posts: 2,308
Default

Above we found a gravity that is 6 times greater than the same mass at a distance equal to the radius of the base if h<<r. But let's say h>>r, extended indefinitely. In that case, we can use the first order for the square root with a very small r/h ratio to get

6 (G M / r^2) [1 - 1 / sqrt[1 + (r/h)^2]]

= 6 (G M / r^2) [1 - 1 / (1 + (r/h)^2 / 2)]

= 6 (G M / r^2) [ 1 - (1 - (r/h)^2 / 2)]

= 6 (G M / r^2) [(r/h)^2 / 2]

= 3 G M / h^2

so if h is very large in respect to r, the limit for the gravity works toward being 3 times stronger than that of a sphere or point mass with the same mass at a distance of h from the particle.
__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."
Reply With Quote