Re: What would the end velocity be if...?

Wayne Throop wrote:
> : Robert Israel <israel@[EMAIL PROTECTED]
>
> : At 100 g ( 980 m/sec^2), to reach lightspeed (3*10^8 m/sec)
> : would take about 3.06*10^5 sec (ignoring relativity, of course) 
> : or 85 hours.  The accelerator would have to be about 4.59*10^13 m
long,
> : or 307 AU, extending into the inner Oort cloud.
> 
> Which oddly enough (unix "units" confirms for me), is about a hundredth
> of a year.  Which one would expect right off the bat if one happens
> to remember that 1g is about 1c/yr.  So, from my perspective, I would
> say to myself, 100g gives you lightspeed in a hundredth of a year,
> or three or four days.  Arbitrarily saying a tenth lightspeed is below
> what's needed for significant relativistic effects, that means it takes
> you something like 8 hours at 100g before you get significant effects.
> Very handwavy and imprecise, but gives you the general ballpark with
> minimal calculation.

For long trips at constant acceleration, a good fast approximation is

    a*t  =  a*d + 1  =  exp( a*s ) = gamma

for units where c = 1
    a = ****pboard acceleration
    s = ****pboard time
    t = standard time
    d = standard distance
    gamma = ( 1 - v^2 )^(-1/2)

The correct, unapproximated equations are at
    http://www.weburbia.com/physics/rocket.html
and elsewhere.

Jim Burns