Re: 1g trip to Toliman

:: If you sustain 1 g acceleration for 2 years locally, 3,75 years
:: passes on Earth and 2,9 ly is covered.

: macfraggin@xxxxxxxxxxxxxx
: I'm not so sure about this -- 2 years of constant acceleration would,
: going by Newtonian mechanics, give you a delta-V of about 600.000km/s
: - roughly twice the speed of light. What should happen here is that
: the ship's velocity converges against c, and the time frames for ship
: and observer (earth) are dissociated:
: t' = t / (1 - v^2 / c^2)

Indeed. That's how the figure of 3.75 years on earth is derived.
Integrate that expression over the trip.

: So at 99%c - which the ship might reach after one year of travel - the
: time dilation is about 50:1. If the ship just kept coasting for two
: years, a hundred years would pass on earth.

In the stated situation, the ship doesn't coast at .99c for two years.
So how long would pass on earth if one coasted for 2 years at .99c
does not in any way, shape, or form, cast any doubt upon the above
stated relationship.

Now, if you wanted to add up how long passes on earth at a constant speed
that represents the first tenth-year, then the second, then the third,
for each of the 20 tenth-years of the proper time of the trip, and you
account for relativistic velcity addition in working out the speeds you
use for each tenth-year, I think you'll find you get about 3.75 years
when you add them up. That is, after all, what "integration" does,
and what I describe is a crude form of numerical integration.

Or, you could just use mathematical integration, and plug and chug
on the resulting expression. Which is where 3.75 years comes from.


Wayne Throop throopw@xxxxxxxxx http://sheol.org/throopw
.

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