Re: [nbos] [AS] Travel Times
Nyrath the nearly wise
Sat Aug 29th, 2009
Walter M. Scott III wrote:
>>...I am trying to figure out some travel times at slower than light.
>>...Anyone know of any easy way to compute these times?
>>...For example, a sleeper ship that is going from earth to 61 Cygni.
> Assuming acceleration of 3/4 Gs, I was just trying to figure out how
> long it would take to travel.

There are two times: the time as measured on Earth,
and the time as measured on board the starship.

I'm assuming you want a brachistochrone flight path,
where you accelerate to the half-way point, then
decelerate to a stop at the destination.
Otherwise you go shooting through the 61 Cygni system
at close to the speed of light.

61 Cygni is about 11.36 ly from Earth.
3/4 g is about 7.36 meters per second per second

To figure a brachistochrone, you use half the
distance (5.68 light years), do the calculation,
then when you get the elapsed time, you double it.

To figure the time it takes as measured on Earth

t = sqrt[(d/c)^2 + (2*d/a)]
t = elapsed time on Earth (seconds)
d = distance (meters)
c = speed of light in a vacuum (meters per second)
a = acceleration (meters per second per second)

My slide rule says 3/4 g to 61 Cygni is 13.7 years

To figure the time it takes as measured on the starship
T = (c/a) * ArcCosh[a*d/(c^2) + 1]

My slide rule says 6.14 years

To figure the ship's velocity at the midpoint (maximum
v = (a*t) / Sqrt[1 + (a*t/c)^2]

My slide rule says 0.9826 c or 98.26% lightspeed.

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