Re: Quick question about a STL trip - and another...

On Aug 21, 5:14 pm, Jacey Bedford <lookin...@xxxxxxxxxxxxxx> wrote:
IsaacKuo <mech...@xxxxxxxxx> writes

If we're talking about a generation ship, then it's okay to have
acceleration and deceleration times on the order of decades.
This reduces the required power level of the drive, and may
have other practical benefits. In particular, there are no issues
with slanted artificial gravity. Assuming the starship uses
spin gravity, an acceleration or deceleration of 0.1m/s produces
a small slant.

Oh, sorry, I'm showing my ignorance now... Slanted gravity?

Imagine you're standing on a subway train. At the station,
perceived gravity is perpendicular to the floor. You're perfectly
balanced if you stand straight up. However, when the train is
accelerating or braking, you need to lean to stay balanced.

For a starship with spin gravity, the same basic principle will
apply. The starship's spinning axis is along the direction of
travel. Imagine it's a cylinder, with the central axis pointed
at the destination. The only difference is scale. Instead of
accelerating for just a few seconds, you're accelerating for
months or years on end.

The amount of slant depends on the degree of acceleration,
compared to the level of artificial gravity. For instance, with
an acceleration of 1m/s/s and an artificial gravity of 5m/s/s,
the slant is a quite significant 11 degrees. On the other
hand, with an acceleration of 0.1m/s/s and a gravity of
9.8m/s/s the slant is only 0.6 degrees.

It may be optimal to start off as
a bunch of small ships, but to "link up" into one
really big "ship" for most of the journey.

Hmm... Interesting. How would that work in practical terms? Would the
ships be able to easily link to transfer personnel since they
are stationary relative to each other? Would it be something
they would be likely to do casually or would it be a serious and
hazardous undertaking? (Hey, Flash Gordon would have jumped from
one 'wing' to the other!)

Perhaps "link up" gives the wrong connotation. Given the multi-
century
duration of the journey, it would be more like a large construction
project
where the raw materials are modular units. It's like the
International
Space Station. Instead of launching the whole bejesus all at once,
you launch many modules which are then linked together.

This depends on the cruise velocity. With a velocity
of .75c, about 750 years will have passed on Earth.
The starship will be around 550 light years from
Earth, so don't forget to add that time delay to
any communications.

Thanks Isaac, fantastic stuff. .75c is fine.

In practical terms how do I (roughly) estimate the time lag for
contacting Earth at various points on the journey.

Let's call the time of departure year 0, and the current year
is t (in Earth time).

Then the current position of the starship is .75t light years.
The time delay for a signal to reach Earth is .75t, so it
will arrive at Earth at 1.75t.

When the signal arrives at Earth at 1.75t, the starship's
new position is 1.75*.75t. An Earth reply will travel at
c, but the starship is running away at .75c. Therefore,
it's only reducing the distance by .25 light years each
year. So, the amount of time it takes for the signal
to reach the starship is 1.75*.75t/.25 = 5.25t.

The total signal time lag is .75t+5.25t = 6t.

Note that these calculations are all in Earth time.
Ship perceived time will be reduced from Earth time by
a factor of 2/3. Let's call SPT the Ship Perceived Time.

Then t = 1.5*SPT. The current position of the starship
is .75t = 1.5*.75*SPT = 1.125*SPT. The total signal time
lag is 6t = 6*1.5*SPT = 9*SPT.

So roughly, the time lag will be about a decade per
perceived year of travel.

This is assuming an instantaneous acceleration to full
speed, though. With an acceleration of 0.3m/s/s, it
would take decades to get up to .75c.

At any rate, the time lag is such that even before the
acceleration leg is complete, you're not going to be
hold conversations with the folks back home. Instead,
it will be a matter of receiving whatever transmissions
the other side feels like sending.

For this, the time lag is less important than the
distorted time rate. Consider what happens if one of
the regular transmissions is the daily news. You
won't receive one transmission per day. Instead,
the other side is receding at .75c and is time distorted
by a relativistic gamma of 1.5. The situation is actually
symmetrical. (This is REALLY counterintuitive and
demonstrates how weird relativity is.)

In Earth's reference frame, the starship generates
daily news at a rate of only once per 1.5 days.
Because the ship is receding at .75c, the starship
will be 1.5*.75 = 1.125 light days further away when
it generates tomorrow's daily news. Thus Earth
will receive tomorrow's daily news 1.5+1.125 =
2.625 days after today's daily news. In other words,
Earth receives transmissions slowed down by a
factor of 2.625.

Keeping Earth's reference frame, Earth generates
daily news at a rate of once per day. Because the
ship is receding at .75c, light is only catching up
by .25c. It takes 4 more days for tommorow's daily
news to reach the starship. However, ship perceived
time is only going at a rate of 2/3 real time. Thus,
the ship perceived time difference is only 2.667.
In other words, the starship receives transmissions
slowed down by a factor of 2.667.

In reality, those two factors will match exactly.
The reason they don't match here is because I
rounded relativistic gamma to 1.5 to simplify the
math.

My ships have lost contact with Earth many generations earlier. Messages
just stopped for no apparent reason. I need to work out some kind of
timeline

Even before the acceleration run is complete, the round trip
time lag will mean no one is having "conversations".
Instead, it will be a non-interactive form of communication
where both sides passively receive reports and digital
media content from the other.

From the perspective of the ship, they're receiving signals
from Earth as if Earth were slowed down by a factor of
2.667 (or, they seem to be going at 3/8 normal speed).

So, maybe Earth stopped transmitting for some reason
after 90 years. The starship wouldn't notice this until
240 years into the journey (give or take a few decades
for acceleration time).

At this point, the starship may send a question wondering
what happened. This is likely a symbolic act more than
anything else. The time lag would be 240*9 = 2160
years--much longer than the entire journey--if the starship
simply kept on cruising. What will actually happen is that
the starship will arrive at its destination and the total
time lag for a reply would be much lower.

How much lower? This depends on the exact range of
the destination from Earth.

But more plausibly, if anyone on Earth were listening,
they wouldn't be waiting around for the starship to ask
the question before sending the answer. So the people
of the starship know that sending a signal asking what
happened is a hopeless gesture.

When they get to where they are going they find a colony there because
FTL/wormhole technology has overtaken them (not a surprise) but the new
colony is already several generations past their promised supply ship,
abandoned.

Hmm...for such a long journey I think the only practical
method of sending supplies would be more or less
along with the main starship. Any supply ships would
be part of the main starship's convoy.

Hilarity ensues... Or something like that.

If I've got the relative times at the start and end of the journey, how
complicated is it to work out a timeline, Earth subjective time and ship
subjective time?

i.e. Gen ship leaves earth:
Earth Year 3000; Ship Year 0

Wormhole expedition departs from Earth
Earth year (say) 3550 ; Ship year WHEN?
How long for ship to receive message to say Wormhole expedition has
departed?

Gen ship sends last routine message to Earth
Earth year 3552 (Yes?)

What is the earth year at the point at which 'head office/mission
control' should be responding to the routine message?

Gen ship gives up on ever receiving a response from Earth again
Ship year WHEN?

Gen ship arrives at destination
Earth Year 3750; Ship year 500
And presuming they sent a message on arrival - how long for the message
to reach Earth and what Earth year would it arrive? (And how long
ship-time will they wait to see if a reply is coming.)

I really appreciate your help with this. Many thanks.

Hmm...considering the sort of storyline you're already worked out,
it's probably best to avoid relativistic speeds altogether. You'd
spend more time explaining the bizarre and unintuitive time
distortion effects of relativistic space travel and less time telling
the actual story.

The stereotypical generation ship is meant to only go a few
light years, but at very slow speeds. For example, you could
be mounting a mission to Alpha Centauri at a speed of
1%c, or 3,000km/s. This takes about 4.5 centuries. The big
problem with these slow generation ships is that they don't
seem to make any sense if you suspect a century or two
worth of advancing technology will allow you to go faster.

Isaac Kuo
.

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