Re: starship-design: FTL Navigation

[STAR1SHIP@aol.com]

n a message dated 8/24/01 7:54:25 AM Pacific Daylight Time, 
bfranchuk@jetnet.ab.ca writes:

STAR1SHIP@aol.com wrote:
>> 
>>    Part 1.1    Type: Plain Text (text/plain)
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I did not write the above nor know how it got there. What I wrote in response 
to you is included below under the dotted line. 

>1) I hate posts that you can read.

I hate all posts I cannot read myself and some I can read :-)


>2) While I did goof on the math, the whole point was to show that with >out
>si-fi's
>intertial dampers you spend a long time getting to near light speed.
Ben.

Ben,
At 1 g acceleration it takes only 355 days to reach light speed. Conventional 
constructed chemical rockets have the power to maintain that rate of 
acceleration for maybe 15 minutes at best.
355 days/15 minutes
355 times 24 hours times 60 minutes=511200 minutes
therefore:
511200 minutes/15 minutes gives a power ratio of 34,080 to one required to 
reach light speed.

Energy available per equal units of mass gives ratios of Atomic power VS 
Chemical power of 1,000,000 to one. This ratio has been measured in bombs and 
reactors so are expected in atomic rockets of good design. Therefore:
1,000,000/34,080 = 29.3 so
atomic rockets have the potential to propel mass to 29.3 C.  

----------------------------------------------------------
Noting your previous math error, I wrote

To calculate the time to accelerate at 1g to reach light speed.

I use "a" as 1 g = 9.8 meters /sec^2 and light at 2,998 times 10^8 m/s in the 
formula:

c=at        therefore 
t=c/a       and replacing parameters with given values
t= (2.998E8 m/sec)/(9.8 m/sec^2) inverting parenthesized denominator and 
multiplying gives
t=2.998E8 s^2 / 9.8 s  by simultaneously canceling the m in nominator and 
denominator
t=2.998E8 sec / 9.8    by canceling the s in the nominator and denominator
t=3.059E7 sec to reach c at 1 g.

One year in sec = 365.25 days x 24 hours x 60 minutes x 60 seconds or 
31557600 seconds: therefore;
 3.059E7/3.156E7 = .969 years
.969 years times 365.25 days =  353.93 days given some small rounding errors 
as the best measurements of 1 g and c give slightly more than 355 days to 
reach c velocity.

This calculation is valid for any mass falling in a free fall in hypothetical 
unbounded uniform gravitational field of 1 g or an actual object accelerating 
at one g.

Arguing if c or c + v for accelerating rockets is possible is counter 
productive when C + V relativistic calculations and effects are to be derived 
and the work to be discussed. It would be most productive if those that do 
not believe FTL possible join in a different discussion thread and leave this 
thread open to FTL believers so effects for navigation and practical c + v 
star travel can be calculated.

For instance:
There a formula that I don't have to derive myself to find time dilation for 
an accelerating object.

It is t'=d/v with v determined by a * t keeping in mind the frame of 
reference for the a value is wrt to the ship and not a stationary earth 
observer for the acceleration rate relative to the earth observer is always 
less.

I.E. acceleration observable and measurable measured from earth always gives 
sub c final velocities and acceleration measured and observed from the moving 
object can give real above c velocities. You can use the applet and equations 
provided below instead of deriving them yourself by knowing the applet and 
formula considering a rockets constant acceleration for 1/2 distance then 
deceleration at a constant 1 g the remaining distance to determine the ship 
time and from that you can derive the velocity wrt the ship. Note the 
velocity varies with the reference frame.

QUOTE-----------The Relativistic Rocket 
http://ucsu.colorado.edu/~obrian/applets/Rocket/Voyage.html
Applet implemented by Paul O'Brian for the Programming Languages class. This 
applet lets you plan how long a trip will take on a rocket that travels near 
the speed of light. You type the distance of the trip (measured in 
light-years) and the acceleration of the rocket (measured as a multiple of 
Earth's gravity). The rocket will accelerate at that rate for half of the 
trip, then decelerate at the same rate for the second half of the trip. 

The time for the trip is measured in two ways: (1) As seen by a person who 
stays behind on Earth, and (2) as measured by you on the ship. For your 
convenience, space-sickness pills are available aft of the observation 
lounge. The equations for the computations came from the Desy Web Site. Here 
is what I used: Calculate d as the distance of half the trip in meters.

(Note: There are about 9.47e15 meters per light year). Calculate a as the 
acceleration in meters/secē. (Note: The conversion is 9.81 times the 
acceleration measured in gravities.) Set c equal to the speed of light in 
meters/sec (which is 3.00e8). 

The total time on earth, measured in seconds is: 2 * sqrt( (d*d)/(c*c) + 
2*d/a )
The total time for the voyager, measured in seconds is: 2 * (c/a) * asinh(a 
*0.5 * time_earth / c) 

(Note: asinh is the inverse hyperbolic sin function, computed in Java with 
the formula Math.log(x+Math.sqrt(x*x+1)). The Relativistic Rocket Applet / 
Text by Michael Main, Applet code by PaulO'Brian / obrian at colorado.edu / 
Revised April 1999
 ----------END QUOTE

A sample trip inputting 4.25 light years distance given to nearest star at 1 
g acceleration half way then deceleration at 1 g 1/2 way arriving at rest 
near star.

Trip length: 4.25 light years.Acceleration: 1.0 g.
Time on earth: 5.8780560467144 years.
Time on ship: 3.544401860293398 years.
Bon Voyage!

Average Velocity(V)= distance traveled/time traveled.
Relativistic subscript:= rel.
Lorentz velocity: Vrel.=distance traveled/proper time;
Vrel.=D/T
Einstein Velocity: Vreal=distance traveled/ship time; 
Vreal=D/Trel
Note: Ship time is not considered improper time aboard ship.
Vrel.=4.25 light years / 5.878 years = .723 C
Vreal=4.25 light years / 3.544 years=1.20 C

Since a universal law of physics requires it be true that nowhere in the 
universe is a case found in violation of the law, the law is held to be, by 
virtue, a self evident truth.

Therefore in the above case is found a single C + V velocity and no Universal 
law forbidding C + V velocities or math proof of any limit to C velocity of 
objects of mass, can exist.

I rest my case by summarizing: Any claim other wise is held to be without 
virtue and clearly false and those making the claim are seen from this rest 
observer viewpoint as without virtue, truth or other redeeming 
qualities.Skeptics may now state their case beginning with:
Relativity FAQ
http://www.iastate.edu/~physics/sci.physics/faq/FTL.html#7


Tom