Risottia
19-03-2007, 19:34
A candy for SW fans.
Albert Einstein says that the Millennium Falcon kicks ass!
I'll explain.
In "the Empire strikes back", the Millennium Falcon travels between two different systems (Hoth and Bespin) without using the hyperdrive.
Meanwhile Luke goes in hyperdrive from Hoth to Dagobah, stay there with Yoda and is trained by him, then goes in hyperdrive to Bespin - this must have taken some time: let's say at the very least 1 year, but no more than 5 years. The "min 1 year" is because Vader later says Luke "Obi-Wan has trained you well" (or something like that, what the hell, it's Vader complimenting someone's training!), and the "max 5 years" is because Luke looks quite the same age when he departs Dagobah. I'll choose 1 year, so I'll minimise the tentavite evaluation of the Falcon's speed.
The Millennium Falcon is a small craft, and it departed Hoth in a hurry, while still under repair - that's why the hyperdrive isn't functioning. Let's say its food supply is able to support Han, Leia and Chewie for 30 days. Looks reasonable.
Now, let's assume that Hoth and Bespin are CLOSE. VERY close. EXTREMELY close. 1 lightyear. To give you a rule of thumb, the distance between the Sun and Proxima Centauri is about 4 lightyears. 1 lightyear is incredibilly close for two different systems, expecially in the Outer Rim of the SW galaxy. Anyway, let's assume just 1 lightyear.
Ok, now Albert Einstein kicks in.
Let's call S1 a inertial system placed on Dagobah, with t1 its local time (the time lived by Luke). Let x1 be the distance between Hoth and Bespin in this inertial system. v1 is the speed of the Falcon in the S1 system (we can assume it as "fixed", when compared to the Falcon's accelerations).
Let's call S2 the inertial system that moves with the Falcon. t2 is its local time.
c, of course, will be lightspeed in vacuum.
Uncle Albert's special relativity tells us that t2 = (t1 - x1 * v /(c ^2))/((1 - (v1 ^2)/(c ^2))^(1/2)) .
(I'll be using the international system, no Gauss or imperial units.)
Now we know that: t1=1 year=365*86400 s=3.1536*10^7 s . t2=1 month=30*86400 s=2.592*10^6 s
x1=1 lightyear=c*t1=9.45425*10^15 m . c=2.997925*10^8 m/s .
By solving the above formula for v (I'm so old-fashioned that I used Derive), and by substituting our data, we find that the Falcon traveled at 2.95769*10^8 m/s (in respect to the Dagobah inertial system). That is, 0.98658 c . More than 98/100 of the lightspeed in vacuum!
Sorry for the ST ships: they're are credited by their own fans as max 0.75 c with their famed sublight impulse drives. I'd say that SW ion engines are quite faster .
And I've supposed just 1 lightyear between Hoth and Bespin... had I supposed, let's say, 20 lightyears (about two times the distance between the Sun and Sirius, that's not a lot), we'd have the Falcon going FTL on its sublight drives. WOW!
My, what a nerd I am.
Albert Einstein says that the Millennium Falcon kicks ass!
I'll explain.
In "the Empire strikes back", the Millennium Falcon travels between two different systems (Hoth and Bespin) without using the hyperdrive.
Meanwhile Luke goes in hyperdrive from Hoth to Dagobah, stay there with Yoda and is trained by him, then goes in hyperdrive to Bespin - this must have taken some time: let's say at the very least 1 year, but no more than 5 years. The "min 1 year" is because Vader later says Luke "Obi-Wan has trained you well" (or something like that, what the hell, it's Vader complimenting someone's training!), and the "max 5 years" is because Luke looks quite the same age when he departs Dagobah. I'll choose 1 year, so I'll minimise the tentavite evaluation of the Falcon's speed.
The Millennium Falcon is a small craft, and it departed Hoth in a hurry, while still under repair - that's why the hyperdrive isn't functioning. Let's say its food supply is able to support Han, Leia and Chewie for 30 days. Looks reasonable.
Now, let's assume that Hoth and Bespin are CLOSE. VERY close. EXTREMELY close. 1 lightyear. To give you a rule of thumb, the distance between the Sun and Proxima Centauri is about 4 lightyears. 1 lightyear is incredibilly close for two different systems, expecially in the Outer Rim of the SW galaxy. Anyway, let's assume just 1 lightyear.
Ok, now Albert Einstein kicks in.
Let's call S1 a inertial system placed on Dagobah, with t1 its local time (the time lived by Luke). Let x1 be the distance between Hoth and Bespin in this inertial system. v1 is the speed of the Falcon in the S1 system (we can assume it as "fixed", when compared to the Falcon's accelerations).
Let's call S2 the inertial system that moves with the Falcon. t2 is its local time.
c, of course, will be lightspeed in vacuum.
Uncle Albert's special relativity tells us that t2 = (t1 - x1 * v /(c ^2))/((1 - (v1 ^2)/(c ^2))^(1/2)) .
(I'll be using the international system, no Gauss or imperial units.)
Now we know that: t1=1 year=365*86400 s=3.1536*10^7 s . t2=1 month=30*86400 s=2.592*10^6 s
x1=1 lightyear=c*t1=9.45425*10^15 m . c=2.997925*10^8 m/s .
By solving the above formula for v (I'm so old-fashioned that I used Derive), and by substituting our data, we find that the Falcon traveled at 2.95769*10^8 m/s (in respect to the Dagobah inertial system). That is, 0.98658 c . More than 98/100 of the lightspeed in vacuum!
Sorry for the ST ships: they're are credited by their own fans as max 0.75 c with their famed sublight impulse drives. I'd say that SW ion engines are quite faster .
And I've supposed just 1 lightyear between Hoth and Bespin... had I supposed, let's say, 20 lightyears (about two times the distance between the Sun and Sirius, that's not a lot), we'd have the Falcon going FTL on its sublight drives. WOW!
My, what a nerd I am.