How Fast Could a Saturn 5 Rocket Travel in Outer Space with FTL Mechanics?

[chasrob]

I'm writing an SF novel with FTL travel. In my story, there are different motion regimes, including superluminal, based on this https://www.researchgate.net/publication/333614143_A_GENERAL_LOCAL_CAUSALITY_PRINCIPLE_OF_SPACE-TIME_A_PREPRINT I found.

My story: in our (c1) regime, whatever velocity you can achieve via rockets, jets, magic, etc., divided by the speed of light, you can achieve in the c2 motion regime: which, according to the paper, has a speed of light that is 5 E 26 times c!

My question is: if you construct a Saturn 5 rocket in, say, orbit and lit the F1's and various stage engines from orbit, what velocity would you attain with a ~100 ton payload? Divided by c, I can use this ratio to determine the Saturn 5's top end if it were to (somehow) "transfer" to the c2 motion regime of the paper.
Thanks.

 

[Janus]

By a quick estimate, I get a delta v of ~29 km/sec for the three stages of a Saturn V and a 100 ton payload.

But this seems like a bit of overkill. For example, even 1 meter/sec "transfered" to the c2 region equates to ~1.667e18 c. And at that speed, you could cross the 2.5 million ly distance to Andromeda in under 5e-5 sec and the entire width of the observable universe in under 2 sec!

On another issue, if this velocity scale works for everything in this region, then it would effect everything.
Put a person in this realm and all his atoms and molecules that he is made from would suddenly be moving at some multiple of c relative to each other. This would rapidly lead to his dissolution.
Even if something kept him together, his physical processes would be running at some extreme high speed. Getting to Andromeda in a fraction of a sec doesn't mean much if you aged through your entire life in even less time.

 

[chasrob]

True, but if you're traveling at 29km/s divided by 300000km/s ~.0001 c , wouldn't time dilation be close to nil? If regime c2, speed of light = 5E26 our c, therefore .0001 its c would have little relativistic effects, yes?

 

[Janus]

True, but if you're traveling at 29km/s divided by 300000km/s ~.0001 c , wouldn't time dilation be close to nil? If regime c2, speed of light = 5E26 our c, therefore .0001 its c would have little relativistic effects, yes?

That's why I didn't factor any relativistic effects in. 0.0001c times 5e26 c equals 5e 21 c. 2.5 million ly * 365.25 days/yr * 24 hrs/day * 3600 sec/ hr = ~8e13 light seconds( ~2.4e22 meters) distance to Andromeda. 5e21 c is 1.5e30 meter/sec. It takes a small fraction of a sec to cover 3.4e22 meters at 1.5e30 m/s.
The rapid aging I mentioned was not due to Relativistic effects, But by multiplying the increased speed factor to all types of motions/reactions including those that determine metabolism rate.

 

[chasrob]

I see now, you're right, all types of motions would be affected.

 

[chasrob]

In my scenario--to be consistent--someone earthbound could jump up-- and end up in orbit, eh?
Ain't going to work.

 

[chasrob]

If I dropped the "velocity scale" idea but retained the "motion regimes" of the paper, and somehow managed the "discrete transition" from c1 to c2 (and vice versa), I calculate--if a starship could accelerate at 1 g--it could reach ~50c in 17-18 days. That would be a handy FTL velocity.
Or is my math wrong? Would the fuel percentages of payload be astronomical?

 

[Janus]

If I dropped the "velocity scale" idea but retained the "motion regimes" of the paper, and somehow managed the "discrete transition" from c1 to c2 (and vice versa), I calculate--if a starship could accelerate at 1 g--it could reach ~50c in 17-18 days. That would be a handy FTL velocity.
Or is my math wrong? Would the fuel percentages of payload be astronomical?

1 g is ~10m/s². 18 days at this acceleration give you a final speed of ~0.05c.
Now it you might mean that the same equivalent thrust that would result in 1g of acceleration would give you an acceleration that would get you up to 50 c in 18 days. However this would still equate to an acceleration of 9645 m/s² for the ship and anyone in it. Drop a coffee cup from a height of 1 meter and it will hit the deck in 0.0144 sec, moving at a speed of 139 m/s. Even if, in this regime the force of that impact was no more than normal, this high a fall speed would play havoc with the passengers. (walking is a "controlled topple", and if the speed of the topple exceeds the body ability to place the foot forward to "catch" it...)

 

[chasrob]

Drat the luck, the Windows calculator let me down (; . It's ~174 days of 1g acceleration. I suppose fuel requirements would make that a prodigious operation.

 

[Janus]

Drat the luck, the Windows calculator let me down (; . It's ~174 days of 1g acceleration. I suppose fuel requirements would make that a prodigious operation.

Assuming you could use strictly Newtonian physics, the energy needed to get 1kg up to 50c is 1.125e20 joules. It is interesting to compare this to the energy requirement to get 1kg up to the speed that results in a time dilation factor of 50, so by ship time, it takes the same time to make the same trip. It works out to 4.41e18 joules, 1/25 the energy.