How far could a spaceship go if we never ran out of thrust? (2020)
forbes.com
forbes.com
Outside of RS, I also liked House of Sun a lot.
I guess I'm weird.
It was an allegory for the U.S. involvement in the war in Vietnam, in which Haldeman fought.
[spoilers]
Not quite. Humans develop (via cloning and other tech) to the point where they can finally communicate with the hive-mind aliens, and realise that the whole 1000-year war has essentially been a mistake from the outset.
> It was an allegory for the U.S. involvement in the war in Vietnam
Yes. The obvious allegory is that to the very few baseline humans who survive the entire war due to time dilation effects the whole thing was a complete waste of time.
A key subplot in the book is that humanity adopts homosexuality such that in the latter stages of the war, the baseline heterosexual veterans are perceived as weird sexual deviants. This seems to me allegory for the difficulty Vietnam vets had in readjusting to civilian life.
Perhaps it's also to give some perspective of what it can be like for gay people sometimes by providing an opposite world.
The main character is spacially and temporally separated from his love interest/comrade during the war. At the end, he receives a letter saying she's been in cryo sleep aboard a ship experiencing time dilation to wait for his return.
The drive is named posthumously after him based on the design notes found on his computer by his widow.
I think this is a slightly different phenomenon though. The problem with Epstein is rapid acceleration resulting in an increased gravitational force relative to the speed of acceleration well beyond 1g and continuing to accelerate faster until fuel is exhausted.
The scenario in the article is about indefinite acceleration. Indefinite acceleration doesn’t have to be fast to eventually reach near light speed provided enough time.
For a long enough trip, anything over 1G results in your passengers and payload having to deal with excess stresses, up to and including ship damage or passenger death. In the Expanse they are quick to point out the increased chance of stroke due to prolonged and excessive acceleration.
1G is nice because you can move like you would on the surface.
But Ray Porter's voice needs to be applied to many more books. I generally only stop reading audiobooks if I can't listen to the reader any longer
I think the core ideas in Bobiverse keep me hooked as I just enjoy them but I see your point and don’t begrudge anyone who gave up on it.
This is a totally random question but have you ever read the Honor Harrington series? They aren’t related at all (other than “sci-fi”) but I’m always interested in other series people have read and enjoyed (or not enjoyed) and Honorverse is one of my favorites.
I will say that this series is pretty technical (in that I talks about the speeds of things and how fast things are moving) which I greatly enjoy but I know isn’t everyone’s cup of tea.
i kind of hate audiobooks for this reason, my internal voice is just so much easier to listen to.
- All characters are two-dimensional. The further from the main protagonist, the more 2D.
- Dialogues go from wooden to cringe-worthy, with few exceptions.
- Protagonist swings from super over- cautious to careless and back.
- Alien with deus-ex-machina syndrome, always having the perfect tech, material or skill to fill in the lacks of the protagonist.
- Tired trope of amnesia to make the protagonist remember stuff progrssively for the reader.
- Extreme over-usage of flash-back, linked to previous point, but oh boy! Half the book is flashback. Waaay over-used story-telling tech.
The science, outside of the magic fuel and magic alien material is mostly correct. That's the main strong point of the book.If your rocket starts off 2/3rds fuel by mass, this will result in an average acceleration of 1g as the mass of the fuel is consumed.
The most efficient chemical rockets we have today have a specific impulse in the ~470 second range. The highest specific impulse thrusters of any sort that we have in wide use today are ‘ion thrusters’, which have specific impulses in the 50,000 second range (but can’t generate much thrust at all).
So 10-12 hours at 1g is about as much as we can do with existing hardware.
Thankfully! Imagine if systems/cultures commonly differed in fundamental measures of time, just as they sometimes do for volume, distance, weight, etc.
Ah, but now we're talking about "pounds of force", not 'pounds of mass': https://en.wikipedia.org/wiki/Pound_(force)
In mechanics, "impulse" is a word for a unit of momentum. Momentum has dimensions (Mass * Speed), or (force * time), and can be stated in units of Newton-seconds.
"Specific" impulse is simply Impulse per unit mass of fuel (i.e. Newton-seconds per kilogram). The convention of stating it in units of seconds is based on Earth gravity (Newtons per kilogram).
If a system has specific impulse of 100 seconds, 1 kilogram of fuel would be able to accelerate a mass of 1kg at an acceleration of 1 G, for 100 seconds.
Energy is a different thing, but related to specific impulse. In a perfectly efficient system (not what really happens), the decrease in stored energy within the fuel tanks would be equal to the increase in total kinetic energy (i.e. the sum of vehicle and exhaust kinetic energy).
In chemical propulsion, you have the energy in the propellants. There higher ISP is better.
In electric propulsion, you use an external power source. Usually your propellant or reaction mass is inert, like Xenon. There, if you up the specific impulse but keep acceleration and delta vee the same, your power source mass increases. At some point your power source mass is a lot bigger than your propellant mass. Hence, your total mass for the same misaion would be less with lower specific impulse.
So in electric propulsion there can be too high ISP for a given mission and power source technology.
P = 0.5 * mdot * v_ex^2
T = mdot * v_ex
A normal ion thruster might have ISP 4000 or 40 km/s exhaust velocity.From the rocket equation, if our mission requires 10 km/s delta vee, mass ratio is exp(10/40)=1.28. So out of every 1280 kg, 280 kg is propellant.
If we have mass flow of 0.1 gram per second, thrust is 40000 m/s * 0.0001 kg/s = 4 N and power is 80 kW. Acceleration is about 0.27 km/s per day. Not so good for humans through Van Allen belts. But fine for deep space propulsion.
80 kW of solar cells with 200 W/kg weight efficiency would weigh 400 kg. This is ISS level power.
So the spacecraft might have 280 kg of propellant, 400 kg of solar arrays, 600 kg of useful things.
[on edit: the weight efficiency of the solar panels will also depend on where you are in the solar system...]
So 9.8m/s2 times 36ks yields about 360km/s. Not bad. Altho only a thousandth of the speed of light :-(
Remember that when you are travelling to that galaxy 18 billion light years away, you’ll hit every photon it sent our way over 18 billion years in just about 45 years.
As a programmer, this gave me this warm feeling...
* momentum , impulse , force
Force would be negligible of course. But if you are in space, you are surrounded by energy in the form of starlight; it would be weird if that energy could not be used for work.
Whilst photons hit your ship from all direction the photons incoming from the direction of travel would be shifted towards higher frequencies so their momentum would be higher than the photons hitting the ship from the opposite direction so unless there is a sufficient difference in the number of photons hitting you from the back to compensate for it you would still not be able to extract energy to move.
This means that even say a solar sail has a limit on acceleration at a certain speed the photons hitting the front of the sail would be blue shifted enough to counteract the acceleration of photons hitting you from the back, even if you convert them to useful energy it wouldn’t matter since you’ll reach equilibrium.
Given 100% conversion rate you should getting energy via photovoltaic effect, so you use that to accelerate them.
> Whilst photons hit your ship from all direction the photons incoming from the direction of travel would be shifted towards higher frequencies so their momentum would be higher than the photons hitting the ship from the opposite direction so unless there is a sufficient difference in the number of photons hitting you from the back to compensate for it you would still not be able to extract energy to move.
But that's just "friction". Assuming a photonically uniform environment at rest, just buffer energy at rest, accelerate for a bit, goto 10. Eventually you'll get anywhere.
(Assuming a non-uniform environment, you're probably close to a star, in which case gravity outweighs photon pressure anyway.)
What photons do have is momentum, and so due to conservation of momentum, hitting a photon will slow you down.
Relative velocity is a hell of a drug.
It turns out that there is a rest frame in which this background looks the same in all directions. But if you keep accelerating in one direction, the CMB coming from there will keep blueshifting: from microwave to IR, to visible, and eventually hard gamma radiation.
I was really surprised when I heard this for the first time a while ago. Because it means that our universe does have a _preferred_ frame.
Relativity means that there are no special frames where the laws of physics are different.
Good read where you'll also learn about the "The Surface of Last Screaming":
https://ned.ipac.caltech.edu/level5/March03/Lineweaver/Linew...
https://en.wikipedia.org/wiki/Pseudosphere
If you mean object with finite dimensions and negative curvature and no center, there seems to be such a thing, see Fig. n066200e:
https://encyclopediaofmath.org/wiki/Negative_curvature,_surf...
EDIT
Rozendorn's idea seems to be still an open question:
https://mathoverflow.net/questions/52851/the-geometry-of-nad...
- Maneuver, like a sailboat.
- Decelerate. Shut off your thrust and dump the light-absorbing covers to reveal mirrors, for 2x the deceleration. Photobraking?
If we will ever have the technology to instead create proper massive particles at scale you could eject those in orbit around some other massive object and then re-steal their angular momentum to accelerate yourself. But that I believe would be an extremely lossy process so you would lose most of the energy.
now, the question of how to design an actual working solution? i don't know; and basically, it depends. you would then also have the problem of whether it was possible to implememnt that solution, using real matter and physical objects...
unfortunately, that was probably the question you really wanted answered, right?
- all those photons are blue-shifted and becomes hard gamma rays.
- once you get close enough from c, all the stars in the universe appear to be either right in front of you, or right behind you, which means you get hit not only by gamma photons coming from the galaxy you're aiming at, but gamma photons coming from half the universe!
I don't understand that one, could you please expand on how it works ?
If you move fast enough, all of the ultraviolet light coming from behind you becomes visible light. A little faster and all of the ultraviolet light in front of you becomes X-rays. And all of the hard x-rays become gamma rays.
At some point the warp drive might be cheaper than the shielding.
once you get close enough from c, all the stars in the universe appear to be either right in front of you, or right behind you
That's not really right. There is a distortion where things appear more in front of you than they are at the time you see them, but that's only because they were at that angle, but by the time the light gets to you they're not where they appear.Also there's nothing that would shift light to appear behind you other than your movement away from objects that you have passed.
1) Uniquely (to my knowledge for starships in hard-ish scifi) they're are 'aerodynamically' shaped, or at least long and pointy to minimize friction with interstellar mass.
2) Their front surfaces are covered in a thick layer of water ice which acts as an ablative shield against said mass and radiation.
3) The fact that they can accelerate at over 1G means that they can land tail-first on an Earth-type planet.
Scott Manly did a Youtube episode on all sorts of weird propulsion mechanisms that people have come up with over the years a few months ago: https://www.youtube.com/watch?v=QEZv_OXA_NI. There are some interesting concepts in there. Including the anti matter based concept discussed in the article. Particularly fusion looks like it might get us some interesting amounts of delta v.
Just read the book and can highly recommend it. One of the good thing about it is that the main protagonists are nice, curious and friendly. No backstabbing, suprise turns of evilness to create suspense. A pleasant read.
I don’t want to watch movies or read books where people are just awful to other people, I can open the newspaper on any given day to find that.
Can I recommend then Becky Chamber's Wayfarer Series (4 books). What a refreshing change.
I am 1000% with you on this. The success of The Sopranos, Breaking Bad, and Game of Thrones are mystifying to me. I get enough misery and awfulness from the news.
It's funny because even though the book was so loved because it was so rational, and human's actually acted how humans would act in that situation, Hollywood STILL couldn't resist making tweaking the end slightly to make it over the top and impractical. Thus we ended up with Mark Watney flying around like Iron man in space with a hole is his space suit.
Still a great movie though. But a better book.
The chapter where he deduces where he's from based on what units he uses when he thinks about distance is incredible.
I also really liked how he dialed in: - Okay, so I use X unit when I thing of A, and Y Unit when I think of B.... But what kind of person am I that I know those values off the top of my head?
What a brilliant book.
I meant that writing a believable normal person is hard. Most people are normal.
But writing a smart person is hard, because you often just have to have them solve problems faster/remember more/have information that the reader doesn't.
Project Hail Mary did a wonderful job of showing that a smart person doesn't necessarily think "The same, but faster", but that they think differently and deliberately
Spoiler alert, kind of.
Which one do you mean? I didn't like Artemis that much.
What happens if I just keep going?
But “not getting to anything past the furthest thing we can see from earth today” seems fundamentally incompatible with the idea of reaching those farthest points in a reasonably bounded timeframe. There is stuff beyond the limits we can see, it’s just further than light has had a chance to travel so far (and may ever travel).
My intuition is that as you approached those far objects, you’d observe them rapidly evolving forward in time until they reached their “present day” situation, able to see billions in light years in all directions with Earth right at the edge.
But then what happens when you look at Earth? Surely you don’t see it’s billions of years old past. You’d have to see it at least as old as it was when you left. But something doesn’t seem quite right about that to me. Surely I’m missing something.
If you go far enough, stuff moves fast enough away from us than the speed of light. Thus, some places can't be reached from someone starting at our present location, ever, even though we might still see their light. That light is closer to us than the object that sent it out.
Things without mass, instead, can only travel at the speed of light (photons for instance).
Finally, there is a quirk in the math that would allow for the appearance of faster than light travel. If you compress the spacetime in front of you and expand it behind you you could can move faster than light without turning into a black hole or needing infinite energy (Google Alcubierre drive for more information). It is only an appearance than faster than light travel because you would still move at sub-luminal speed in your bubble of "normal" space time, but the compression/expansion effect would drag you through space-time at faster than light speed. This, however, require so called "exotic matter", ie matter with negative energy density (this is not anti-matter, but matter that has a repulsive gravitational field) and it is probably only a quirk of the math and nothing more.
You are quite right that no matter nor energy nor information is traveling faster than light here.
That way, there really isnt a point that is traveling or moving, its just our perception mistaking it for a point because it looks and move like one.
The thing is that lots of our 'concrete' real world objects have more in common with the later pointer point than with physical reality. Concreteness is a bit of an illusion, it's all wave functions at the bottom.
(Of course, real world objects still can't go faster than light.)
We are able to see gravitational waves at this point. Where is a gravitational turbulence, created by the massive expansion?
(Non-native speaker, but you got the idea).
If you can get there in 45y, that doesn’t mean 45y has passed at that location. In fact if it’s 18bnly away, that means you’d arrive in 18bn years from their perspective. And not 18bn years from what you saw when you left, but 18bn years from when they saw you leave. By that time, space will have expanded enough that it’s no longer possible to see past.
Though perhaps the amount of energy it would take to accelerate that much exceeds the available energy in the universe? So maybe that's what balances it.
So you're still as far away from your destination as in the beginning (or even further), but now you're the same distance from your starting position as well and are effectively stranded.
I don't know whether you observe this or not.
But if the expansion of space is accelerating (which we believe currently), this is not true. There really would be destinations that are unreachable.
You would continue to travel further from your origin, but also witness your destination accelerate away.
A constant lab frame acceleration is incompatible with special relativity.
We're at turn 0, at point A. Point B is 600.000.000 distance-units apart. We have infinite! acceleration and accelerate to 300.000.000 units/turn, and start our travel to point B. We move 300.000.000 units. Distances double. We're at turn 1. Point A is now 600.000.000 units behind us, and point B is still 600.000.000 units ahead of us. We travel 300.000.000 units! Distances double. We're at turn 2. Point A is now 1.800.000.000 units behind us, and point B is still 600.000.000 ahead of us. We're starting to wonder if we should have stayed at point A... hopefully there is a point C that was between point A and point B that we can still get to, because we don't seem to be making much progress.
The universe is a bit like that, except that it looks more continuous, it has some more dimensions, and it's not doubling quite so quickly.
First, like any other gravitational effect, locally, spatial expansion would manifest as pseudo-forces that can be counter-acted by all the other forces that are far more relevant at human scale.
Second, the local effect of spatial expansion should be an indirect one: Friedmann cosmology - which is how we describe an isotropic, expanding universe - is a large-scale approximation. More realistic would be 'swiss-cheese' models, where spacetime in our neighbourhood can look vastly different from the Friedmann one, except that the spacetime patches need to properly fit together to yield the correct large-scale behaviour.
Point is, illustrative models and analogies are limited. Ideas like 'space itself expanding' or 'space flowing like a river and falling into a black hole like a waterfall' might help visualize some things, but can also lead to wrong ideas if taken too seriously.
Oh hmm, I see.
> but can also lead to wrong ideas if taken too seriously.
Yeah, and it's hard to know how far to take the analogy unless you're already familiar with the concept it's trying to describe, unfortunately.
If expansion never stops accelerating, one day in the far future it will overcome all the other fundamental forces and everything will be torn apart in a Big Rip.
If you could drastically increase the mass of the local group, then you could increase the range at which gravitational attraction to it was dominating, but it would require seriously increasing the mass of the local group.
i'm not sure i get it. as i understood it, it was the fact that forces over a small scale dominate the effects of space expanding that prevents e.g. atoms getting bigger. so why would my space-railway tracks (made of continuous welded steel space-rails) not stay the same size (2m wide by thousands of light years long) as well?
The space expansion effect is very weak at small scales, so it's easily overcome by small objects, such as a short rope (or a railway). But this small force acts on the entire object, so when the object is twice as long, it pulls twice as hard. When distances become extreme, it always wins. Imagine a railway where the the far ends are moving apart from one another faster than the speed of light. It's either an infinitely stretchy railway, or it's breaking (probably long before we got to this point).
edit: also, thanks for the explanations - i think i need to learn more and/or head to physicsoverflow ;)
At the risk of adding yet another analogy. Imagine we have built an enormous balloon the size of a small moon. You and I are put on the balloon with our two vehicle and a steel winch. If they continue to blow up the balloon, things will get farther apart, but it isn’t going to tear the front times from the ear tires, and if we put the cars 1 meter apart, and connected the steel winch cable, it wouldn’t be an issue. At 1 meter, the balloon is expanding by a centimeter an hour. But if you drove 150 kilometers away from me, with the cable connected, and we tried to hold them together at the same distance, the balloon is moving at 25 meters per minute. To each of us, things would look and feel normal, but the pressure on the cable would snap it immediately. If you then decided to keep driving, there would be a point where you could never drive back to me because the distance between us as the balloon was expanding, would be more than the top speed of your car.
The graphic novel version is great too, if you can find a copy:
The first three that come to mind are: Heinlein's "Time for the Stars", Haldeman's "The Forever War", and Anderson's "Tau Zero".
From those titles, a DDG search finds http://sf-encyclopedia.com/entry/relativity listing more, also containing the line "Very many sf stories use relativistic time dilation for one-way Time Travel into the future."
Star Trek's "Space Seed" - 200 years in sublight stasis, no mention of speed or distance. Could be 0.5c for all we know. 100 ly at Enterprise's warp 6 cruising speed would take about 4 months, which seems not unreasonable.
The movie "Alien" - stasis, but seemingly with FTL given the times and distances involved. (https://avp.fandom.com/wiki/LV-223 says it was a 2 year voyage to the moon LV-223 in Prometheus.)
The TV series "Red Dwarf" - sublight, though it did break the light barrier once. Science in general is only relevant for comedic effect. https://www.ganymede.tv/2004/04/the-science-of-red-dwarf/ .
None of these seem to be characterized as "it takes you 150 years of travel at light speed to get to a place that is 150 light years away".
Which one am I missing?
It doesn't say if that's 120 ship years or Earth years. I'll assume ship years as that makes the most sense in context.
Assuming constant acceleration to the 1/2-way point, flip, deceleration, and using http://www.projectrho.com/public_html/rocket/slowerlight3.ph... :
T = (c/a) * ArcCosh[a*d/(c^2) + 1] (given acceleration and distance)
60 years = (c / a) * arccos(a * 30 ly / (c^2) + 1)
1893456000.0 = (3E8/a) * arccos(a * 3.15576 + 1)
Using Wolfram Alpha to solve - https://www.wolframalpha.com/input/?i=1893456000.0+%3D+%283E... a = 0.14748 m/s^2 or about 1.5% g
Time elapsed on Earth is only a bit longer than ship time: t = (c/a) * Sinh[a*T/c] = 1.15 * ship time ("proper time")
Final velocity at flip is: v = c * Tanh[a*T/c] = 0.73 * speed of lightI created a list of all these works I could find a few years ago. Here is one link:
https://tvtropes.org/pmwiki/discussion.php?id=l6q90mvssgscsj...
I think this is a complete list of the films and tv series:
- The Star Lost
- Pandorum
- Passengers (2016)Indeed, while I remembered the importance of time dialation in Forever War , I didn't remember the FTL travel between collapsars.
Most of Alastair Reynold's novels have FTL - I only know of one that counts, which is Pushing Ice.
The 3-body problem has FTL also.
The chronologically earlier novels in his Known Space universe (the Ringworld one) are mostly around near-c Bussard ramjets.
> Most of Alastair Reynold's novels have FTL
Hmm, wait, which ones? Only one I can think of is House of Suns, in a very restricted manner.
> The 3-body problem has FTL also.
It has FTL communications, but not travel.
For [science] read [magic], more or less, but yeah. In the very first stories they were Bussard ramjets, but this got retconned out (and a Bussard ramjet actually shows up in a later book as a failed experiment). In most of the books they're more or less applied magic, though.
This, incidentally, seems to be a common theme, as later discoveries tended to fall down on the side of Bussard ramjets not working (due to insufficient density etc). The last of Niven's Known Space books have some special pleading for how the pilot has to carefully direct the ramjet to get sufficient combustion volume, a detail that was never present in the old ones.
This omission makes it easy for the writers to introduce relativity as a nerdy plot point. For example, StarGate: Atlantis had an episode with a ship traveling absurdly close to the speed of light, which was devised as a convenient way to introduce characters that should've been dead for many thousands of years.
Or maybe they know you wouldn't travel at light speed in the first place.
I just discovered Andymon.
A 1982 sci-fi novel, where a interstellar spaceship reaches the destination star, after travelling a very long, but unknown time (part of the plot).
I do not want to spoiler too much, but it was written by a academic physics/philosopher and his wife a mathematician. Deep shit. Should be standard read in schools.
And ofcourse the small issue of sex being 80% of what's on their mind. Perfectly natural and healthy.
A fascinating thought. The ship and crew would surely be long forgotten. You may be greeted as an alien visitor, until the people of that time recognize your relatively ancient technology from fragments of historical records. Too bad you speak a language nobody else even remembers.
Or perhaps you emerge as gods on a pillar of fire from the sky, witnessed by the primitive-again survivors of whatever has played out since you left.
I'm strangely tempted. If you offer me a ticket on such a ship, I might just come along.
That is perfectly reasonable! But I hope you can appreciate that the imagined feeling/thought is not shared by everyone.
With today's technology, yes.
And as others pointed out, life on a new continent wasn't all roses, either.
This is also a very eurocentric point of view that ignores that people were already living in the Americas. What happened in 1492 was not grand explorers finding undiscovered country in the star trek sense. It was conquerers finding a new land they were ignorant of rich with resources they could take by force via superior military power.
I ask myself the same question whenever I leave my city.
I guess I'm not really a traveller person.
There was a paper considering making a shield against it, either lead, or electric field, or magnetic field, and resources required for it.
As you approach 'c' time dilation shrinks time for you. Keep accelerating and eventually a million years outside your reference frame is mere days or hours inside the spacecraft. You could travel to the Andromeda galaxy or beyond as long as you were okay never returning to Earth or returning to a different geological epoch than the one you left. Go far enough and the sun might be in its red giant phase when you get back. You may have aged a few years or decades.
This of course requires stupid amounts of energy and theoretical near maximum specific impulse, what I once heard called a "physicists' nightmare propulsion system." Something like a "photon rocket" or a relativistic velocity ion drive (propellant exit velocity near 'c') plus a very efficient fusion or antimatter reactor might be able to get you there. It was called a physicists' nightmare because if containment fails you become a flash of gamma rays in less than a nanosecond.
One of my favorite wild speculations is that hypervelocity massive particles like the "OMG particle" are the jet wash from someone's engine.
> If it weren’t for Einstein’s relativity, you might think that, with each second that passes by, you’d simply increase your speed by another 9.8 m/s. If you started off at rest, it would only take you a little less than a year — about 354 days — to reach the speed of light: 299,792,458 m/s. Of course, that’s a physical impossibility, as no massive object can ever reach, much less exceed, the speed of light.
> The way this would play out, in practice, is that your speed would increase by 9.8 m/s with each second that goes by, at least, initially.
From the point of view of an external observer, this seems clear enough: the ship's acceleration would reduce, at first gradually, then ever more sharply as its velocity approached c.
But what about from the point of view of the ship's crew? Would they also measure a drop in acceleration -- e.g., would they weigh less?
Or would it be that they would measure the same acceleration, but the final picosecond (according to their clock), which would without relativity push their velocity to and past c, instead stretches out infinitely, thanks to ever-increasing time dilatation?
So the practical answer to what the crew would experience on the 355th day of 1G acceleration is: “That’s impossible.” The energy requirements approach infinity, and so does the speed of time for the rest of the universe they’d see out their window.
When they look out the windows, they will see odd things with respect to the apparent speed of other visible objects (including they never get farther/closer at a rate faster than C). But there's nothing theoretical that prevents you from continuing to accelerate at 1G forever.
Edit: I guess what I don't like about your description is that you mix reference frames. A spaceship can maintain 9.8m/s^2 (from its perspective) infinitely with constant energy expenditure. Energy expenditure rises asymptotically only if you require constant acceleration of the spaceship from Earth's perspective. But that's a peculiar way of framing it.
You could draw up a table mapping shipboard times to Earth times: the length of time passing on Earth between each onboard second/millisecond/microsecond etc. would get longer and longer, with the final moment at which the ship achieves c never actually arriving.
ETA: basically what @ninkendo said (but they said it better, and first).
There’s all the interesting idea of just accelerating forever, till the end of the universe (which comes faster than you think if you’re going that fast).
What happens if say we double the thrust, presumably halving the timescales and doubling the experienced "gravity"... would a human body be able to adapt and get stronger? or would we experience adverse side effects? (not necessarily mutually exclusive). It could even be a way to acclimatise to a different planet's mass before arriving.
[EDIT]
Looks like 2g is reasonable. The limit is higher but it sounds a bit ridiculous, astronauts would all have to compete in the strongman competitions for 4g. Any higher and we wouldn't be able to walk without breaking our bones.
https://www.discovermagazine.com/the-sciences/whats-the-maxi...
https://www.reddit.com/r/startrek/comments/3aajfy/how_much_h...
but also, what about deceleration?
You gotta stop some time to smell the roses... so would you cut that acceleration time in half to decelerate?
I was wondering, what if there was a spaceship circling outside the solar system at near light speed (not dwelving into whether it is possible ever to design such a ship or what the centigular forces inside would be), if there were people on such ship, that would experience 27,000 years in 20 years, would it be possible to communicate with them given the close proximity? Wouldn't it be weird that they are experiencing time in a much different way?
Heck, even with a rocket that is simply moving away from Earth, the messages that are sent should eventually reach the ship? (because it's not travelling faster than light, and at times it's even slower) How can the ship receive 27,000 years worth of messages in 20 years?
Clarke explores the idea that in a future where fusion reactors can be built, a spacecraft can have a fusion-powered motor for which the fuel is simply water. In the book, a spacecraft travels from Earth (or maybe Mars, it's been a while since I read it) to Jupiter, and does it the "brute force" way by simply pointing at Jupiter and thrusting at 1G until they are half way there, and then turning around and slowing down at 1G until they arrive.
This has the bonus side effect of allowing the spacecraft to have normal gravity inside it.
This is actually pretty obvious when you look at a launch and how slowly it accelerates.
What when someone else in a few hundred earth years invents the 1.1g rocket to go mine those same space diamonds? They will arrive millions of (local) years before you. By the time you arrive, the space diamonds will be all mined and you'll be seen as a cave man.
That reason alone means it's never worth departing on a long journey, because someone else always has an incentive to overtake you and get there millions of years sooner.
I think the reason to leave will have to be something other than space-diamonds, or other monetary needs. More like planetary conquest and scientific advancement.
[For one light take on this, the original Marvel "Guardians of the Galaxy" (the year 3000 versions) have Vance Astro, Major Victory, go on a 1000 year journey to Alpha Centauri, only to find other humans got there centuries earlier and were waiting for his arrival]
You sacrifice 30 years to see what someone potentially achieved within 1 million years. I'm sure there would be people willing to do that.
Let's say I'm an uber billionaire (trillionaire in the future), aged 45, I might think that I have tried already everything there's to try on earth and want to see the future. I would build a ship with more than enough entertainment for following 30 years and invite bunch of other people and just start with the journey.
Maybe I could even leave some money behind for other groups to keep building better solutions that would reach the destination much sooner so they can already start building out the destination and have millions of years of time to do that before I reach there.
It would be an enormous risk of course, but it could also pay off very well if for example you still own a large proportion of the business you leave behind to build the following spaceships and if it ever should reach the destination was still legally upholding the ownership you have. In fact in this case you could be magnitudes more richer in the new location when you arrive as compared to when you left 30 years ago in your time.
Or if something like cryogenic freeze is possible, you could also do that for some of the years if you ever got bored in the ship.
No they won't – in the frame of reference of the galaxy, both you and your pursuer will spend most of the journey traveling at very close to the speed of light. The difference won't be enough to catch up.
Put another way, in the frame of reference of the galaxy, you get to Andromeda (2.5 million light-years away) only about two years later than light would. Your pursuer, traveling at 1.1 g, would get there about a year and 9 months after light. So anyone chasing you would have to take off within about three months – and after a year, nothing could catch you.
This arrival time delay relative to light is pretty much constant (for fixed g) for any distance over about 1000 light years. For this reason, sci-fi authors who want ships to be overtaken by later models either slow the old ships down to much less than light-speed (i.e. generation ships) or introduce FTL travel.
versus
"I am a Ph.D. astrophysicist"
I'm confused.
In other words: How is he planning to catch up to a photon?
* The whole space between start and destination, of course