11 ms·
I got into the Wait Calculation[1] a few weeks back and made a Jupyter notebook out of it. At our current max speed (692,000 km/hr, stated max speed of Parker
by tunesmith 7y ago
I got into the Wait Calculation[1] a few weeks back and made a Jupyter notebook out of it.
At our current max speed (692,000 km/hr, stated max speed of Parker Space Probe), it would take about 173,000 years to get to that planet.
We could instead choose to Wait and grow our tech. By picking a constant annual growth rate and then doing some calculus to find the minimum, we can calculate the shortest possible time it will take for us to arrive there.
One common recommendation for annual energy growth rate is 1.4%, and then taking the square root to get velocity growth rate since velocity has a square root relationship with energy.
By plugging that in, we can minimize our time by growing for 1020 years, and then traveling for 144 years, for a total time-from-now at 1164 years.
Another paper[2] estimated an annual velocity growth rate of 4.72%, quite a bit faster. Plugging that in, it says we should wait 195 years for a travel time of about 21 years, or 216 years overall. This is of course incorrect since it assumes being able to travel FTL. So if you instead look at how long it would take to get to light speed travel at that rate, you're looking about about 159 years, or arriving at the planet at a time-from-now of about 270 years.
Of course, if you're seeking to minimize time-from-now from the perspective of a traveler, maybe you'd take off sooner. Kind of a tradeoff - less time to wait for the traveler, more time to wait for the home planet. I haven't figured out that part of the math yet.
[1] https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Wait_Calculation.html https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1m...
[2] https://arxiv.org/abs/1705.01481 https://arxiv.org/abs/1705.01481
- Simon_says 7y ago> taking the square root to get velocity growth rate This is your mistake. It's an approximation that works well only at low speeds.
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- dylan604 7y agodoes this take into consideration that you would need to start slowing down halfway there?
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- rackad 7y agoWhy do you say that? Why 10x speed of light?
- healsjnr1 7y agoIt wouldn't need to be halfway. At 3gs acceleration, it would take about 115 days to accelerate up to the speed of light. You'd then travel ballistically for the majority of the journey before having to decelerate for another 115 days. Given the total journey would be ~40,000 days the 230 days of acceleration probably isn't going to impact things too much. Even if you brought it back to 1g acceleration, it's still only around 700days out of 40,000.
- neals 7y agoI just read somewhere in this thread that 'ship-time' at the speed up time is zero. So that would mean 230 consecutive days of acceleration.
- tunesmith 7y agoNo, it assumes you start and end at whatever that maximum velocity is that we've been able to achieve. That'd be fun to add, though. I'm not really sure what human-safe acceleration is - people here assume it's in the 1g-3g range. (That seems like a lot to me though, particularly for a long period of time - I think anything more than a fraction of g would be wildly uncomfortable.)
- quickthrower2 7y agoWouldn't 1g be perfect? I've been enjoying it for a few years now on this planet.
- narrator 7y agoProgress in physics was much faster in the early 20th century when it wasn't so fascinated with deep space. Yes, you needed to observe eclipses to verify relativity, but that was a tool, not the end in itself. Cosmology involves distances that are so great that it seems like it's pouring a whole bunch of smart people's efforts down the drain in an ultimately futile waste of brain power that will never amount to anything much at all. Besides, when we get faster than light travel we can just pick up exoplanet research where we left off and it will actually be practical and probably far more efficient with the computers and such we will have developed by then.
- vermilingua 7y ago> when we get faster than light travel FTL requires numerous things to be true about our universe, that all signs say are not.
- glup 7y ago...crushing all my dreams of being a starship captain, thanks.
- ddingus 7y agoI am reading big space operas right now. What we know of this reality is so limiting compared to what we can imagine. Good dreams. Many of us have them. I also like to dream the knowable remains much larger than the currently understood too.
- temporalparts 7y agoDoes this take into consideration that your mass increases as you travel closer to the speed of light?
- tunesmith 7y agoNo, I'm not sure what that would suggest - how would that need to be accounted for? Maybe some fraction of light speed would need to be the upper bound, low enough that mass increase wouldn't have a material impact? I'm having trouble understanding what impact the mass increase would have in the first place.
- temporalparts 7y agoIt's a cool project! Just as others say, once you get to a notable fraction of the speed of light, you need to account for relativity.
- skrebbel 7y agoAs a startup founder, I learned the hard way to not assume progress will ever be exponential.
- blencdr 7y agoAs a guy who lives in a finite world where energy comes mainly from fossil fue in a way or another, I do not assume that any constant progress in energy supply is something achievable.
- tachyonbeam 7y agoNo, and traveling near lightspeed is likely hardly possible. However, fusion will likely become a reality within our lifetimes, and if we can build fusion powered spaceships, we could likely reach a fraction of the speed of light, say, 0.2c. I don't think it's that crazy to think we could do that a few centuries from now. That still means it would take over 1000 years to reach that planet. Personally, I think that if humanity progresses that far technologically, without destroying itself, we probably won't care that much about habitable planets or planets with water. We'll just live in space and harvest the energy and resources that are available nearby. There are a lot of other planets much closer to us than K2-18b. We could just build bases in orbit around those stars, harvest asteroids for minerals and hydrogen for fusion power. Alpha Centauri would "only" take 22 years to reach at 0.2c (plus some time for acceleration and deceleration). You could leave earth and live to see that solar system, and you could travel there on a ship that is basically a large city that will just park itself in orbit around the star on arrival, acquire resources, and start building something bigger.
- sireat 7y agoBesides fusion I think hibernation will also become a reality within this century. This will make the 22 year trip to Alpha Centauri more palatable. 1000 year trip in a single lifetime will require some life extension as well
- sgt 7y agoAlthough it seems unlikely now, imagine if we could ever reach 0.9c or maybe even 99.9% of the speed of light. Perhaps not ships containing humans, but some kind of other tiny ship containing a replicator machine and DNA for humans. For 0.999c, it would only take around 71 days to reach Alpha Centauri from Earth (as seen from the ship). That's pretty mind boggling.
- radeklew 7y agoAs others have said, E=mv^2/2 only holds at very small fractions of the speed of light. I believe the equation you need is E=mc^2/sqrt(1-v^2/c^2)-mv^2. https://en.wikipedia.org/wiki/Kinetic_energy#Relativistic_kinetic_energy_of_rigid_bodies https://en.wikipedia.org/wiki/Kinetic_energy#Relativistic_ki...
- tunesmith 7y agoCan you explain this further? It seems this is relevant more for something other than the Wait Calculation. The original Wait Calculation doesn't factor in mass at all. I'm having trouble understanding what this impacts. Is this more about relativistic time passage, like from the ship traveler versus the observer? Most scenarios I've explored - low velocity growth rate, nearby planets/stars - the Wait Calculation tells you to stop researching and start launching long before your tech gets to significant fractions of light speed.
- radeklew 7y agoHonestly, I made that comment without fully thinking through how to implement my suggestion, and now I realize that I've stumped myself. However, let me explain what I meant anyway: First of all, you're right that this won't really impact your answer at insignificant fractions of light speed. You mentioned that using the 4.72% growth rate, the equation tells you to wait until you've passed the speed of light, and I thought it might be interesting to more accurately model the energy required at relativistic speeds. So the same way that you used the classical mechanics equation for kinetic energy, E=mv^2/2, ignoring mass and solving for v, to get v=sqrt(2E) and approximating to v=sqrt(E), I thought you could manipulate the relativistic equation similarly. Now, having gotten a solution from WA, I'm starting to think that I overestimated the effect on accuracy that changing the equation would have. I want to approximate the solution by ignoring some terms or changing an nE to an E^2 or something, but I think that might negate any gain in accuracy. So to answer your questions more directly, I was attempting to address the error you get when the calculation tells you to wait until you can travel above or near the speed of light, and I only included mass in my equation to try to communicate it to you more accurately, with the assumption that when actually using it you would ignore the mass. Anyway, I hope I at least clarified my previous comment, even if it turned out not to be very useful! If anyone has a better understanding of how to better model relativistic speeds I'd love to hear their explanation.
- gregmac 7y agoDoes that include slowing down and stopping, or would you be at max speed by the time you got there? I always thought that was a very well thought out aspect of The Expanse: spend half the trip accelerating, then flip the ship around and spend the other half slowing down (aka accelerating in the opposite direction).
- mAritz 7y agoDisclaimer: Just an arm-chair Space Engineers player here. > I always thought that was a very well thought out aspect of The Expanse: spend half the trip accelerating, then flip the ship around and spend the other half slowing down (aka accelerating in the opposite direction). With current technology you would not do this, since that means using extra fuel that weighs a lot and thus increases the force required for the same amount of acceleration as you'd get with less fuel and less burn. Of course that changes drastically if the fuel required for more acceleration (and its container) is very light-weight. I would assume fusion or fission based thrusters would be better in this regard, however I think currently those produce very little acceleration in a vacuum compared to combustion thrusters.
- dredmorbius 7y agoAny impulse / reaction engine is subject to the Tsiolkovsky rocket equation. It's just that with higher specific impulse and reactant velocity the total mass is reduced. Since the rocket equation is a function of the effective velocity times the natural log of the wet/dry mass ratio, changes in exhaust velocity matter more than changes in propellant mass: you're better off with heavier propellant moving faster, than lighter propellant moving slower. Ion drive engines tend to use xenon (a heavy nobel gas) for this reason. Unfortunately, xenon is rare even on Earth, and extraordinarily rare in space -- tanking up on a road trip would be difficult.
- babuskov 7y ago> One common recommendation for annual energy growth rate is 1.4% Where does this come from? Does it even hold water when compared to past data? Looking at some Wikipedia data for the past 20-30 years, it seems that the increase in speeds is much higher: https://en.wikipedia.org/wiki/List_of_vehicle_speed_records#Spacecraft https://en.wikipedia.org/wiki/List_of_vehicle_speed_records#...
- hoseja 7y agoThat's a lot of hand-waving. Reminds me of Drake equation. Why not just admit we have no clue yet? Also the Parker Solar Probe speed is due to orbital mechanics of basically free-falling towards the sun and you'd have to do things very differently if you wanted to have that speed going out of the solar system.
- mk89 7y agoSo our only hope to see a planet different from ours is that some advanced alien population comes to "see" us, with all the implications this has...
- nannal 7y agoHistory does not favour the civilization which is visited.
- bakuninsbart 7y agoOur history doesn't.
- maehwasu 7y agoGiven what we see in non-human nature, the tendency of visitees to get rekt by visitors is much, much more likely due to the dynamics of competition for life than to some human-specific variable.
- alexgmcm 7y agoWhy is annual energy growth rate or industrial growth rate assumed to correlate to the speed of space travel? Just because we build more power plants or sell more tractors doesn't imply a corresponding improvement in spacecraft technology. The Wait Calculation seems to make even less sense than the Drake Equation - which is at least correct in theory even if the actual variables have so much uncertainty it is useless.
- neuronic 7y agoThis completely dismisses any tangential factors, of course. Going earlier might be an advantage, as new ways to kill each other (or kill Terran ecosystems) emerge. Going later to optimize for time is one aspect of deciding how to spread throughout the galaxy. Another question might ask, which is the most risk reducing strategy? And the answer might be completely different.
- wazoox 7y agoYeah. Well. That's a fun math game and not much more. Other view on "energy growth rate": https://dothemath.ucsd.edu/2011/07/galactic-scale-energy/ https://dothemath.ucsd.edu/2011/07/galactic-scale-energy/ Energy growth is due to end sooner or later. First, in the real world, any long term exponential growth is actually the upward branch of an S (that plateau at some point) or of a bell curve (that falls down after a peak). Second, with such an energy growth rate we'll boil the ocean from heat dissipation long before we reach the stars.
- imtringued 7y agoThere is also the problem that as you get away from the sun you receive less energy. Making your own portable mini sun with a fusion reactor is essential for interstellar travel.
- eru 7y agoMostly I agree. But: we can keep our energy curve growing for a bit longer, if we branch out into the local space around us. No worries about boiling the ocean, when the energy stays in orbit.
- numerobis 7y agoWhy don't you stick to the energy growth rate (instead of the 4.72% velocity growth rate) and then use the relativistic formula of the kinetic energy (in which the relationship between energy and velocity is not quadratic — the quadratic approximation is valid only for small velocities)?