Relativity calculator for interstellar journeys

Thanks Vertigo,

I just found your program and, after digging up a laptop that runs windows, I've got it running and providing the journey times I need. Very handy indeed!

Is there a source for the formulae you use that someone like me with only 'A' level math could cope with?

I'd like to do some playing around with the effects of varying accelerations, calculating energy requirements etc. and everything I've googled seems a bit confusing.
 
Sorry Paul, I completely missed your question. Not sure how! :eek:

I got my formulae from a variety of places and to be frank it took a bit of work to whittle them into something easily usable. Here's a couple of pages I bookmarked in the process:

http://www.projectrho.com/rocket/index.php Actually I've been going to this one for a while - very very good site
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html This has formulae and some stuff on fuel requirements

Again, apologies I didn't see your post before!
 
No worries. Thanks for the info.

I'm struggling to make sure my stories involving Generation Ships are plausible and this information is really helpful.
 
What I want to do is given say 0.6C speed in deep space (let's say 17 light days from Earth), and desire to rendezvous with a shuttle type craft (better than NASA's retired ones) on a flypast of a planet, chose the best combination of coasting (or 0.5G deceleration) at 0.6C vs deceleration. Obviously too, perhaps you have a limit based on the biological crew/passengers as to the maximum g force (which for longer periods needs to be lower than maximum they can cope with, say 5G short period and 1.5G ). Assume the fuel / power consumption / ship mass / engine power isn't a limiting factor.

I've found this hard to calculate. The aim being to work out the shortest time for the passengers, to allow perhaps a 6 day window for rendezvous (i.e. perhaps 3 days before close point and 3 days after). Obviously an unpowered hyberbolic orbit can't work as the relative speed to planet is highest at closest approach.

It would be very obvious that the new light in space isn't natural, to any Earth based observers. They'd quickly conclude the "light" is the "engine exhaust" (actually plasma ejected up to 0.95C, don't even think about where they get the power!). So Obviously the least energy path with no engines running is a bit less than 38 days as the ship would speed up! (and shorter for those on board). The shortest time is hard to calculate, even if you don't care about the deceleration. The maximum deceleration is limited physically by power driving mass of plasma x exit speed of plasma and to an extent how hot the plasma is. But more practically limited by the biology of the Passengers. Humans can take very high G but only for a short while. Of course liquid tanks and sedation could raise the prolonged G that can be sustained. But Lets assume ordinary life for the period of time. Which might be more than 6 months?
 
Sorry, I must admit I was struggling to decipher the question in your post? Are you basically talking about an object coming in to the solar system and a human ship attempting to make a rendezvous on it before it leaves again? Rendezvous with Rama style?
 
A ship is at 0.6C speed 17 light days from Earth (It's not important how it got there*). Rendezvous as it passes Earth. Obviously for current Technology rendezvous it needs to slow HUGELY. I think it might be six months duration to reach earth as it decelerates. If it didn't massively slow, it's hard to imagine even any Alien owned "Shuttle" that could leave the ship, land on Earth and catch up with it again, never mind an Earth vessel reach ship, stay on board a few days and manage to get back to Earth! I actually envisage that Humans will visit Ship and Aliens Earth at same time (in their own "shuttle" crafts or whatever). Obviously likely to be more of a technical Challenge for 1995 to 2035 Era Humans than Aliens that can build such a Starship.

I found the sums hard. I haven't looked at the Calculator here yet though.


I have to admit I know nothing about "Rendezvous with Rama". Except is it a very late A. C. Clarke?


(*If you want, it "Jumped", but can't engage "Jump" drive any closer to our Sun than about 17 light days for arrival or departure, thus if 6 months is a feasible period to decellerate any interstellar travel is about a year minimum, assuming a "jump" takes no time. Obviously when leaving you will accelerate from Earth at as fast as possible to get 17 light days away. BUT, you will have the same vector after Jump. The rotational speed of our Galaxy actually seems to be a lesser problem.).

The Aliens would have liked to visit unobtrusively. But that's hardly practical in a giant Starship many miles long decelerating "standing" on its own Plasma / Ion drive Exhaust.
 
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Sterling work, that man. Thank you.
 
The calculator doesn't deal with any kind of orbital mechanics. It is purely designed to calculate journey times in straight line acceleration and deceleration and, in particular, the relative external and internal times (time dilation).

So what it can tell is that to decelerate from 0.6C to 0 in a distance of 17 light days would require a deceleration of 3.5g and would take around 60 days (a bit more for the observer and a bit less for the ship itself).

I would add that to avoid being seen maybe you would direct your course and exhaust to one side of the solar system and so long as your exhaust is well contained with little 'spread' which I imagine you would want for maximum efficiency then it probably would not be visible from Earth. Then as your speed drops your ship can just drop into a cometary style orbit.
 
You know... I might be getting a little greedy here, but I'm going on a don't ask, don't get ethos. Have you ever considered factoring in energy requirements and specific fuel consumption calculations? (I'm presuming wildly in not talking jibber jabber to you based on the fact you wrote the program!) and then extrapolating for potential future 'space drives'. I'm sure some reasonably legitimate projected figures can be found for the SFC of things like fusion/antimatter etc etc. That way for those who are quite interested in ensuring their SF ships are kept plausible they can actually have some basis for sizing them (fuel tanks/engines and so on).

As I say. It's awesome what you've done so far and makes a mockery of my scribbled note pad of calcs. :)
 
Vertigo said:
The calculator doesn't deal with any kind of orbital mechanics. It is purely designed to calculate journey times in straight line acceleration and deceleration and, in particular, the relative external and internal times (time dilation).
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I Understood that. At such high speeds and deceleration, we can almost neglect Orbital Mechanics. Besides that's "ordinary rocket science", it's a little easier.
Vertigo said:
So what it can tell is that to decelerate from 0.6C to 0 in a distance of 17 light days would require a deceleration of 3.5g and would take around 60 days (a bit more for the observer and a bit less for the ship itself).
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Thanks. I'll install and do a piece wise solution. I think 3.5G is only feasible for crew and passengers for short periods. So 60 days is too short a time, my original 6 months seems more likely. I'll look at something like 1.5G for most of it and then ramping up deceleration for a short period for final approach. Which will result in a massive "firework" display. It also will have to be curve, but I can take more steps of straight lines at end of transit.

Besides, then they have more time to learn English :)

Vertigo said:
I would add that to avoid being seen maybe you would direct your course and exhaust to one side of the solar system and so long as your exhaust is well contained with little 'spread' which I imagine you would want for maximum efficiency then it probably would not be visible from Earth. Then as your speed drops your ship can just drop into a cometary style orbit.
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Only if there is no engines running do you get "cometary style" orbit (true hyperbolic orbit with highest speed at the peak of orbit.). Once the Earth shuttle is about to dock they will reduce Starship to 1.2G deceleration. The faster fusion & plasma powered alien "shuttle" can leave the Starship earlier and decelerate enough before atmospheric entry, then when enough into atmosphere it can switch to using air as plasma source instead of on board water. For landing and take off or slow flight it adjusts wings. As soon as the Earth shuttle has left and their own "shuttle" has rejoined then they will switch to 1.5G, then after 6 months of best trajectory at that Acceleration it will jump. I'll look and see if Jupiter helps at all for arriving (probably not) or for leaving (possible). Or even if sling-shot around sun helps to leave faster. But I suspect the Starship doesn't need Jupiter or Sun's assistance. The Fusion powered 18km long plasma (made from water cooked to plasma by fusion power, and electrons stripped) fed linear accelerator (output near 0.95C is possible) is capable of more sustained acceleration than anyone can cope with. The temperature and recombination with electrons at the Accelerator "Exhaust" port will make for a pretty show many thousands of km long. Since the ship is either accelerating or decelerating by rotation of 180 degrees, "down" is always toward the linear Accelerator exhaust port I think. But habitat area is gimballed anyway so that "down" is away from ship's core if there is no acceleration or deceleration. Though due to Coriolis effect you can't spin too fast or people will be ill. However the diameter there is over 1km (on Habitat sections), so rotation doesn't have to be too high for a reasonable "artificial" gravity.


The aliens considered every possibility of stealth approach. I think you underestimate the visibility of the propulsion system. Also as they get closer a somewhat larger than 18km long starship will reflect a lot of sunlight. So they announced their arrival, artificially frequency shifting ONE of the duplicate transmissions to compensate for Doppler Effects. Really it would have been simpler without the UN, Europeans, Chinese, Americans etc.

Of course the direction you "leave" a solar system in, affects the relative velocity at "jump" destination, so you accelerate away from Earth to a path into deep space to suit the next destination. Which in this case was not where they came from. I'm quite sure the Alien Navigation computer programming is simpler than any Banking system. I should write a simulation of it and then the story would be totally realistic :)
 
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Only if there is no engines running do you get "cometary style" orbit (true hyperbolic orbit with highest speed at the peak of orbit.).
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That was my though for a stealthy approach. Come in off centre until almost stationary relative to the solar system and then let yourself sort of 'fall in' maybe using the gas giants to brake a little on your way. Probably a ridiculous idea though; as I say my orbital mechanics knowledge is distinctly sketchy.

Surely an 18km object is only going to become noticeable through reflected sunlight when it gets to within say the asteroid belt.
 
Sorry for the double post but I should add that this program is not a project that is under active development. I can't justify spending the time on it so, apart from anything else, it is rather ragged and not the most friendly bit of software out there :oops:. So if anyone is trying it out and is confused feel free to ask here and I'll explain as best I can!
 
I hated the terminology with a vengeance - massively confusing I thought - but throughout my research it was what was consistently used so...

The way I remember it is think map and coordinates are used to describe your position and velocity relative to the frame of reference - eg. the rest of the galaxy. So map time and distance refer to the outside observers view as does coordinate velocity (why couldn't they be consistent and say map velocity?). The same goes for the other way around it is travel time (map distance is the same of course it - it doesn't change) but then it is 'proper' velocity and acceleration. So those three are all the travellers perceived time, velocity and acceleration which are all different to map due to the time dilation. That said at your alien's 0.6C there is that much of a time dilation.
 
My feeling is that if your Starship has jump drive you are only asking for trouble getting any faster than 0.6C because of the time taken then at a reasonable deceleration to slow enough to have Planetary Rendezvous. Going into any kind of orbit for sensible longer term visit allowing short duration shuttle flights takes longer, and possibly an initial flyby.

The Milky Way rotates about 789,120km per hour (at the distance our Sun is from Galactic core) or about 219 km per second. A velocity of 0.6C is about 180,000 km /s (= 300,000,000 x 0.6 m/s, actually speed of light is a little less).
at worst case one side to other of the Galaxy rim is a maybe a worst case differential 1450 km per second. Then there is the orbital velocity of desired planet around its star. For Earth it's 30 km/s. Because Jupiter is further away from sun it orbits at about 13km per second.

So we see the issue is having to use the Jump Drive at least 17 light days from a Sun (depends on mass of Sun, Gas Giants etc) and the desire to go fast is simply to get to "deep space" (about 17 light days distance).

I've used this Online calculator
http://www.calculatorsoup.com/calculators/physics/velocity_a_t.php

also some listed here
http://wiki.kerbalspaceprogram.com/wiki/Calculation_tools
 
Vertigo, you've created an awesome bit of kit as it was. I was just being greedy (and lazy!).
 
Yeah that's a problem I've had to address too. In my works, I use an Alcubierre drive (a warp drive)... Which is awesome other than the small fact of matching velocity with a target!

I've kinda addressed it by saying that there is a 'tolerance' where one can match velocity (as in vector) for a rendezvous. Outside of that tolerance and any attempt to match would rip a ship apart through stress. I did manage to factor in a bit of drama by a ship having to match velocity at the edge of that tolerance level. I suppose the key is trying to build consistency within your own universe and, much like in the Honorverse novels, you can create ropey situations and drama.

Of course that all naturally leads into presenting that with only a modest infodump... Which as forgiving as I am of them... I don't want pages of theory to preface a few paragraphs of excitement.
 
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