Welcome to the new version of European Tribune. It's just a new layout, so everything should work as before - please report bugs here.

Going places

by Migeru Fri Nov 1st, 2013 at 05:21:59 AM EST

This week eurogreen started a thread about spaceflight and the discussion quickly took an interestellar turn. Naturally, relativistic spaceflight made an appearance along with the usual misconceptions and misunderstood heuristics. Special relativity is obviously unintuitive, and unfortunately there is no substitute for a little linear algebra if one wants a reality check for one's heuristics.

Here I will describe the main features of the simple-minded interstellar flight strategy of accelerating at the rate \(1g\) of Earth's gravity for the first half of the trip and decelerating for the second half.

No, this is not a picture of a relativistic spacecraft with a van-Allen-like cosmic ray shield


Kinematics

There is no substitute in this discussion for a little spacetime geometry. I will keep the algebra to the minimum, taking to heart Stephen Hawking's quip that every equation loses you half of your readers, but this will be heavy on spacetime diagrams.

A spacetime diagram. One dimension of space is along the horizontal axis, and time is upwards on the vertical axis. The units are chosen so that the speed of light is 1. For instance, time in years and distance in light-years. Then, light through the origin of the diagram travels along the main diagonals. The dark area is the "interior of the light-cone" and includes all the points in the "causal past" or "causal future" of the origin (the observer). The light area is outside the light cone and it is "spacelike separated" from the observer. Questions in the comments.

Fun fact: in a spacetime diagram, a uniformly accelerating trajectory where acceleration as experienced by the accelerating object is constant looks like a hyperbola:

Hyperbolic motion for various values of the acceleration \(a\). The hyperbolas satisfy \[\Bigl(x+{c^2\over a}\Bigr)^2 - c^2 t^2 = {c^4\over a^2} \] Observe that, near the origin, \[x = {c^2\over a}\Bigl(\sqrt{1 + (a/c)^2t^2} - 1\Bigr) \approx {a\over 2}t^2 + O(t^4)\] which looks like uniform acceleration at \(a\).

The hyperbola is such that the asymptotes in the \((x,t)\) spacetime diagram cross a distance \(-c^2/a\) behind the vertex of the hyperbola where the accelerating object is momentarily at rest. In the case of acceleration at Earth's surface gravity \(g\), this characteristic length is \(c^2/g \approx (0.9684~{\rm lyr})^2\), so assuming that the natural distance \(c^2/g\) is one light-year is good enough for blogging work. Conveniently, therefore, the relationship between distance and (Earth-based) travel time at constant \(1g\) acceleration followed by constant deceleration is as follows (with all times and distances measured in years—or light-years): \[(1 + D/2)^2 - (T/2)^2 \approx 1\] which implies that accelerating at \(1g\) takes you to light-speed so quickly that it takes just under two years longer (Earth-time) than light to get to your destination. But the real boon of relativistic travel is time dilation, thanks to which the ship-measured time is greatly reduced.

The rule for proper time is \[(c{\rm d}\tau)^2 = (c{\rm d}t)^2 - ({\rm d}x)^2 = (c{\rm d}t)^2 \bigl(1 - (v/c)^2\bigr).\] The quantity \(1/\gamma = \sqrt{1-(v/c)^2}\) is the inverse of the so-called Lorentz factor which governs relativistic time dilation and length contraction. Because time dilation is speed-dependent, the proper time for a trip is path-dependent. However, travelling at constant speed maximizes the proper time, so we can give a simple upper bound for on-ship time for hyperbolic travel: \[T_{\rm ship}^2 \le T^2 - D^2 \approx (2 + D)^2 - 4 - D^2 = 4D\] That is, it takes at most \(2\sqrt{D}\) years to travel to \(D\) light years by first accelerating and then decelerating at \(1g\).

In our discussion, the examples of Tau Ceti (12 lyr) and Gliese 581 (22 lyr) featured prominently. Alpha Centauri (4+ lyr) is also of interest. The upper bounds we have found for travel times are:

  • Alpha Centauri (4+ lyr): at most 6 years Earth-time and at most 4 years ship-time
  • Tau Ceti (12 lyr): at most 14 years Earth-time and at most 7.5 years ship-time
  • Gliese 581 (22 lyr): at most 24 years Earth-time and at most 9.5 years ship-time

Propulsion

Among the key laws of physics are the conservation of energy and the conservation of momentum. In relativistic physics they are part of a single conservation of energy-momentum. Energy and momentum are components of a vector, and for an object of rest mass \(m\) they are related by \[E^2 - (p c)^2 = (m c^2)^2\]

Sorry, Albert, that's as close as we're going to get to your obsolete and deprecated formula

The Energy-momentum vector \((E,p c)\) is proportional to the tangent vector to the trajectory, \((c{\rm d}t,{\rm d}x)\): \[(E, p c){\rm d}\tau = mc(c{\rm d}t,{\rm d}x)\] and this means that the speed of motion is \(v/c = pc/E\). The point of all this is that, if the spaceship accelerates changing \(v\), since energy-momentum is conserved there must have been some transfer of energy-momentum to the environment. This may or may not result in a change in the rest mass of the ship, too. For instance, if the ship slows down by friction with the interstellar medium and some particles from the medium stick to the ship, the mass of the ship will have increased. Or if the ship is firing its rockets it's ejecting mass (and the lost mass is carrying away the necessary energy-momentum). Or, as Dodo pointed out in the other thread, if the spaceship is carrying a mirror light may have bounced off of it, imparting it some momentum but leaving its mass unchanged. Therefore, the same path in space, at the same speed and acceleration, will result in widely different payloads reaching the destination.

Light sailing

As Dodo pointed out, "using starlight" allows the entire initial mass of the ship to be delivered as payload at the destination. Starlight is "used" by bouncing it off a rear-facing mirror. In practice, the "mirror" is a huge reflective sail that's deployed from the ship, like so:

The mechanics of light sailing are illustrated in the following diagram:

Dynamics of light sailing. This diagram is in momentum coordinates \((pc,E)\) rather than in spacetime coordinates \((x,ct)\). The dashed hyperbola \(E^2 - (pc)^2 = (mc^2)^2\) is called the mass hyperboloid. The solid arrows are the energy-momentum vectors before and after accelerating, and the dashed segments represent the energy-momentum of incoming and reflected light. Note that the energy of the light changes on reflection: it is redshifted (becomes less energetic) if it shines from behind and accelerates the ship, and it is blueshifted (becomes more energetic) if it shines from the front and slows it down.

We assume the the energy-momentum change comes entirely from the incoming and reflected light

Light sailing won't provide uniform acceleration, though. It will accelerate you away from the nearest star but the acceleration rate will be proportional to the star's apparent brightness, so you will accelerate more at the start of the trip, stop accelerating around the middle of the trip, and then start braking at an increasing pace as you get closer to your destination. You can adjust this somewhat by changing the size and orientation of your sail, but there's a limit to how large the sail can be.

In fact, it turns out that the amount of light pressure needs to be larger in the middle section of the flight if you intend to go at constant acceleration, and that is the opposite of what would happen with starlight.

Light rocketing

Alternatively, we could design the ship as a rocket. The rocket principle is that energy is shed at high speed, so that the ship accelerates even if the combined energy-momentum of the ship and the ejecta stays constant. It turns out that the optimal rocket in terms of fuel and payload (highest thrust per mass, lowest mass loss for given thrust, or highest delivered mass for a given trajectory) is a light-rocket: the rocket consists basically of a powerful light source. This can be seen in the following diagram:

Dynamics of rocketing. The diagram is analogous to the light-sailing diagram above: the solid arrows are the energy-momentum vectors before and after accelerating. The dashed segment joining the tips of the two arrows represents the energy-momentum of the rocket ejecta. It can be seen that the smallest loss of energy (or of rest mass) is achieved when the ejecta is at 45 degrees in the diagram that is, it is massless (i.e., radiation). Such a diagram can be used to show that the payload to fuel ratio of a light-rocket depends only on the maximum speed attained in the trip.

Something that is relatively easy to deduce from this is just how expensive in terms of deliverable payload it is to accelerate to relativistic speeds with a rocket. The maximum speed attained accelerating and then decelerating at \(1g\) on a trip to a distance of \(D\) light-years is \({v\over c} = {T\over 2+D}\), attained at the midpoint of the trip. It can then be seen that the delivered payload is \(\bigl({2\over 2+D+T}\bigr)^2\) times the starting mass. As this is an upper bound on the payload for any rocket accelerating a \(1g\), we see that the delivered payloads are, to use proper spacecraft engineering jargon, piss-poor:
  • Alpha Centauri (4+ lyr): at most 1:35 payload to fuel
  • Tau Ceti (12 lyr): at most 1:195 payload to fuel
  • Gliese 581 (22 lyr): at most 1:575 payload to fuel

Display:
Not going faster than 0.8 c also featured in the discussion; if I calculated right, getting there at 1 g acceleration would take a bit over 14 hours Earth time.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Fri Nov 1st, 2013 at 08:34:06 AM EST
That can't be right, even without apparent mass increasing with relativistic speed, it has to take 0.8 years approximately to get to \(0.8c\). That calculation works like this: \(x^2 - c^2 t^2 = (c^2/g)^2\) implies \(x{\rm d}x - c^2 t{\rm d}t = 0\) so \(v = {{\rm d}x\over{\rm d}t} = {c^2 t\over x}\). Plugging that back in, you get \((c^2 t/ v)^2 - c^2 t^2 = (c^2/g)^2\) or \[(ct)^2 = {(c^2/g)^2\over (c/v)^2 - 1}\] With everything in years, the time to accelerate to \(v/c = 0.8\) is \[{1\over\sqrt{(1.25)^2 - 1}} = {4\over 3}\] or 16 months.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 08:56:44 AM EST
[ Parent ]
My mistake was km->m. I shouldn't design Mars orbiters :-)

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Fri Nov 1st, 2013 at 07:48:52 PM EST
[ Parent ]
Nobody should design anything by themselves.

I'm sure the actual engineers in the house will concur.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 07:57:56 PM EST
[ Parent ]
An experimental physicist acquaintence who built the meson facility at Los Alamos described the process of funding government projects thirty years ago like this:
"Well, first you find the guy you want to lead the project and budget $150K/year, then you have to find him an assistant - he has to have somebody to talk to - budget another $125K, and hire a secretary,..... The relevant part is 'have somebody to talk to'. That helps in catching oversights and errors as well as keeping one sane.

"It is not necessary to have hope in order to persevere."
by ARGeezer (ARGeezer a in a circle eurotrib daught com) on Fri Nov 1st, 2013 at 09:47:48 PM EST
[ Parent ]
Thanks for this, Mig. I need to spend some time with the Wiki article on space-time diagrams. Had I come upon them in the early 60s I might have developed a better practical understanding of special relativity. I recall that Einstein worked with mathematicians. Unfortunately the course in vector and tensor analysis started off presuming a basic knowledge of the subject and went directly into applications. As a result I had to drop it as I could not keep up.

"It is not necessary to have hope in order to persevere."
by ARGeezer (ARGeezer a in a circle eurotrib daught com) on Fri Nov 1st, 2013 at 09:37:55 AM EST
If you have time and either money or a library, I suggest Spacetime Physics by Taylor and Wheeler. It's extremely pedagogical but doesn't make concessions on rigour.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 09:56:22 AM EST
[ Parent ]
The Blue Box White Paper is also helpful:

http://arxiv.org/abs/1310.7983

by njh on Fri Nov 1st, 2013 at 12:25:28 PM EST
[ Parent ]
Not that it changes anything, but in your second space-time diagram is it not better to put the hyperbolic motion curves in the top and bottom as that is where our bold spacefarers will travel?

Sweden's finest (and perhaps only) collaborative, leftist e-newspaper Synapze.se
by A swedish kind of death on Fri Nov 1st, 2013 at 10:11:16 AM EST
I don't see your point. The lines on the left and right quadrants are the hyperbolic trajectories. The only problem with the second diagram is that the starting point of travel, the vertex of the hyperbolas, does not coincide with the centre of the diagram, which is where the light-like asymptotes cross.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 10:18:52 AM EST
[ Parent ]
If you're just pointing out that the hyperboic trajectories don't go through the origin of the diagram yes, that can be seen as a flaw. But that's also where the (D+2) comes from in all the formulas for trip times.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 10:26:21 AM EST
[ Parent ]
I think the question is why are the trajectories in the v>c part of the chart.
by asdf on Fri Nov 1st, 2013 at 01:48:46 PM EST
[ Parent ]
The accelerating object does not pass through the origin of the coordinate frame. The diagram is drawn from the point of view of an observer that is never closer than a distance (c^2/g) to the accelerating objects (there's more than one, each with its own (g) and all coming at rest and beginning to accelerate away at the same time (t = 0)).

That means that, if you're a distance (c^2/g) (or more) behind a uniformly accelerating object, there is no way for you to send signals to it (because your signals would have to go faster than light).

Definitely the diagram is misleading, I'll draw another one.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 02:29:18 PM EST
[ Parent ]
For reference, since I changed the diagram, this subthread refers to this version:



A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 03:44:23 PM EST
[ Parent ]
New version expresses it clearly.
by asdf on Fri Nov 1st, 2013 at 04:21:04 PM EST
[ Parent ]
I recommended this diary without understanding it, because I believe the author does.
by afew (afew(a in a circle)eurotrib_dot_com) on Fri Nov 1st, 2013 at 01:35:57 PM EST
That's not right, you should be asking questions.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 01:43:57 PM EST
[ Parent ]
What happens if your spaceship is traveling at 99.99999999999999999999999999999% of the speed of light and the auxiliary Trebuchet Propulsion System bolted to the deck starts throwing really big rocks out the back?

Or, at the same speed, if a bahzillionjillionwatt laser pointed at the front of the space ship is turned on.

:-þ

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Fri Nov 1st, 2013 at 01:56:11 PM EST
[ Parent ]
Nobody would notice the laser, because you would already be impacting interstellar charged particles at sufficient relative velocity that you would be shedding a wavefront of hard gamma rays.

Shedding hard radiation like that is a message to anybody downrange of your vehicle. It says "I have right of way, and I brake for nobody."

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Sat Nov 2nd, 2013 at 01:37:14 PM EST
[ Parent ]
I was being silly.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre
by ATinNM on Sat Nov 2nd, 2013 at 04:45:05 PM EST
[ Parent ]
Noooo!

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Sat Nov 2nd, 2013 at 04:47:29 PM EST
[ Parent ]
Well assuming ATinNM's ship has effective radiation shielding, a planet-based bazillion laser (or, even better, a custom pulsar or quasar) could be used to slow ATinNM's ship down. But the aliens who would want to send him back home would have to notice ATinNM in time, that is, be impacted by your hard gamma wavefront a couple of years before his arrival, which wouldn't happen unless ATinNM were travelling to the regions well beyond the current de-facto event horizon (the source of the cosmic microwave background radiation reaching us right now).

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Sat Nov 2nd, 2013 at 05:19:26 PM EST
[ Parent ]
mmm OK, but it might be a useful setup for a commuter shuttle.

It is rightly acknowledged that people of faith have no monopoly of virtue - Queen Elizabeth II
by eurogreen on Sat Nov 2nd, 2013 at 05:53:00 PM EST
[ Parent ]
Well assuming you're conent with returning home sometime after the heath death of the Universe :-)

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Sat Nov 2nd, 2013 at 06:00:36 PM EST
[ Parent ]
a custom pulsar or quasar
In two threads full of suspension of disbelief, DoDo takes the cookie!

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Sat Nov 2nd, 2013 at 06:03:40 PM EST
[ Parent ]
And there is the minor problem a bahzillionjillionwatt laser would punch a hole in the front of the spacecraft causing explosive decompression of the spacecraft

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre
by ATinNM on Sun Nov 3rd, 2013 at 12:03:27 PM EST
[ Parent ]
This is a good reminder of what went on in physics in the 20th century.

In 1900, people were flummoxed that it was possible to send messages through the aether wirelessly, and sitting around puzzling about that, and radiation. Then, out of the blue, Einstein shows up with SR and at first people are like "wow, that's cool, lots of train pictures." But they really didn't pick up on how complicated it really was. Not understanding the stuff that is in discussion on this thread, for example.

Then, while everybody else was trying to get their heads around SR, Einstein & Co. are off figuring out GR, which is 10x more complicated. And then immediately after that, the quantum theory people got their stuff figured out which is even less believable or understandable. Then QED.

Over the course of 50 years, physics went from "really hard, but possible to understand if you work at it" to "impossible for 99.999% of humans to understand except in the most general way."

Then we got to the standard model and string theory, which are both complete fictions..   :-)

by asdf on Fri Nov 1st, 2013 at 04:28:06 PM EST
you know you wanted to say
This is a good reminder of what went wrong in physics in the 20th century.


A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 04:46:35 PM EST
[ Parent ]
But they really didn't pick up on how complicated it really was. Not understanding the stuff that is in discussion on this thread, for example.
It's actually not muh more complicated than trigonometry and planar geometry, triangles and stuff. The difference is that in relativity we have no intuition whatsoever, so we have to rely entirely on the algebra.

When doing geometry, it is possible to think of algebra as a bookkeeping device. But here all there is is the bookkeeping. And you have to train your intuition to work without that bookkeeping. That is the really hard part.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 04:50:06 PM EST
[ Parent ]
The difference is that in relativity we have no intuition whatsoever, so we have to rely entirely on the algebra.

Well that's a stretch. There is the Minkowski diagram. All you need to get some intuition is to grasp that the x coordinate (contemporary) axis of the rest frame of an object moving relative to you is tilted the same way as the t axis.

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Fri Nov 1st, 2013 at 08:05:13 PM EST
[ Parent ]
You're an engineer. Would you argue that the Coulomb, Faraday-Lenz and Maxwell laws of electromagnetism (in terms of charges, currents, fluxes, circulation, etc, and the language of field lines and flux tubes; I don't mean Maxwell's partial differential equations) would be "really hard, but possible to understand if you work at it" or "impossible for 99.999% of humans to understand except in the most general way"?

Just because we have electricians doesn't mean the electricians "understand" electromagnetism "except in the most general way". Certainly electronics doesn't require "understanding" quantum mechanics.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 04:58:04 PM EST
[ Parent ]
I agree with you, the problem is that there is a big problem trying to apply intuition to relativity. That doesn't make electromagnetism easy, but maybe you don't have to bend your mind so much to make your way through it...
by asdf on Fri Nov 1st, 2013 at 06:30:17 PM EST
[ Parent ]
You exaggerate. 0.001% of Americans is 3000 people. and the US churns out a few hundred Physics PhDs every year...

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 05:10:39 PM EST
[ Parent ]
A lot of graduates from the physics/Mathis/applied maths areas will have a reasonable understanding of this too. Enough to know not to trust intuition anyway ...
by Colman (colman at eurotrib.com) on Fri Nov 1st, 2013 at 05:22:49 PM EST
[ Parent ]
I'm putting bachelors' degrees in the "in the most general way" category.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 05:29:05 PM EST
[ Parent ]
How many of them will be foreign students?

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Fri Nov 1st, 2013 at 07:55:44 PM EST
[ Parent ]
About half. See Physics PhDs Awarded in the U.S. [PDF] from the American Institute of Physics.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Fri Nov 1st, 2013 at 07:57:05 PM EST
[ Parent ]


A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Sat Nov 2nd, 2013 at 06:32:13 PM EST
[ Parent ]
The high score should be more like about 200.
by asdf on Sun Nov 3rd, 2013 at 10:41:49 AM EST
[ Parent ]
 <
>I will keep the algebra to the minimum, taking to heart Stephen Hawking's quip that every equation loses you half of your readers, <
>

so far I get 18 equations, so seeing as at least I have read this far, you must have started with 262,144 readers?

Any idiot can face a crisis - it's day to day living that wears you out.

by ceebs (ceebs (at) eurotrib (dot) com) on Sat Nov 2nd, 2013 at 05:19:30 PM EST
I think you would have to factor in the image content which always attracts the eye, especially if in colour and properly endowed with hyperbolic curves. One must also not forget the author's rye humour, engaging personality, and linguistic inventiveness, all of which stimulates the likeminded to express themselves in tune or hang around in mute admiration of this tussle of thought.
by de Gondi (publiobestia aaaatttthotmaildaughtusual) on Sat Nov 2nd, 2013 at 05:32:44 PM EST
[ Parent ]
Or 10 readers giving an average of 0.00003814697266 of their attention.

Which actually sounds about right.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sat Nov 2nd, 2013 at 09:17:29 PM EST
[ Parent ]
I may yet remove all the equations, but making diagrams is hard work.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Sun Nov 3rd, 2013 at 04:40:22 AM EST
[ Parent ]
the energy-momentum change must come from the incoming and reflected light

Actually, even if the light sail has an effective radiation protection, there is a non-negligible counter-force: drag from interstellar gas.

the acceleration rate will be proportional to the star's apparent brightness

It will also decrease because of the ship's increasing speed: the reflected light will be increasingly redshifted and thus the radiation pressure will drop. Or, to say it another way, if we consider the apparent brightness as viewed from the light sail, it won't drop due to distance only but due to redshift, too. The opposite will be true in the deceleration phase, though: blueshift will make "braking" more effective at greater distances.

the amount of light pressure needs to be larger in the middle section of the flight if you intend to go at constant acceleration

Indeed you would have to ditch at least constant deceleration (a giant laser could help with constant acceleration, which would be desirable anyway to ionise everything in your path). However, considering that your rest mass doesn't change and that your sail will be gigantic anyway (not to mention the size of whatever you use to generate the radiation protection), artificial gravity with rotation could be an option.

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Sat Nov 2nd, 2013 at 05:44:57 PM EST
Artificial gravity with rotation is a necessity in any case because these kinds of spacecraft must be assembled and inhabited in space, and before and after the hyperbolic flight they have to be able to maintain a (1g) environment without linear acceleration.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Migeru (migeru at eurotrib dot com) on Sun Nov 3rd, 2013 at 10:18:44 AM EST
[ Parent ]
Yeah, Venus is looking better and better, eh? All you have to deal with there is a 93 bar, sulphuric acid atmosphere at 740 Kelvins, with winds at 360 km/hr. Orders of magnitude easier.
by asdf on Sun Nov 3rd, 2013 at 10:45:36 AM EST
[ Parent ]
A piece of cake, given sufficient time.

"It is not necessary to have hope in order to persevere."
by ARGeezer (ARGeezer a in a circle eurotrib daught com) on Sun Nov 3rd, 2013 at 11:26:46 AM EST
[ Parent ]
Well, the lack of an internal magnetic field might pose a problem and the current atmosphere is low on hydrogen in any form. There are trace amounts of sulfuric acid. 99% of the atmosphere is CO2 and nitrogen and half of the remaining 1% is SO2, so there is not much to work with. Sulphur, carbon and oxygen as your primary components seems unpromising. From wiki:
Terraforming Venus was first seriously proposed by the astronomer Carl Sagan in 1961.[1] The minimum adjustments to the existing environment of Venus to support human life would require three major changes to the planet. These three changes are closely interrelated, since Venus's extreme temperature is due to the greenhouse effect caused by its dense carbon-dioxide atmosphere:

    Reducing Venus's 450°C (850°F) surface temperature.
    Eliminating most of the planet's dense 9 MPa (~90 atm) carbon dioxide atmosphere, via removal or conversion to some other form.
    Addition of breathable oxygen to the atmosphere.

Furthermore, the following two changes would also be highly desirable:

    Establishing a day/night light cycle shorter than Venus's extant solar day (presently 116.75 Earth days).
    Establishing a planetary magnetic field or substitute for protection against solar and cosmic radiation.


Sounds like a multi-millennial project, but we are more likely to need some of these projects for earth long before we could tackle Venus, and in a couple hundred years our capabilities might be seriously degraded due to the effects of climate change - depending on how we respond.

 

"It is not necessary to have hope in order to persevere."

by ARGeezer (ARGeezer a in a circle eurotrib daught com) on Sun Nov 3rd, 2013 at 11:57:55 AM EST
[ Parent ]
"we are more likely to need some of these projects for earth"

Egg-zackly.

by asdf on Sun Nov 3rd, 2013 at 03:13:31 PM EST
[ Parent ]
'We have met the problem and it is us.'

So maybe escape is the best of the bad options. :-)

"It is not necessary to have hope in order to persevere."

by ARGeezer (ARGeezer a in a circle eurotrib daught com) on Sun Nov 3rd, 2013 at 11:07:13 PM EST
[ Parent ]
I'm starting to think the Doctorow/Stross concept of rapture of the nerds (digitizing each individual human consciousness, then uploading it to off-planet data centres) isn't the best way of perpetuating our culture, if not our flesh and blood (a variation on the matrix, etc theme)

Of course, if this turns out to be feasible, then encoding the DNA of the individual as a sort of file attachment is trivial. And reincarnation on some other planet, some other time, would not be out of bounds.

It is rightly acknowledged that people of faith have no monopoly of virtue - Queen Elizabeth II

by eurogreen on Mon Nov 4th, 2013 at 03:47:42 AM EST
[ Parent ]
It may be a little more complicated than that, to take just this one example.
by afew (afew(a in a circle)eurotrib_dot_com) on Mon Nov 4th, 2013 at 04:34:56 AM EST
[ Parent ]
I was thinking that too. But no, it only increases the complexity of the process. The genome of every cell of each individual would need to be scanned and stored, as well as the function of each neurone (in the novel, this is a destructive process).

This would be a snapshot of the individual at the time of upload.

It is rightly acknowledged that people of faith have no monopoly of virtue - Queen Elizabeth II

by eurogreen on Mon Nov 4th, 2013 at 05:23:50 AM EST
[ Parent ]
Not sure I see the point of preserving our "culture," especially if we are on a planet that is in intergalactic quarantine. We're quarantined for a reason.
by asdf on Tue Nov 5th, 2013 at 12:41:39 AM EST
[ Parent ]
Isn't it because Ron Hubbard put all the intergalactic bad guys under our crust?
by de Gondi (publiobestia aaaatttthotmaildaughtusual) on Tue Nov 5th, 2013 at 06:08:07 AM EST
[ Parent ]
The only way to get much use out of Venus would be to disassemble it. Once you are off earth, you are going to be living in a 100% engineered environment no matter what, at which point Venus is a lot less interesting than a collection of asteroids with useful raw materials.
Planets in other star systems are even less useful. Either they are as hostile as the rocks around sol, but obnoxiously far away, or they are life-bearing, in which case settling on them would be unspeakably criminal - the entire biosphere would have to be wiped out in favor of an earth-compatible ecosystem. It might be very interesting to investigate such a biosphere with carefully sterilized robots, of course, but that means you can go the "Very, very small starship" route, which makes things a lot easier.

For off earth settlement, making the dyson swarm around sol bigger is always going to win. Building an entire earth-surface worth of idyllic habitat out of the shattered remnants of asteroids, being a heck of a lot easier/faster than shipping meatsacks across the void. Not easy, but.. all things are relative, right?

by Thomas on Mon Nov 4th, 2013 at 04:29:39 AM EST
[ Parent ]
India's Mars probe aims to steal technological star status from China | World news | theguardian.com

The cyclone season is almost over, the planets are in alignment, the countdown has started. On Tuesday at 2.46pm local time, a rocket will blast off from the Indian space port on a small island in the Bay of Bengal, heading for Mars.

Its course will be closely followed. The $70m (£45m) mission - India's first attempt to reach the red planet - aims not just to gather information that might indicate if life has ever existed or could exist there, nor simply to showcase Indian technology, but to steal an interplanetary march on its regional rival, China.

"In the last century the space race meant the US against the Soviets. In the 21st century it means India against China," said Pallava Bagla, one of India's best known science commentators. "There is a lot of national pride involved in this."

Sounds promising : competitive emulation may push the technological envelope. How is Brazil's space program shaping up?

But wait : sounds like a long shot.

The scientists will also have to hit a five-minute window for the launch. If they miss it, they will have to wait another two years - or possibly five - for another chance.


It is rightly acknowledged that people of faith have no monopoly of virtue - Queen Elizabeth II
by eurogreen on Mon Nov 4th, 2013 at 05:51:07 AM EST

Suck on this, China

It is rightly acknowledged that people of faith have no monopoly of virtue - Queen Elizabeth II

by eurogreen on Tue Nov 5th, 2013 at 07:42:39 AM EST
[ Parent ]
That sucker was a hot rod! Apparently it was launched on a polar satellite launch rocket, which would account for the high rate of acceleration when used in an equatorial launch mode.

"It is not necessary to have hope in order to persevere."
by ARGeezer (ARGeezer a in a circle eurotrib daught com) on Tue Nov 5th, 2013 at 11:55:05 AM EST
[ Parent ]


Display:
Go to: [ European Tribune Homepage : Top of page : Top of comments ]

Top Diaries

The Brexit effect

by Frank Schnittger - Oct 25
20 comments

A Trip to the Woodshed

by Cat - Nov 3
20 comments

Catalonia?

by Frank Schnittger - Oct 28
17 comments