# Traveling to α-Cen; what is good there? **URL:** \ **Category:** Factual Questions\ **Created:** [December 15, 2016, 5:56am UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750 "2016-12-15T05:56:46Z")\ **Posts on this page:** 16\ **Page:** 2
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [December 15, 2016, 5:10pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/21 "2016-12-15T17:10:36Z")
And in fact, what Newtonian mechanics is actually calculating (though Newton didn’t realize this) is not the velocity, but what’s called the “proper velocity”, or gamma\*v, which can grow without bound without a problem. Newton actually set up his laws of mechanics in a very robust way, much more robust than the simplified version of it that’s usually taught in schools. As a result, if you start from what Newton himself actually said, rather than what schools usually say about what he said, the transition to relativity is fairly painless. For instance, most students learn in school that F = m\*dv/dt, which doesn’t hold in relativity… but what Newton actually said was that F = dp/dt, which does (well, actually, he didn’t say either, because he was using his dot notation instead of Leibnitz’s superior d notation, but it amounts to the same thing). ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [December 15, 2016, 5:48pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/22 "2016-12-15T17:48:30Z")
> [@Stranger\_On\_A\_Train](#): > > This is not correct. The occupant in the space vessel that is traveling at 0.9_c_ will see the outside world as compressed along the direction of vessel motion, but objects inside the craft will appear normal. Only an outside observer in an unaccelerated reference frame will see objects within the spacecraft as being compressed along the axis of motion. Special relativity is well understood, and in fact the basic calculations of time and distance transformations can be made by anyone with basic algebra and some very simple trigonometry. Calculating the total effects in a non-inertial reference frame (e.g. when the vessel is under acceleration) is a little more complex but can be understood by anyone who has passed a couple semesters of basic calculus and knowledge of hyperbolic trig functions. Actually this is quite not true: you have to apply a greater constant acceleration to the back end of the ruler than to the front end in order to stop it from deforming in its own rest frame. This is an illustration of the problems of spatially-extended non-inertial frames of reference in special relativity. Technically if length of the ruler is less than L[sub]max[/sub], where L[sub]max[/sub] = c[sup]2[/sup]/a[sub]f[/sub] and a[sub]f[/sub] is the constant acceleration applied to the front end of the ruler, you could carefully apply different constant accelerations along the length of the ruler so that it does not become deformed in its rest frame. However for any practical purpose the ruler must be deformed in its rest frame. Luckily though for a spaceship accelerating at 1g (within an order of magnitude of the maximum acceleration we would expect for ship carrying people), L[sub]max[/sub] is about 10 light-years and we would expect a ruler to be many magnitudes of order smaller. This means that the deformation of the ruler in its rest frame would be negligible. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [December 15, 2016, 5:58pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/23 "2016-12-15T17:58:58Z")
Should’ve added, for further info see: [http://www.mathpages.com/home/kmath422/kmath422.htm](http://www.mathpages.com/home/kmath422/kmath422.htm) ---
**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\ **Post date:** [December 15, 2016, 7:19pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/24 "2016-12-15T19:19:04Z")
If the ship passes too close to that super-Jovian rogue planet out there, that no one is aware of until less than a couple AU ahead, how will GR affect the time dilation on the ship, and how is that adjusted for? > [@Stranger\_On\_A\_Train](#): > > The bigger problem, assuming that you have some kind of propellantless or inertial propulsion which eliminates the need to carry [POST=16494836]massive amounts of propellant[/POST] is the waste heat produced by the nuclear reactor or whatever other heat engine used to accelerate the vessel and provide environmental control and other support services to keep the occupants alive. Yeah, that is the perplexing thing. When asked, one of the engineers said that the power source was a really big array of RTG units, capable of producing the GWs needed to run all the systems – but that still fails to address the waste heat dissipation in the generators. Another engineer spewed some blatherdegoop about how it is an aneutronic loop fusion collider that captures the energy of the reaction products directly, through a particle decelerator. Looking around, one of the crew is a manicurist, one is a Sierra Club chapter president, at least three have long histories as political protesters and over there is a telephone sanitizer: it might be time to consider trading in that ticket … ---
**Author:** ![billfish678](https://avatars.discourse-cdn.com/v4/letter/b/7bcc69/32.png) [@billfish678](https://boards.straightdope.com/u/billfish678)\ **Post date:** [December 15, 2016, 8:55pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/25 "2016-12-15T20:55:48Z")
> [@Some\_Call\_Me.Tim](#): > > Thankfully Chronos would be just as short and wouldn’t even notice such shrinkage in his own reference frame. I think I saw that episode…his girlfriend “suddenly” canceled the weekend at the Hamptons while Chronos was yelling “but I was going .9995C !” ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [December 15, 2016, 9:18pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/26 "2016-12-15T21:18:30Z")
> [@](#): > > Quoth **Asympotically Fat** : > > Luckily though for a spaceship accelerating at 1g (within an order of magnitude of the maximum acceleration we would expect for ship carrying people), Lmax is about 10 light-years… I think you dropped a decimal point there somewhere, or maybe used g = 1 m/s^2. 1 g is about 1/yr. ---
**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\ **Post date:** [December 15, 2016, 10:12pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/27 "2016-12-15T22:12:38Z")
My sloppy math would suggest that if it were possible to accelerate at a steady .17g for five years, one would reach .9c having traveled about two and a quarter light years. Not accounting for SR, and, of course, one would have to trim the output of the engines at a steady curve to offset the gravity of the solar system. One g, by basic math, would reach light speed in a little over ten months. Damn this is confusing. Almost like rocket science or something. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [December 15, 2016, 11:02pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/28 "2016-12-15T23:02:37Z")
> [@Chronos](#): > > I think you dropped a decimal point there somewhere, or maybe used g = 1 m/s^2. 1 g is about 1/yr. Yes you’re right - just a rounding error. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [December 15, 2016, 11:09pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/29 "2016-12-15T23:09:23Z")
> [@](#): > > Quoth **eschereal** : > > Looking around, one of the crew is a manicurist, one is a Sierra Club chapter president, at least three have long histories as political protesters and over there is a telephone sanitizer: it might be time to consider trading in that ticket … I thought that the key crew members were a peaceful doctor, a Russian university provost, a Scottish environmental activist, a Central American colonel, an American religious extremist, an African CEO, and a Chinese communist philosopher. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [December 16, 2016, 12:19am UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/30 "2016-12-16T00:19:54Z")
> [@eschereal](#): > > My sloppy math would suggest that if it were possible to accelerate at a steady .17g for five years, one would reach .9c having traveled about two and a quarter light years. Not accounting for SR, and, of course, one would have to trim the output of the engines at a steady curve to offset the gravity of the solar system. One g, by basic math, would reach light speed in a little over ten months. > > Damn this is confusing. Almost like rocket science or something. Accounting for relativity, accelerating at 0.17g it would take 115 years from the Earth frame to reach 0.9c, having travelled 72 light years. Only 82 years would’ve elapsed in the frame of the ship. ---
**Author:** ![TSBG](https://avatars.discourse-cdn.com/v4/letter/t/77aa72/32.png) [@TSBG](https://boards.straightdope.com/u/TSBG)\ **Post date:** [December 16, 2016, 6:44am UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/31 "2016-12-16T06:44:26Z")
This could be an impossibly dumb question, but could the waste heat from a spaceship be transformed into propulsion/braking energy? ---
**Author:** ![Some\_Call\_Me.Tim](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Some\_Call\_Me.Tim](https://boards.straightdope.com/u/Some_Call_Me.Tim)\ **Post date:** [December 16, 2016, 7:43am UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/32 "2016-12-16T07:43:31Z")
> [@TSBG](#): > > This could be an impossibly dumb question, but could the waste heat from a spaceship be transformed into propulsion/braking energy? Yes and no, with the no being to what you might first think of. The usual ways that we think of as generating energy from heat are really generating energy from a _difference_ in temperature rather than simply from something being hot. Without a planet to dump the excess heat to there’s nothing to cool things off again, so a steam engine works once when the water evaporates… then without a planet to cool the steam back to liquid, no more work is done as the water stays steam. Similarly a Stirling engine requires a cold(er) plate and a hot plate to generate power, two hot plates generate no power. Hot things do radiate black body radiation. In principle, one could imagine designing the ship such that the emitted black body radiation is asymmetric, pushing the ship in a particular direction, a la the [Pioneer Anomaly](https://en.wikipedia.org/wiki/Pioneer_anomaly). However, this again requires asymmetry of the heat, you still don’t get any net propulsion from the whole ship getting uniformly hotter. Also, radiant heat is usually a very very weak form of propulsion. ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [December 16, 2016, 8:42am UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/33 "2016-12-16T08:42:30Z")
> [@TSBG](#): > > This could be an impossibly dumb question, but could the waste heat from a spaceship be transformed into propulsion/braking energy? Well, it’s energy, so in theory it could. The first problem you’d have is that to produce thrust, you have to expel matter. So you’d still have to carry aboard some substance to use as an inert propellant. At best you might be able to minimize the amount needed with a clever engine design that imparted very high velocity and hence high specific thrust, but you’d still need lots of it. The bigger problem is that there typically just isn’t that much energy there. To take the ISS as an example, the six HRS panels described in the link have a total heat rejection capacity of 70.8 kW (to put it in familiar terms, just over 96 horsepower). Which isn’t much if I haven’t screwed up the math here too much. The incremental kinetic energy of an extra 1000 m/s for a 1000 kg mass is 139 kWh, which means this amount of power would accelerate this mass by 509 m/s/hour. The ISS has a mass of 419,600 kg. Let’s simplify things and ignore the propellant mass and the gradual loss of it and just get a quick first approximation from the net mass of the space vehicle. With an absolutely 100% efficient heat engine and the right propellant we could accelerate it 1.21 m/s/hour with our excess heat energy. So after one year of constant acceleration, we’d be going 10,600 m/s, or about 23,711 mph, faster than we were the year before, but in reality much less because of the propellant mass. If we’re planning to get to Alpha Centauri this way, we may as well stay home. Not to mention that I would imagine most of the heat in the ISS comes from solar radiation, which we wouldn’t have in interstellar space, but presumably we’d have a nuclear source of energy producing waste heat. We also wouldn’t have the mass of the solar panels, but we’d have the mass of the reactor and shielding instead. ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [December 16, 2016, 9:17am UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/34 "2016-12-16T09:17:23Z")
There’s also a fundamental entropy problem here. You couldn’t collect ambient waste heat to do useful work without expending yet more energy and creating more heat. It might be possible to rig this up to expel a super-heated propellant to achieve both propulsion and some amount of heat removal, but you’d likely still need radiators to get rid of the excess. And as mentioned above, radiant thrust is negligibly tiny. ---
**Author:** ![kanicbird](https://avatars.discourse-cdn.com/v4/letter/k/5f8ce5/32.png) [@kanicbird](https://boards.straightdope.com/u/kanicbird)\ **Post date:** [December 16, 2016, 12:05pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/35 "2016-12-16T12:05:47Z")
> [@Stranger\_On\_A\_Train](#): > > …is the waste heat produced by the nuclear reactor or whatever other heat engine used to accelerate the vessel and provide environmental control and other support services to keep the occupants alive. While it is popularly thought that space is ‘cold’, it is actually a nearly perfect vacuum, and like a high quality thermos or vacuum flask, that means it keeps the interior well insulated and retains the heat that is generated within, only expelling excess heat through the mechanism of radiation. Ablation is a possibility, phase change and expelling the material, is another means of shedding heat and already used during reentry. Not terribly practical here since it is of limited supply and runs into the same carrying fuel/mass issue, but radiation is not the only method, perhaps there are more. > [@](#): > > Even keeping low power spacecraft or small shuttlecraft from overheating is a challenge–hence why the STS Orbiter Vehicle e.g. ‘Space Shuttle’) always orbited with the cargo bay doors with attached radiator panels fully open–much less a large vessel occupied for years or decades. Any spacecraft carrying people on an interstellar journey would require radiating panels with enormous surface area. > > Stranger Nitpick: The shuttle, while at first did this, later would have one door fully open the other half open, The orbiter would be positioned so the half open door ‘side’ was pointed in the ‘forward’ direction, this was to protect the radiator surface from micro-meteor and debris impact. > [@](#): > > Interesting. You could mount the engines at the end of a long boom structure, couldn’t you? The heat would be well away from the insulation of the interior. The ship in 2010 had this design. That’s what I was thinking, design it to operate at high temperatures, the higher the temperature the more radiational cooling. Though what are the limits of high temperature materials that this could be build with, especially in a zero pressure environment. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [December 16, 2016, 3:37pm UTC](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750/36 "2016-12-16T15:37:14Z")
If you wanted to use your waste heat for propulsion, you’d make the front surface of your spaceship as white or silvery as you possibly could, and your back surface as matte black as possible. This would indeed result in the waste heat having a propulsive effect, and would be as much of a propulsive effect as you could possibly get from it. But it’d be such a small effect that you’d probably be better off making the whole ship matte black, cutting the radiator size in half, and using the weight savings from that to include a little bit more of whatever your primary propulsion system is. [Previous page](https://boards.straightdope.com/t/traveling-to-cen-what-is-good-there/774750.md?page=1)