Flying to Alpha Centauri

Discussion in 'Science' started by fnp, Jan 4, 2021.

  1. fnp

    fnp Member

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    From the X-files thread I started to reply to a post thinking about just how difficult it would be to achieve interstellar travel but it ended up turning into a wall of text that probably justifies it's own thread.

    So, here goes. Warning, very geeky massive wall of text.

    Thought this might be an interesting place to do some back of the envelope calculations, and also to illustrate some of the logistical difficulties of interstellar travel. For the sake of argument, let's assume that one day we have some technology and we want to send a manned spacecraft to the nearest star system, Alpha Centauri. We also want to get there in a reasonable amount of time, no generation ships. For the sake of argument I make the following assumptions:
    • Distance of 4.37ly (41.344 x 10^12km) to Alpha Centauri
    • Spacecraft of total mass 10 tonnes - mass is the difficult thing about space travel. Every gram you take makes things that much more difficult.
    • c = 300,000km/s (yes I know it's slightly under this value)
    • To get there reasonably quickly, spacecraft will achieve and cruise at 0.5c (half the speed of light)
    • Maximum acceleration of 10m/s/s (slightly over 1g, probably about the most humans can tolerate for long periods of time without negative effects)
    • Assuming no economic or political constraints

    Firstly, I've assuming a max acceleration of 10m/s/s. This means you will be walking around on the back wall of your spaceship, and have an Earth-like just over 1g inside. You would accelerate at this rate until you reach your cruise speed then turn your engines off and coast, at while point the spacecraft will be at 0g (no gravity). At the other end of the journey you would need to reverse thrust or turn the ship around and fire the engines in the other direction to decelerate back down to 0 or you're just going to go sailing past your destination. Assuming you want to reach half the speed of light (150,000km/s), you will need to accelerate at this rate for about 173 days. Same amount of time to decelerate at the other end. Assuming you spend the middle of your trip cruising at 150,000km/s, your trip to Alpha Centauri will take 3449 days or 9.45 years (assuming linear acceleration, average speed during acceleration and deceleration phases of 75,000km/s for 173 days covers a distance of 1.121 x 10^9km leaving 40.223 x 10^12km to cover at cruise which will take 3103 days @ 150,000km/s). Also note you'll be in zero G conditions for most the trip unless you spin the ship for centrifugal force or similar.

    Next problem - the energy required to go that fast. This dictates how much fuel you need to bring along. Our spacecraft is assumed to be 10 tonnes. An object of mass 10 tonnes travelling at 150,000km/s possesses kinetic energy of KE = mv^2 = 10,000 * 150,000,000^2 = 225 x 10^18 joules = 225,000 petajoules. 225,000PJ is 810,000,000PJ.h of energy. You will also need to slow down at the other end using the same amount of energy again, so double that budget. Our spaceship therefore needs to carry fuel with an energy content of 450,000PJ. In real world terms this is an enormous amount of energy.

    For context, according to https://www.iea.org/reports/world-energy-balances-overview#world worldwide energy production in 2018 was 14,421Mtoe (millions of tonnes of oil energy equivalent - one MToe is 41.868PJ) which works out to 603,778PJ. So our spacecraft will need the equivalent to about three quarters of the entire global energy production for 2018. Imagine the mass of the fuel and the machinery/power stations globally and they obviously at far greater than our 10T spaceship - a demonstration of why current technology and conventional fuels are not even close to being capable of achieving a velocity of 0.5c. The energy density of typical fuels we have is simply not even in the ballpark. All of this is also assuming your engines are 100% efficient at converting your fuel into thrust, and also does not allow any more fuel for maneuvers like actually achieving orbit at Alpha Centauri and course adjustments in flight.

    Engine power required next. We need to do 225,000PJ of work in 173 days. This will require engines to maintain a power output of P = W/t = (225 x 10^18) / (173 * 24 * 3600) = 15 x 10^12 watts = 15TW = 15,000,000MW of power for 173 days in each acceleration/decelleration phase. Again for comparison, the hydroelectric Three Gorges Dam in China is the most powerful power station in the world, producing 22,500MW. A typical coal fired power station might have a generation capacity somewhere around the 500MW range and a typical windfarm somewhere around 5MW (yes I know there are bigger ones, these are just typical values). Again conventional technologies don't have the ability to deliver the energy quickly enough and fit in our 10T spacecraft budget, even if you could bring along unlimited fuel energy somehow. Once again this is assuming engine technology which is 100% efficient.

    More realistically from a fuel density point of view, we have fusion power. This has a far greater energy density than conventional fuels. Nuclear fusion potentially offers much greater energy outputs than even conventional nuclear fission power stations. We haven’t managed to actually build an operational fusion power plant yet, but we know it is at least possible - this is exactly what the sun does. I don’t know a lot about fusion power but I’ll give it a shot. Deuterium in conjunction with tritium is often spruiked as a fuel for fusion power. Deuterium is an isotope of hydrogen, a very common and readily produced substance. Refining it into deuterium isn’t cheap, exactly, but it is at at least easily possible and has been routinely produced for years. Deuterium can also be found naturally in seawater. Tritium is a bit more difficult but it can be produced from lithium and again is within our technological means.

    There are not yet any practical fusion stations in operation, so it’s hard to cite real world figures. However, from https://www.iter.org/sci/FusionFuels they cite an example of a fusion reactor design capable of producing 1000MW of power and requiring 250kg of fuel (50/50 deuterium/tritium) for a year of production. Producing 1000MW of power for a hour is 3600MW.h of energy. The quoted 250kg fuel budget for the year producing 1000MW for a year must means the 250kg of fuel in this fusion design contains (3600 * 24 * 365) = 31.536 x 10^6MJ of energy from the 250kg of fuel - this design therefore achieves a cool 126,144MJ per kilogram of fuel. Awesome! - petrol only manages 46MJ/kg and coal typical 24MJ/kg.

    Again our spaceship needs 450,000PJ of fuel energy. This fusion reactor design and fuel density will therefore need a total mass of fuel m = (energy required/specific energy density) = (450 x 10^15) / (126.144 x 10^9) = 3,567,351 kilograms worth of fuel. Way more than the ship’s weight budget. Damn. Looks like fusion power isn’t up to the job either. Our fuel isn’t even close to the density we need and the 1000MW output of the plant is far too weedy for the acceleration we need. It also needs to be noted that fusion power needs a constant input source of energy, usually in the form of a laser, to maintain the reaction. I’m not sure if this design includes the energy for that or not in the figures quoted. Besides the inadequacy of fusion power, I leave the difficulties of building a fusion power station and carrying radioactive tritium fuel on a 10T spaceship as an exercise to the reader.

    Let's get greedy and pie in the sky. Let's assume we manage to crack the highest energy density source theoretically possible, mass-energy equivalence, given by Einstein's famous equation, e = mc^2. Mass-energy equivalence is how much energy would be released if you had some machine that could turn it into energy. It's important to note this is *not* exploiting chemical energy content, or nuclear fission or fusion, or any technologies like that. It's if you theoretically had the ability to turn mass into energy - the material of the mass is irrelevant. Practically you would probably want a dense substance to take up less room on your spaceship. We know how much energy our spaceship needs, and want to know how much mass we need to bring along. Using e = mc^2 and solving for m, m = e / c^2 = (450,000 x 10^15) / (300,000,000^2) = 5000kg. Half our spaceship mass budget, just on fuel! Subtract however much the spaceship itself weighs and you might not have much of a payload budget left over to actually carry people and supplies, etc. Even the might of mass-energy equivalence is only just sufficient.

    This is all very general and back of the envelope. I am not a scientist and I am not NASA, and I have neglected all sorts of other problems, like radiation and how you get people to survive a nine year trip in a spaceship. But it is a fun little exercise and illustrates the sheer scale of the problem at hand. I also couldn't find my graphics calculator and had to do this with Windows calculator (bleh). I don't *think* I missed a decimal point or slipped a prefix anywhere but feel free to check.

    Another very interesting side effect of travelling at such high velocities is time dilation. Essentially, the faster you go, the slower the passage of time passes in relation to an observer that is not moving at that same velocity and vector. In the nine years it takes you to fly to Alpha Centauri, much more time than nine years will have elapsed on earth. I might do another post dealing with time dilation, but this one is long enough as it is.

    tldr = we can't go to Alpha Centauri.
     
    Last edited: Jan 4, 2021
  2. SLIMaxPower

    SLIMaxPower Member

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    Conventional travel just won't cut it. We can't even fly in space.. nuff said.
     
  3. luke o

    luke o Member

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    You send a small probe type stealth ship. Equipped with AI, no living beings. Most of the ship is fuel (assuming fusion or something like that), you can get a small craft to a high enough relativistic speed to cross interstellar space, with an AI you can also be content with about 0.1c and just take more time to get where you are going.

    When you arrive you could either have carried your biological equivalent of eggs, and have the AI build a habitat and grow them and teach them. Or you have the AI just build robots and load up whatever program you like. Even more future tech you grow bodies and you upload digital copies of the conscious beings into them!

    Either way you've crossed interstellar space you've got a small base/habitat setup somewhere in the target solar system and you can then proceed to do whatever you like, colonise, explore, do science, exterminate... whatever floats your boat. Communicating with home is relatively easy, albeit limited to light speed. High power lasers will do the trick, highly targeted you'll know exactly where to focus them and in reasonably sort time periods be able to download any updates to your mission parameters and send any findings back to the mother AI :)
     
  4. Snoops

    Snoops Member

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    Imagine being the poor sod who has to open a SSH session for some kind of remote fix with a round trip latency of about 9 years...
     
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  5. Quadbox

    Quadbox Member

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    Bearing in mind time dilation here's about the same order of magnitude as the passenger's observed trip time... (for accel to 0.5c and decel back to relative zero straight away) so if what people on earth observe is as important as what the crew observe it's even less sensible
     
  6. JSmithDTV

    JSmithDTV Member

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    Yep... travelling 20 light years and back (40 total) would mean about 1200 years had passed here. Not to mention travelling at such speed is close to impossible.



    JSmith
     
  7. Zee

    Zee Member

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    By which time we may well have crack FTL, in some way, shape or form.

    One of the interesting little storylines in Elite: Dangerous was the concept of Generation ships, that had launched many centuries ago (oddly enough, current time being about the year 3300). Thus, there are generation ships in flight to stars that can now be reached within minutes.

    If we ever get to that stage of space travel without killing ourselves first, I'm sure that's something many will consider.

    Back to current reality though, I doubt we'll be going too far in our lifetime.

    Z...
     
  8. Bion1c

    Bion1c Member

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    Fun writeup showing the figures involved :). A lot of people just seem to think "anything's possible", but don't have room in their imagination to think that some things just might not be.
    The answer to the fermi paradox might just be that it isn't possible to transport living beings successfully across such distances.
     
  9. Tinian

    Tinian Member

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    How much could you reduce your initial acceleration fuel requirement by slingshotting around planets and have you considered using something like the NASA Evolutionary Xenon Thruster (NEXT) ion thruster as well?
     
  10. Phido

    Phido Member

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    I don't know why people would be surprised that an interstellar ship would be mostly fuel or would take a tremendous amount of energy to get somewhere in our lifetimes. Space rockets are typically 90% fuel, and they just get us into space.

    Most of the semi realistic ideas for interstellar spacecraft are small unmanned probes. 1kg-1000Kg.
    Currently we have no where to send anyone anyway. We haven't found any habitable planets and we would want to check the hability before sending people.

    Yes and no. Yes its possible. But what overtaken Voyager 1 which was launched in the 77? Nothing. What will overtake Voyager 1? Nothing, not even new horizons will ever catch it and New horizons was the fastest thing we could build. It won't even over take the pioneer probes in distance until the 22 or 23rd century.

    https://futurism.com/will-new-horizons-leave-solar-system-long-can-survive
    https://en.wikipedia.org/wiki/List_of_artificial_objects_leaving_the_Solar_System

    Voyager has already been travelling for over 43 years. Its still operational and will likely make it to ~47 years. So a 50 or 100 year mission IMO is pretty feasable, we are already doing 50 year missions currently.

    IMO it would be great to have a specific interstellar probe built and launched. Say a 500 year fuel source, ion drive, launched on the next generation of the fastest rockets. Do a mutliplanet fly by..

    But the other point is why do that when there are so many places in our own solar system we haven't yet even explored or mapped or photographed.
     
  11. Zee

    Zee Member

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    Funny you should mention Voyager - as the probes are in game and reachable, if you can work out where they should be in the year 3300, then fly at several times the speed of light for about 45 minutes *from memory*.

    Agree though, lots to see in our own solar system, heck, we don't even truly know just how far out it goes, based on what I've been reading of late. Would love to see close ups of the rings of Saturn, and hi-res "Google Earth" style maps of all the planets, just blindly scroll along the landscape and check it out in a way I'll never get to in real life.

    Z...
     
  12. OP
    OP
    fnp

    fnp Member

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    Well, sort of. The distance you travel is irrelevant. The time dilation (also known as the Lorentz factor) or the difference in time experienced by two people or objects depends on the difference in velocity between those two people or objects. An object or person moving relative to a stationary one will experience time slower than the stationary one, and the faster you go, the slower time goes. But it is not a linear relationship. The Lorentz factor is given by the equation:

    [​IMG]

    The Greek letter gamma () is used to represent the Lorentz factor. The Greek letter delta () is used to indicate the difference between two quantities, in this case, time. The difference in velocity between the two observers is v and the speed of light is c.

    Graphing out the Lorentz factor with a range of velocities from 0.1c to 1.0c produces a graph that looks like this. The table shows how long a stationary observer would experience relative to an observer spending one year moving at a given velocity. Also please note that physics as we currently understand it does not allow for an object to achieve or exceed the speed of light. If you add enough kinetic energy to your spaceship you can theoretically go 0.9c, or 0.99c, or 0.999c or as close as you like to the speed of light, but even if you have unlimited energy and time it is not possible to go that final bit faster and reach 1.0c - note the ‘cannot divide by zero’ error at 1.0c. Isn’t it nice how maths comes together.

    [​IMG]

    Even at the extremely high velocity of our hypothetical spacecraft (half the speed of light) the time difference is not as extreme as you might think. Factoring in it’s acceleration and deceleration phases, it’s average speed is about 138,741km/h and total flight time is 9.45 years. Plugging that into the Lorentz equation shows that relative to the ship, a stationary observer would experience 10.66 years.

    But that’s not actually correct. Because time dilation due to relative velocity is not linear, you can’t take a simple average of the ship’s velocity. You would need to use calculus to integrate the change over time of the ship’s velocity and then calculate the total area under the curve, so to speak.

    The time dilation I have discussed so far is due to extreme relative velocities between two points. But there is another cause of time dilation - gravity. Time passes faster at points further away from the deepest point of a gravity well, the deepest point of a gravity well being the center of mass of an object causing the gravity well. Denser objects generate higher gravitational forces and slow the passage of time more. The further away you move from the centre of the object, the less the gravitational attraction and the less severe the slowing effect. On Earth, if you were to put two identical clocks on a high shelf and a low shelf, the higher one will tick ever so slightly faster, something predicted by Einstein’s Theory of Special Relativity and since verified with atomic clocks. This means that your head is slightly older than your feet, assuming you spend most of your time not upside down.

    In many real world practical situations time dilation is nothing more than an interesting curiosity - the velocities and gravitational potentials involved in day to day situations are too small to make a notable impact. You don’t ‘gain’ a longer life than your friend by living on the top floor of a building where gravity is lower. Supersonic aircraft don’t find that they’ve gone so fast they land in what they would perceive as the future. It is true that astronauts speeding around Earth in orbit further away from the Earth’s centre of mass age slightly differently than they would on the surface, but it’s a negligible amount. In fact, relative to a stationary observer on Earth, the passage of time an orbiting astronaut experiences goes a bit slower due to velocity time dilation, but speeds up a bit due to lesser gravitational time dilation than the Earthbound observer experiences. The velocity time dilation slowing is more severe than the gravitational time dilation speeding, so the net result is our astronaut in orbit ages slightly slower than they would on Earth.

    GPS satellites is one common area where time dilation is actually something you need to compensate for. This is because GPS relies on extremely accurate measurements of time, and the difference between the passage of time on earth and from the satellite’s point of view are sufficient to impact GPS accuracy. A quick Google told me that GPS satellites orbit at a distance of 20,000km at a speed of 14,000km/h. Relative to a stationary observer on Earth, they therefore ‘loose’ 45 microseconds per day due to their velocity but ‘gain’ 7 microseconds per day due to their greater distance from Earth’s gravity. The net result is a clock on the satellite ticks 38 microseconds a day slower than one of Earth, which doesn’t sound like a lot but is enough to cause an accuracy error of 11.4km, the distance light can travel in 38 microseconds. If you want GPS accuracy down to the meter, the timekeeping needs to be correspondingly more accurate.

    This will be a fun post. I'll do this one next.

    The Voyager probes are interesting. They made extensive use of gravitational assists from Jupiter and Saturn and Voyager 2 headed off to the outer planets - it was a real rush to get them built and launched on time to take advantage of the orbits of the planets happening to line up in a very advantageous way to a spacecraft trying to reach the outer solar system. This drastically reduced the amount of propellant they needed to take along and allowed them to get moving pretty damn fast. As a result as you say the velocity they achieved is huge, higher than any other man made objects. Voyager 1 is travelling at 17km/s and even at that speed it took 22 years to reach interstellar space. Voyager 2 took a longer path going past the outer planets and only achieved 15m/s.

    New Horizons actually launched at a higher velocity than the Voyager probes but only had a gravitational assist from Jupiter.

    Indeed. Jupiter's four main moons all on their own are fascinating. They're worlds in their own right.
     
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  13. Phido

    Phido Member

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    Ganymede and Titan are larger than mercury. Callisto, Io, Europa and Triton are all larger than Pluto.

    Jupiter has 79 moons (that are currently known)
    Saturn has 82 moon (that are currently known)

    Humans could certainly explore any of those 161 areas and even return safely in a life time with technology we have today and the sort of technology that would allow a Mars colony. Then you have the trans-Neptunian objects like Eris and inner solar system objects like Ceres. At Jupiter it is still viable/cheaper to use solar panels for unmanned probes. https://www.solarquotes.com.au/blog/nasa-chose-solar-power-nuclear-juno-space-probe/

    I think there is an argument for sending an unmanned probe to a star, I think that would be a great technical achievement. But within our solar system are literally hundreds of worlds to be explored, and can easily be explored, by humans directly. Worlds with oceans, worlds with atmospheres, many worlds rich in iron, water, organics, carbonates.

    While Voyager took on the grand tour with 4 planet gravity assist, Jupiter and Saturn did most of the heavy lifting. Neptune actually slowed it down.
    [​IMG]

    These slingshots were really designed for best imaging and study rather than highest speed. In ~12 years we went from knowing nothing about the gas giants to knowing heaps about them. The success of the Voyager probes also demanded further probes to follow up.

    While Voyagers have been successful as far as interstellar probes go, nobody is crying out for more interstellar probes. They are unlikely to be funded.
    Alignments between Earth, Jupiter and Saturn happen all the time, and really you could probably leave earth out of it most of the time.

    Back to stars

    In comparison we know very little about our surrounding nearby star systems.

    Alpha Centauri's system has 2 planets and 1 possible planet. Proxima B is a earth sized in the habitable zone, Proxima C is a super earth ( 7 times more massive) 1.5 Au away with a temp of about 40K.

    While Proxima Centauri b is in the "habitable zone" for temperature (expected average a bit less than earth, -18c), it orbits very close to it star, and would receive a tremendous amount of solar wind and radiation from it. Proxima Centauri is a very erratic star and has tremendous flares. It is expected that on the surface of the planet it would receive about 400 times the x ray dose that the earth gets. The solar wind has likely blown any atmosphere away from it, unless it had a tremendous magnetic field.

    So before any interstellar mission could even begin we would have to fund more astronomy research about the Alpha Centarui system. We know almost nothing about it. We thought there was another planet there but that was disproved.. We talk about planet candidates rather than planets.

    Stars are very very far away.

    Projects that have looked at unmanned interstellar projects are much larger than that being theorized here. They are talking about tens of thousands of tons and multistage fusion powered setups.

    https://en.wikipedia.org/wiki/Project_Daedalus
    https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)
    https://en.wikipedia.org/wiki/Project_Longshot

    In the next 10,000-20,000 years the stars will be much closer, by almost a whole light year.
    [​IMG]
    I think sending humans to the stars is silly right now. But in 10,000 years time it will be very optimal. We will be as close as possible Barnards star which will then quickly move away. Its currently moving to us at 110Km/s. I don't think we will send living humans, but fertilized embryos and robots.

    There have been stars very close to us in the past and will again in the future. If we have a human society on multiple planets, then it would be fairly easy to wait just a few thousand years for one of these close approaches.

    The other aspect is the ort cloud probably contains bodies from previous stellar approaches. So travelling around the ort cloud we might be able to find things from other stars.
     
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  14. ShaggyMoose

    ShaggyMoose Member

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    Does this consider the fact that the weight of the spacecraft is diminishing as the fuel is consumed and at the other end, the bulk of the empty fuel container could be discarded prior to braking?
     
  15. OP
    OP
    fnp

    fnp Member

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    No - I was more trying to demonstrate the problems of fuel density and the extremely large energy requirements to travel so fast.

    I suppose you could posit a scenario where 10T of fuel contains the 450,000PJ and have the ship's launch weight at 15T dropping to 5T by the end of the journey. The work done would be the same. On the other hand, I allowed no energy budget for actually running the ship - I only considered the energy required to move the Alpha Centauri at that velocity, since it's by far the majority of the energy consumption. Ballpark feasibility calcs :)
     
  16. ShaggyMoose

    ShaggyMoose Member

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    Yeah, I figured it wouldn't make up for the whole 3.5 million KG of fuel :)
     
  17. JSmithDTV

    JSmithDTV Member

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    Indeed, it is enormous… some interesting information, formulae and calculations on this;

    https://www.sciencedirect.com/topics/engineering/propellant-mass

    Constant acceleration could be used to create artificial gravity;

    https://www.technologyreview.com/20...-used-to-produce-artificial-gravity-in-space/
    Sorry to be picky, but you mean mass (inertial mass) I gather. ;)



    JSmith
     
  18. Phido

    Phido Member

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    I think it was in A.C Clarke's 3001 where the space craft was designed to provide 1 G acceleration when travelling around the solar system, so didn't need to spin or anything like that. 1 G accel and then 1 G decel. It still took weeks to get about the solar system even with such a magic and fantastical craft. (looks like it was 2061 and it was .2G, which was enough that people could move around fairly normally).

    [​IMG]
    1G acceleration is completely decedent.
     
  19. Urbansprawl

    Urbansprawl Member

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    Intersteller probes will be the size of cellphones or tablets for this reason. Work from a 2kg mission weight budget :)
     
  20. RnR

    RnR Member

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    Could you pack in sensors and light year communications inside that weight budget?
     

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