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Ask Slashdot: How Would You Build a Microsatellite? 117

Posted by samzenpus
from the your-own-personal-satellite dept.
Dishwasha writes "A fellow co-worker of mine turned me on to CubeSat; apparently there are commercial space companies that will launch CubeSat systems from their payload for a modest fee. Is anybody in the /. community involved in amateur microsatellite systems? How would I go about getting involved at an amateur level? Are there any amateur user groups and meetups I can join? I have limited background in all the prerequisites but am eager to learn even if it takes a lifetime. Any links to design and engineering of satellites would be appreciated."
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Ask Slashdot: How Would You Build a Microsatellite?

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  • Anybody can build a satellite.

    The hard question is, how are you going to get it launched?

    • by jerquiaga (859470)

      Apparently that isn't the hard part, as the poster already identified a company that will do it.

      • Apparently that isn't the hard part, as the poster already identified a company that will do it.


        I'd suggest that the poster take a harder look.

      • Apparently that isn't the hard part, as the poster already identified a company that will do it.

        According to this article [] the cost to launch a typical CubeSat is about $40k.

        • That's why I'd go for a TubeSat [] instead. Launch costs are within what mere mortals might spend on a hobby at $8kUS.

          • Buyer beware. Interorbital has never launched a satellite. $8k gets you some not-very-expensive parts and a voucher for a launch to take place some time in the future. They say launches will start next year. They've been saying that for years but have seldom test-fired their engine.
        • The cost is about $40k if you can find someone who has extra space and will sell it to you at that price. There are more CubeSats than there are launches.

          Most CubeSats are launched through NASA's ELANA program. The launch is free if you win the ELANA lottery. Most people who enter lotteries don't win them.

          All launches at the moment are rideshares with larger payloads. There have been attempts to develop dedicated launchers for small satellites but none have made it to the launching pad. NASA created the

    • Re: (Score:2, Informative)

      by qubezz (520511)
      I would pay commercial space companies to launch my CubeSat systems for a modest fee. RTFA.
    • if you're the Best Korea, you can't build a functioning satellite but you can launch it into orbit.

    • by PlusFiveTroll (754249) on Wednesday December 19, 2012 @07:56PM (#42343457) Homepage

      Anyone can build anything, the question is, will it work when it gets there.

      Space is a totally alien environment from habitable earth. It's like being in the desert Antarctic and the inside of a nuclear reactor at the same time. If you're in the sun it's very hot and out of the sun it is very cold. There no atmosphere and whatever particles are around can contain high energies. Many substances stable at atmospheric pressure become volatile. Special lubricants have to be used to avoid all kinds of issues with evaporation, freezing, or sticking. Solar flares can fry you.

      Any leaks or evaporation from the satellite can cause it to spin out of control. Any control system failure is fatal. You don't get to test the unit in zero gravity before hand. Your solar and power storage have to deal with all the above issues. Oh, if your components get hot, they have to radiate the heat away, no convection to do the work for you.

      • by AikonMGB (1013995) on Wednesday December 19, 2012 @09:03PM (#42343861) Homepage

        A metal cube in low Earth orbit will equilibrate to about 25C if you cover the outside with solar cells and some reflective tape. The radiation environment isn't really all that bad below the Van Allen belts; use automotive grade parts and in general you'll be fine. No need to worry about lubricants because you shouldn't have any mechanical actuators (unless it's part of your payload or you really want to fly a reaction wheel). Good thermal ground planes in your boards and metal bosses tieing them to the structure will move heat away from components just fine. No need for a "point-or-die" solution, just put solar cells on all faces of your satellite; if you lose control authority (e.g. computer crash) you still generate enough keep-alive power. Gravity doesn't really have any impact unless your payload is a mechanical actuator, which again is not very common at the amateur cubesat scale. Leaks -- don't use pressurized gases or fluids; evaporation, just pick materials with < 1% total mass loss and less than 0.1% CVCM (i.e. Teflon insulation on wires instead of PVC).

        As it turns out, amateur space isn't all that hard to do.

        • What about communications in an uncontrolled spin? Can you radiate enough power omnidirectionally to establish communications with the ground, or other sat? I would assume that directional communications would be the preferred method. That said, I am ignorant of the methods small sats use for communication.

          • by AikonMGB (1013995) on Wednesday December 19, 2012 @09:26PM (#42344009) Homepage

            Yeah, you can have omnidirectional antenna coverage for both uplink and downlink. Our S-band transmitter is capable of 1 Mbps omnidirectional downlink at 650 km. This is the preferred method if you can close your link and data budgets because it makes the system vastly simpler and inherently fail safe (if it crashes and you lose attitude control, you can still talk to it). A secondary directional downlink may be reasonable if you have very high data requirements (e.g. streaming video or ultra high definition imagery), but generally speaking you never want to be in the situation where you can't talk to the spacecraft if it can't point at you, even in big space.

            • by Animats (122034) on Thursday December 20, 2012 @01:48AM (#42345285) Homepage

              Yeah, you can have omnidirectional antenna coverage for both uplink and downlink. ... This is the preferred method if you can close your link and data budgets because it makes the system vastly simpler and inherently fail safe. ... A secondary directional downlink may be reasonable if you have very high data requirements (e.g. streaming video or ultra high definition imagery)

              Most commercial and military satellites have a low-bandwidth omnidirectional uplink and downlink for control. USAF satellites used to have (and may still have) almost a complete separation between the "bus" and "payload" sides, with the "bus" side on omni antennas. At the ground end, the USAF had big steerable dishes at about six tracking stations around the world. The spacecraft was piloted through those. Command and control of most USAF satellites were run from the Blue Cube in Sunnyvale until that operation was moved to Falcon and Vandenberg AFBs.

              Once the spacecraft was in the desired orbit and oriented, directional antennas were used by the payload to communicate with the payload user's control center. With directional antennas, smaller ground-side dishes could be used. The big steerable dishes were a scarce resource needed for multiple satellites, so tying them up for payload data like imagery was avoided.

              Back in the early 1980s, one of the amateur radio satellites was incorrectly commanded to transmit on its own control receive frequency. This blocked the receiver from receiving further commands. To recover the satellite, the Stanford Dish [] was used. That 46 meter steerable radio telescope had, left over from old USAF work, a 3MW transmitter. The combination of a huge dish and a high powered transmitter allowed focusing enough power on the satellite to get through to the receiver and tell the satellite to change its transmit frequency. It took two tries (the first time the codes sent were wrong) but on the second try it worked.

          • by abushga (864910) * on Wednesday December 19, 2012 @09:30PM (#42344041)

            One tried and true anti-spin method utilized with CanSats (predecessors to CubeSats, see [] is to attach a refrigerator magnet to one end of the satellite. The 'sat will flip 180 degrees as it passes over north and south poles, but remains otherwise in stable orientation. Sometimes simple is good :-)

            A man is rich in direct proportion
                      to the number of things he can afford
                                to leave alone.
                                                                              — Thoreau

          • by Shavano (2541114) on Wednesday December 19, 2012 @11:10PM (#42344611)

            You can slowly kill the spin by loading the satellite with magnetic torque rods. The rods cause the satellite to orient to the Earth's magnetic field. There are active and passive systems.

            For coms that are effective in a spin, a couple of omni whips at right angles should do it. The basic unit is called a 1U Cubesat and it's 10cm x 10cm x 10cm container, but they can have mechanisms to pop out antennas as soon as they get out of the container. Some of the designs I've seen have pop-out arrangements of solar cells so they can have up to 500 cm2 of solar cell area and are made to orbit with them pointed away from the Earth. Cubesats can be stacked several in a launch container. (Like a six-pack.) There are 1U, 2U and 3U designs.

            This year's Smallsat Conference is at Utah State University - Logan Utah, August 10 – 15, 2013

            Smallsat []

            • by Dishwasha (125561)

              Thank you, that was a very useful link!

            • by Gordonjcp (186804)

              Here's a photo [] of my cubesat ground station ;-)

              Most cubesats up there transmit telemetry via Morse code on UHF, up around 435MHz. With a simple homebrew 4-element Yagi and a cheap multi-mode HT (it can receive SSB, but only transmits on FM) I can pick up the signals from any cubesats that go past.

              The stack of Zip disks is an accurate (to a couple of mm) representation of the size of a cubesat. Yes, really. That's what I'm listening to, at somewhere around 1000km away. When the cubesat is launched from i

    • Anybody can build a satellite.

      The hard question is, how are you going to get it launched?

      Have you tried asking North Korea? They have the launch rocket but unable to get the satellite to work..

  • by frovingslosh (582462) on Wednesday December 19, 2012 @07:28PM (#42343223)
    You might want to get a ham radio license, and even if you don't, visit the website of Amsat (, a worldwide group that has put many satellites in orbit. You are welcome to join even without an amateur radio license.
  • by eldavojohn (898314) * <> on Wednesday December 19, 2012 @07:30PM (#42343235) Journal
    Disclaimer: I have no personal experience doing this. I noticed on O'Reilly there is a cheap series of books [] by Sandy Antunes []. I think surviving orbit will be your biggest challenge []? No clue on the quality of those books ...
    • by Dishwasha (125561)

      Bad@SS!!! That is most perfect. If I could mod replies to my posting I would mod you +1 Very Helpful!

  • If only there were some place to search for knowledge. But even if there were, it would be unlikely to contain technical knowledge, or any way to get like minded people in touch with each other.
    Sounds like a great idea for a new business. I am sure it would be a real money maker.
    • With this business philosophy, one could have regional offices that collect this knowledge and store documents of it in little cannisters. When someone in one region needs to access the knowledge from a different region, they could send a request and have that cannister (with the relevant document inside) sent along a pneumatic piping system, just like at the bank teller window. One could call this business The National Tube Service, or simply The Tubes(tm).

    • Re:If only (Score:5, Insightful)

      by garyebickford (222422) <.gar37bic. .at.> on Wednesday December 19, 2012 @08:32PM (#42343677)

      It would be even better if there was a way for many different people to add information, make corrections, discuss the implications, and point others to places that contain additional resources.

      • Re: (Score:3, Funny)

        That's just crazy talk! You need to lay off the drugs.
        • Actually I don't need drugs any more. I have this thing where I just type on a keyboard, look at cat pictures, and every time I click the mouse I get a Dopamine rush. It's kind of addictive as a result of all those D hits though.

  • Essentially all the parts of a microsatellite are deeply involved with electronics.
    The smaller you can make them, and the lower power, the better.
    Lower power smaller electronics mean simpler cases, lighter batteries, solar cells, ...
    Cleverer electronics can remove the need for mechanical parts - if you can trigger the shutter of a camera when pointing in the right direction, versus having a fully stabilised satellite, for example.

    • by tibit (1762298)

      This is not very informative. Size and power consumption matter, but what really matters is reliability and survivability. And forget the whole thing if you don't intend to perform full-on hardware-in-the-loop testing. Ideally in a vacuum chamber. Yes, even if you don't do such testing, you may be lucky and it may work. Or I may win enough in a lotto drawing to order a Falcon Heavy launch from Space X. Your pick.

      • Or I may win enough in a lotto drawing to order a Falcon Heavy launch from Space X. Your pick.

        This is irrelevant, but this line got me thinking. You are actually in the ballpark. Imagine that - space technology has gotten to the point where Joe Shmoe from Poughkeepsie could buy a lottery ticket, and a few weeks later start getting prepped for a trip into orbit on his own Falcon. Has anyone drunk a beer in space?

        • by ganjadude (952775)
          I do recall hearing about a special space brew. I am not talking about the "space brew" that they made from yeast brought into space, but a specially brewed brew that was consumable in space. It was on one of the beer shows in nat geo or history

          On another note, I work in poughkeepsie from time to time.
          • You'd also need bottles with a tube and a ball valve because otherwise the pressure would probably force a great deal of beer into the cabin. No gravity to keep it in the bottle, and free flowing liquids amongst that number of life-preserving computers is not something that I'd like to test.

            For the beer itself: it seems you'd want a strong tasting beer. Taste buds down in space (well, actually it's smell) [], so I'd advise a very malty brown beer. No pils malt (3-5 EBC), replace that with munich malt (15 EB
            • by Gordonjcp (186804)

              I think something like a nice hoppy IPA would work well, with a good sharp citrus-y flavour and not too gassy.

              You definitely wouldn't want anything like the mass-produced carbonated fizzy juice that is sold as "beer", like Stella or Budweiser ;-)

      • Before you have to make something that works in space, you first have to be able to make something equivalent that does not work in space.

        • by tibit (1762298)

          That's true, of course, but there's no reason to do two designs. Do it right the first time.

  • How much for a payload of just ball bearings?

    • by Shavano (2541114)
      That would not be allowed. The government reviews your payload to make sure you're not just launching space junk. Also, slots on the cubesat launchers are highly coveted and there would be mobs of university students who would skin you alive and feed you to the rats over in the biology lab.
      • by Yoda222 (943886)
        Which government ? The one from the launcher company* ? Just ask Congo for a slot in the next launch [] , you can probably get it if you pay enough. * In fact if you are in the US or use any US space equipment, the US government take also a look. But just move to Europe and buy european stuff...
    • I believe these kind of armature cubesats are usually deployed at low altitudes, before the upper stage lights up to boost the main satellite into a higher orbit. Such orbits are only short term, even under the most optimal circumstances they could only stay up about 25 years, most deorbit within a couple years.

    • Absolutely! While I support doing things just to learn and have fun. You really shouldn't launch junk into orbit just because its cool. It messes with things that are actually doing stuff.

      Its the equivalent of running seti@home on a heavily loaded production server: stupid.

  • easy (Score:5, Funny)

    by geekoid (135745) <dadinportland AT yahoo DOT com> on Wednesday December 19, 2012 @07:43PM (#42343343) Homepage Journal

    I would use tiny tools.

  • by Anonymous Coward

    You want to talk to AMSAT, the ham radio homebrew satellite group. They've been building and launching homebrewed satellites for a long time, roughly since the start of US spaceflight. If you are outside the US, you will want to talk to the AMSAT like group in your home country.

    This is not a project to undertake lightly. Putting something into space involves a good bit of regulatory compliance. For example, properly documenting that your satellite will deorbit as

    • by nospam007 (722110) *

      "This is not a project to undertake lightly. Putting something into space involves a good bit of regulatory compliance. ....since the launch is likely to take place outside the US."

      So, if you use a foreign rocket on foreign soil, WTF does the US government have to regulate it?

      • by Shadowmist (57488)

        "This is not a project to undertake lightly. Putting something into space involves a good bit of regulatory compliance. ....since the launch is likely to take place outside the US."

        So, if you use a foreign rocket on foreign soil, WTF does the US government have to regulate it?

        There's a whole list of technology the U.S. does NOT want shipped to certain hostile or potentially hostile powers. It's not a laughing matter.

        • by Yoda222 (943886)

          It's not a laughing matter.

          In fact it's quite funny to see of this protective law has failed. You can go in Europe and ask european manufacter to build an ITAR-free satellite. A satellite without any US technology. Good for US business.

          • No, you can't. Just having technical discussions with a foreign citizen falls under ITAR control.
            • by Yoda222 (943886)
              Only if you are in the unlucky less than 5% of the population of Earth which is US citizen. But yes I forgot that crazy detail.
      • by Yoda222 (943886)
        That's because of law to protect the US space industry. To protect this industry against increasing revenue.
  • by camperdave (969942) on Wednesday December 19, 2012 @07:45PM (#42343357) Journal
    The most important thing is to decide what you want your CubeSat to do. Are you out for a Sputnik style beacon that you can detect when it goes overhead? Are you going to be taking pictures of all the balloon cameras that didn't make it into space?

    Once you decide what you are going to do, then you can start in on the design. [] has all sorts of design guidelines, etc.

    As for organizations, mailing lists, and the like, the external links on the Wikipedia page you linked into your article should provide an excellent starting point.
  • by Shavano (2541114) on Wednesday December 19, 2012 @07:50PM (#42343415)

    Stanford and Cal Poly has been involved from early on and has a lot of experience with cubesat launches. UNM also has a program and I think UM and U of Utah Logan. Probably lots of others. Basically schools with a strong Aerospace program are likely to be involved and help with getting in contact with good people. You may, if you have interesting tech knowledge, be able to advise a group of students on a project they are already doing.

    Also the air force schools do projects (AFA and AFIT) but they might be harder to work with.

    • And as a followup, there are very good reasons to get involved via a program like this: they have necessary equipment to be sure an assembled cubesat will actually survive. Most especially, a shake table and a vacuum chamber. Don't even try if you can't get access to both of these things. Vacuum is tough enough to deal with, but the worst part is the launch itself. The shake table will let you know if your cube can survive launch.

      • by drinkypoo (153816)

        there are very good reasons to get involved via a program like this: they have necessary equipment to be sure an assembled cubesat will actually survive. Most especially, a shake table and a vacuum chamber. Don't even try if you can't get access to both of these things

        A vacuum chamber is easy to build or buy. It's an old school pressure cooker, and any vac pump, some are quite inexpensive. I use a compressor-driven one that just uses a venturi which produces surprisingly low vacuum. You're not going to get the kind of vac they get, but you'll get enough to pop anything cheap. A shake table is tougher. Get in contact with an orchard :)

  • ...very small.

  • by binarstu (720435) on Wednesday December 19, 2012 @08:07PM (#42343537)
    Well, I would start with a bunch of nucleotides (A, T, G, and C), then assemble them into a DNA strand such that the same short sequence of nucleotides is repeated over and over again in the strand. That's all you need for a microsatellite, really. Doing this will not be easy, of course, without access to some very sophisticated lab equipment... Oh, wait -- you aren't talking about that kind of microsatellite []. Moving along...
  • by Anonymous Coward

    First you build a large machine capable of building both a same-size satellite and a copy of itself at half its original size.

    Then you just turn it on.

  • by werepants (1912634) on Wednesday December 19, 2012 @08:14PM (#42343567)
    I was involved in a recent university project that launched a payload on a suborbital sounding rocket. Depending on your objectives, getting into Arduino or Beagleboard or Gumstix or some similar low-power microcontroller will really open up a lot of possibilities for you. We launched a capsule that radio'd back inertial data using largely off-the-shelf components from places like Sparkfun.
  • by Audrey23 (663718) on Wednesday December 19, 2012 @08:28PM (#42343659)
    You will find much information on AMSAT ( , JAMSAT ( or AMSAT-UK ( for some of the amateur organizations around the world, they have been around for decades and have a wealth of experience and can use any offered help! Also get your amateur radio license and then you can access the existing birds that are up there, ARRL (American Radio Relay League) or RSGB (Radio Society of Great Britain) or other organizations are a good place to start. I can't seem to get links to work on /. so will have to leave it up to you to google the above acronyms to find out more. I have built my share of down-converters and donated my share of money to get some of the satellites into orbit, it is extremely expensive to get something into orbit, not so hard building it in comparison, most of the expense is just getting it out of the gravity well and orbiting. In fact if you go to the UK AMSAT web site they have a bit on the latest cubesat on there now :)
  • this book [] is the standard intro to general space engineering according to my lecturer (I'm doing an MSc in Astronautics and Space Engineering)

  • by AikonMGB (1013995) on Wednesday December 19, 2012 @09:08PM (#42343889) Homepage

    Generally speaking, microsatellites are in the range of 10 kg to 100 kg. What you are talking about are cubesats, which are generally nanosatellites (1 kg to 10 kg) and picosatellites (< 1 kg). As others have said, the AMSAT programme is a great starting point; next August come out to the Cubesat workshop [] and, if interested, hang out for the USU Small Satellite Conference []; lots of industry, academia, and government representation. We host a booth every year, as do most relevant players in North America.

    • by Tammuz (320333)

      I was also going to recommend and The mailing list at is active with numerous ongoing projects, mostly university-based. There are ITAR issues with American citizens participating in open projects, but there is a one-man korean satellite/art project at that has scheduled a launch.

      Another collaborative effort is the GENSO organization, attempting to coordinate a federation of volunteer ground stations to expand telemetry coverage.


      • The RF communications aren't that hard depending on the frequency range you're allowed to work in. Main problem I see is that you'll probably have to go for GaAs based amplifier designs, they tend to perform better in hostile environments like space. But GaAs devices have a few nasty things about them, they tend to oscillate at frequencies you wouldn't expect at the start. Combined with the better characteristics in general they're a good choice for spacecraft. Avago has a few nice GaAs power FETs. Combined
  • by Anonymous Coward

    As many have said, the amateur radio community has been working in that realm for a while and is a great place to start. The best resource for a general but complete understanding of satellites and their design from a mission perspective (including satellite busses and subsystems) is Space Mission Analysis and Design (see which is now in essentially the 4th version and is really an excellent text. I had an opportunity to attend the actual course taught by Dr. Wertz and it was great and I read

  • most likely with pliers....
  • For "conventional" cubesats, there are many universities working with the US Naval Academy. They have a "2U" cubesat design with a slightly-smaller-than-1U-sized plug-in compartment, which provides power and communications to a plug-in experiment provided by a university research partner. So, the university partner provides the experimental plugin, and a Really Good Story to convince the USNA that the experiment is worthwhile. USNA launches the cubesat, and the middies manage it, to get experience manag

    • For the last four years, I (and a tiny part-time team of volunteers) have been working on a different way to think about satellites: []

      These will be 3 gram, dinner-plate-diameter 50 micron thick satellites, based on some recent advances in semiconductor technology and Ivan Bekey's "Advanced Space System Concepts and Technologies: 2010-2030+". We are doing most of this as open technology, and I make presentations to groups that might help. Monday at NIST Gaithersburg, for example.


  • by wakeboarder (2695839) on Thursday December 20, 2012 @01:03AM (#42345109)

    Having been on a team that has built and launched two cubesats, I consider myself somewhat of an expert in the area. I'll answer this question to the best of my knowledge, I've been to the cubesat conference for several years now (it's mostly academics but most of the launch companies are there.) The first couple of years as a student I would get all excited whenever companies like this would start up. I noticed quickly that the same company never came around to the conference more than a few years, why? Because they couldn't get the funding, a launch requires some where in the range of 10$ million. There are plenty of companies that start up and claim that they will launch a rocket with a 50-100 (or so cubesats) and that will cover there costs, the problem is they have to find that many people to fill the spots. No one has done that yet. Cubesats were designed as a containerized system to mitigate the testing and integration launch costs. Everything that goes to space has to be thoroughly tested, when you have to do this on a case by case basis, it takes a lot of time (=money). So if you already know your payload will fit in a 10cm x 10cm x 10cm (1U) and has a ~1kg weight then that saves a lot of testing. Another benefit of the container is NASA can slap them all over their rockets and launch 10's of them (currently) at a time. Since every rocket has tons of payload margin (you want to ensure your payload reaches space you size its mass several percent smaller than what the rocket can handle to ensure delivery) and some payloads are in the tons, throwing on a few cubsats won't really do a thing to your mass budget. Now NASA has a program for this: [] this has been successful. As far as launching your own, I wouldn't count on it in the near future. Launching a satellite is not trivial, you have to make sure its not going to break apart, or damage other payloads on the way out of its container. Look up ISBN: 047075012X . You have to make sure its not going to outgass because volatile compounds evaporate and can cause problems. You have to use materials that can withstand the rigors of space, atomic oxygen and radiation can be rough on most materials. Plus some materials like PVC will evaporate in a vacuum. Another problem is ensuring you have enough battery and solar power to support your payload. You have to make sure you payload will not shake apart on the way up (rockets are very very bumpy rides). The satellite should have an attributed and control system to make sure it can orient itself in the right direction (for your solar cells and radio). And last but not least is the radio and comm system. A ground station is needed and the appropriate radio frequencies used (if you want anything fast you have to get a license from the gov, this is very difficult). The satellite itself needs to have a good antenna (if you have any nulls in your antenna pattern then you won't be able to communicate with it when the null is pointed at you. Oh, and if you put a camera on it the NOAA has to know about it and approve of your data (really stupid, but that's the way the government is). Anyway I could go on for a long time... Building a satellite requires people from many different disciplines to pull it off. Unless you are going for insanely simple you would have to have a group of people to accomplish the task. If there is available access and launch costs come down I could see a few hobbyists groups pulling it off in 10 or so years if they can clear all of the governmental hoops. I won't believe any commercial venture claiming that they will launch cubesats (or tubesats []) until they actually do.

    • by Dishwasha (125561)

      A fantastic, knowledgeable, and extensive response to my question. Thank you for all the fair warning.

  • If you want to get an idea of what's involved, have a look at the FunCube project - []

    It got back from vibration testing in early November - []

  • by Quila (201335)

    Hey, some guy just built a helicopter, why not the first Lego satellite?

  • As the AmSat Guys, they have huge amounts of experience building micro satellites (and deploying them).
  • Professor James Cutler: []
    RAX: []

    Prof. Cutler works on novel nanosats and how to streamline the nanosat process. He will probably push you off to his students, but I am sure they can point you in a better direction, what sort of commerical off the shelf (COTS) parts you can get and applicable restrictions.

I have yet to see any problem, however complicated, which, when you looked at it in the right way, did not become still more complicated. -- Poul Anderson