Could a cubesat be propelled to the moon?












4












$begingroup$


Is it possible with current technologies to propel a cubesat, which is launched from Earth, to the moon?



If current propulsion systems are able to do so, how do I continue the research in this topic and what calculations do I have to do to to continue?










share|improve this question







New contributor




reason1337 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$












  • $begingroup$
    It may be helpful to change the title to reflect your question better. Do you mean for the cubesat to be carried by a larger rocket, or for the cubesat to propel itself? If the latter, would it be from low Earth orbit? You've gotten answers that address both possibilities but clearing the title up would help future viewers of this question.
    $endgroup$
    – ben
    50 mins ago


















4












$begingroup$


Is it possible with current technologies to propel a cubesat, which is launched from Earth, to the moon?



If current propulsion systems are able to do so, how do I continue the research in this topic and what calculations do I have to do to to continue?










share|improve this question







New contributor




reason1337 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$












  • $begingroup$
    It may be helpful to change the title to reflect your question better. Do you mean for the cubesat to be carried by a larger rocket, or for the cubesat to propel itself? If the latter, would it be from low Earth orbit? You've gotten answers that address both possibilities but clearing the title up would help future viewers of this question.
    $endgroup$
    – ben
    50 mins ago
















4












4








4





$begingroup$


Is it possible with current technologies to propel a cubesat, which is launched from Earth, to the moon?



If current propulsion systems are able to do so, how do I continue the research in this topic and what calculations do I have to do to to continue?










share|improve this question







New contributor




reason1337 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




Is it possible with current technologies to propel a cubesat, which is launched from Earth, to the moon?



If current propulsion systems are able to do so, how do I continue the research in this topic and what calculations do I have to do to to continue?







propulsion cubesat






share|improve this question







New contributor




reason1337 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question







New contributor




reason1337 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question






New contributor




reason1337 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 6 hours ago









reason1337reason1337

211




211




New contributor




reason1337 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





reason1337 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






reason1337 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • $begingroup$
    It may be helpful to change the title to reflect your question better. Do you mean for the cubesat to be carried by a larger rocket, or for the cubesat to propel itself? If the latter, would it be from low Earth orbit? You've gotten answers that address both possibilities but clearing the title up would help future viewers of this question.
    $endgroup$
    – ben
    50 mins ago




















  • $begingroup$
    It may be helpful to change the title to reflect your question better. Do you mean for the cubesat to be carried by a larger rocket, or for the cubesat to propel itself? If the latter, would it be from low Earth orbit? You've gotten answers that address both possibilities but clearing the title up would help future viewers of this question.
    $endgroup$
    – ben
    50 mins ago


















$begingroup$
It may be helpful to change the title to reflect your question better. Do you mean for the cubesat to be carried by a larger rocket, or for the cubesat to propel itself? If the latter, would it be from low Earth orbit? You've gotten answers that address both possibilities but clearing the title up would help future viewers of this question.
$endgroup$
– ben
50 mins ago






$begingroup$
It may be helpful to change the title to reflect your question better. Do you mean for the cubesat to be carried by a larger rocket, or for the cubesat to propel itself? If the latter, would it be from low Earth orbit? You've gotten answers that address both possibilities but clearing the title up would help future viewers of this question.
$endgroup$
– ben
50 mins ago












3 Answers
3






active

oldest

votes


















2












$begingroup$

Very Possible



Cubesats are small - typically the base cube is 10 cm square and under 1.5kg and larger cubesats can be made of combinations of this base size. Much larger spacecraft have been sent to the moon, and I imagine there are any number of possible launchers and propulsion systems to allow this. In fact, multiple groups are currently working on it:




  • ESA Contest

  • Vermont Technical College

  • JPL


Cubesats have already been to Mars, as part of the InSight lander mission.



Self Propelled



It's not clear from your question if you are asking about a self propelled cubesat, possibly starting at LEO? If so, check this recent paper out. A lot of the necessary equations are explained within. The concept of cubesats with significant propulsion capabilities is newer, but presumably one could add modules containing enough fuel for a cubesat to get itself to the moon.



What Do You Need To Study?



Maybe start with the vis viva equation and the rocket equation and their respective formulations. This is a decent primer on orbital mechanics if you are starting completely from scratch.






share|improve this answer









$endgroup$









  • 1




    $begingroup$
    +1 That's a really interesting review paper on cubesat electric propulsion!
    $endgroup$
    – uhoh
    4 hours ago





















2












$begingroup$

Yes, but it has not been done yet.



NASA is currently sending three CubeSat missions I know of to the moon on EM-1 sometime in 2020 (according to current estimates of the SLS timeline). I believe they are all 6U spacecraft.
http://exploredeepspace.com/news/the-cubesats-of-slss-em-1/



The three missions are:




  • LunaH: http://lunahmap.asu.edu/

  • Lunar: IceCube https://en.wikipedia.org/wiki/Lunar_IceCube

  • SkyFire: https://en.wikipedia.org/wiki/SkyFire_(spacecraft)


All three will use solar-electric propulsion to change orbits. Only LunaH and Lunar IceCube will actually establish orbits around the moon though.



Further study of orbital mechanics will help in evaluating the trade-offs between the delta-v provided by the launch vehicle, solar power systems, and low thrust trajectory optimization.






share|improve this answer











$endgroup$





















    2












    $begingroup$

    Let's look at some possible examples, building on @ben's answer and @ Knudsen's answer.



    We know that the MarCo cubesats were able to navigate from Earth to Mars, with




    • attitude control via reaction wheels and cold gas thrusters

    • science data and image collection

    • communication directly with Earth via a unique pop-up flat high gain antenna

    • 70W of solar power at 1 AU via two deployable solar panels plus battery storage

    • standard 6U form factor


    for more see this answer and links therein.



    So let's adopt the MarCo design. They didn't provide their own propulsion, so let's add a propulsion system directly to MarCo's 6U, 14kg initial configuration, and call it 10U and 22 kg. The extra 4U volume is mostly for engines and extra propellant, the extra 8 kg mass budget is for engines and additional solar panels for more electric power, especially out near Mars and a whole bunch more propellant!



    Looking for at least apparently existing cubesat electric propulsion systems that you could put in a 3U cubesat today (or soon), the first one that came up in my search is the IFM Nano Thruster for CubeSats. I am sure thee are other options out there, let's just use this as an example. According to that page:



    Dynamic thrust range        10 μN to 0.5 mN
    Nominal thrust 350 μN
    Specific impulse 2,000 to 5000 s
    Propellant mass 250 g
    Total impulse more than 5,000 Ns
    Power at nominal thrust 35 W incl. neutralizer


    Our cubesat will have enough electric power for two engines at 1 AU, since we've expanded the form factor by 4 U and mass budget by 8 kg will allow for larger solar panels.



    Our two off-the-shelf engines with 250 g propellant tanks each can provide a total impulse of as much as 10,000 Newton seconds. With an average mass of about 20 kg, that only provides a delta-v of 500 m/s. But how much do we need?



    Luckily there's an existing mission that addresses this already! Answers to Going from LEO to lunar using only low-thrust ion propulsion - can it be done? say that the SMART-1 mission has done this already!



    According to that article the propulsion system used to provide a trajectory from GTO to the Moon (crash landing) demonstrated a total delta-v of about 3,900 m/s.



    Luckily we'd added 8kg to our mass budget, so if we'd added an extra 5 kg of propellant we'd have a total impulse of 100,000 Newton seconds and a delta-v of about 5,000 m/s.



    Conclusion:



    A back-of-the-envelope calculation starting with a MarCo-like cubesat with demonstrated capability of going from Earth all the way to Mars, augmented from 6U 14 kg to 10U 22 kg with two existing engine designs and another 5 kg of propellant, we can get from GTO to the Moon using solar-electric propulsion.



    The extra delta-v allows for maneuvering near the Moon and doing a bit of sight-seeing and selfie-taking.



    Alternatively you could use the extra delta-v to boost yourself from LEO to GTO, allowing for a more standard cubesat deployment option as long as the inclination were not too high. That would probably need another few kg of propellant, so it's marginal. Best way to proceed would be to piggy-back on one of the many existing launches to GTO in a similar way to how the MarCo's piggy-backed to the transfer orbit to Mars.



    MarCO: Mars Cube One piggy-backing to Mars



    Source: MarCO: Mars Cube One





    below: Source: Emily Lakdawalla's Planetary Society blogpost MarCO: CubeSats to Mars!



    Found in this answer.




    MARCO SPACECRAFT: Engineer Joel Steinkraus stands with both of the Mars Cube One (MarCO) spacecraft at NASA's Jet Propulsion Laboratory. The one on the left is folded up the way it will be stowed on its rocket; the one on the right has its solar panels fully deployed, along with its high-gain antenna on top.




    MARCO SPACECRAFT from Planetary Society blogpost





    An alternative, future propulsion system with even higher Isp and therefore needing less propellant mass:




    • http://neumannspace.com/science/

    • https://spacenews.com/more-startups-are-pursuing-cubesats-with-electric-thrusters/

    • Will the Neumann drive start testing aboard the ISS some time in 2018?

    • Which way will the Neumann drive (on the ISS) point, what will be its maximum possible thrust?




    An encouraging video:











    share|improve this answer











    $endgroup$









    • 1




      $begingroup$
      Excellent answer! I did not want to venture into the math but my guess was the required size would be much larger than 10U. Turns out this is a really attainable mission for a group with a (relatively) small grant.
      $endgroup$
      – ben
      54 mins ago










    • $begingroup$
      @ben I think it's at least a few million $US just to buy all of the parts, put them together, and do some basic tests. Maybe you can save some if you build every component from scratch, but that's not going to be so reliable. There's also significant expense in making them spaceworthy and to do all of the logistics of preparing them for launch, obtaining all of the permission. This doesn't include an actual launch, which for such a large cubesat would require special arrangements. If that's still considered (relatively) small, then you're good to go!
      $endgroup$
      – uhoh
      49 mins ago








    • 1




      $begingroup$
      Oh no doubt this is a subjective statement. No one is doing this in their garage for instance. It's just cool to think that we are at a point where for instance a small university research group could actually attain enough funding to send a mission to the moon. Of course this would also require hitching a ride (like you say, a bit complex with the size) or securing NASA or equivalent support for launch. It's cool to watch space become more accessible. Even if they are baby steps they are steps in the right direction.
      $endgroup$
      – ben
      36 mins ago








    • 1




      $begingroup$
      @ben absolutely! This answer is base on a proven design. No doubt if you started here and went back to the drawing board you cold find lower cost solutions. Comms would be easier to implement since the Moon is a lot closer than Mars. Remember that the radiation is higher than in LEO, so all of the electronics will have to be somewhat radiation resistant and tolerant to regular faults and crashes, but that's doable with redundancy which is probably cheaper than top-of-the-line rad-hard electronics. The triple-junction solar cells are really pricey, lower efficiency silicon will lower cost.
      $endgroup$
      – uhoh
      23 mins ago











    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "508"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });






    reason1337 is a new contributor. Be nice, and check out our Code of Conduct.










    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fspace.stackexchange.com%2fquestions%2f34767%2fcould-a-cubesat-be-propelled-to-the-moon%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    2












    $begingroup$

    Very Possible



    Cubesats are small - typically the base cube is 10 cm square and under 1.5kg and larger cubesats can be made of combinations of this base size. Much larger spacecraft have been sent to the moon, and I imagine there are any number of possible launchers and propulsion systems to allow this. In fact, multiple groups are currently working on it:




    • ESA Contest

    • Vermont Technical College

    • JPL


    Cubesats have already been to Mars, as part of the InSight lander mission.



    Self Propelled



    It's not clear from your question if you are asking about a self propelled cubesat, possibly starting at LEO? If so, check this recent paper out. A lot of the necessary equations are explained within. The concept of cubesats with significant propulsion capabilities is newer, but presumably one could add modules containing enough fuel for a cubesat to get itself to the moon.



    What Do You Need To Study?



    Maybe start with the vis viva equation and the rocket equation and their respective formulations. This is a decent primer on orbital mechanics if you are starting completely from scratch.






    share|improve this answer









    $endgroup$









    • 1




      $begingroup$
      +1 That's a really interesting review paper on cubesat electric propulsion!
      $endgroup$
      – uhoh
      4 hours ago


















    2












    $begingroup$

    Very Possible



    Cubesats are small - typically the base cube is 10 cm square and under 1.5kg and larger cubesats can be made of combinations of this base size. Much larger spacecraft have been sent to the moon, and I imagine there are any number of possible launchers and propulsion systems to allow this. In fact, multiple groups are currently working on it:




    • ESA Contest

    • Vermont Technical College

    • JPL


    Cubesats have already been to Mars, as part of the InSight lander mission.



    Self Propelled



    It's not clear from your question if you are asking about a self propelled cubesat, possibly starting at LEO? If so, check this recent paper out. A lot of the necessary equations are explained within. The concept of cubesats with significant propulsion capabilities is newer, but presumably one could add modules containing enough fuel for a cubesat to get itself to the moon.



    What Do You Need To Study?



    Maybe start with the vis viva equation and the rocket equation and their respective formulations. This is a decent primer on orbital mechanics if you are starting completely from scratch.






    share|improve this answer









    $endgroup$









    • 1




      $begingroup$
      +1 That's a really interesting review paper on cubesat electric propulsion!
      $endgroup$
      – uhoh
      4 hours ago
















    2












    2








    2





    $begingroup$

    Very Possible



    Cubesats are small - typically the base cube is 10 cm square and under 1.5kg and larger cubesats can be made of combinations of this base size. Much larger spacecraft have been sent to the moon, and I imagine there are any number of possible launchers and propulsion systems to allow this. In fact, multiple groups are currently working on it:




    • ESA Contest

    • Vermont Technical College

    • JPL


    Cubesats have already been to Mars, as part of the InSight lander mission.



    Self Propelled



    It's not clear from your question if you are asking about a self propelled cubesat, possibly starting at LEO? If so, check this recent paper out. A lot of the necessary equations are explained within. The concept of cubesats with significant propulsion capabilities is newer, but presumably one could add modules containing enough fuel for a cubesat to get itself to the moon.



    What Do You Need To Study?



    Maybe start with the vis viva equation and the rocket equation and their respective formulations. This is a decent primer on orbital mechanics if you are starting completely from scratch.






    share|improve this answer









    $endgroup$



    Very Possible



    Cubesats are small - typically the base cube is 10 cm square and under 1.5kg and larger cubesats can be made of combinations of this base size. Much larger spacecraft have been sent to the moon, and I imagine there are any number of possible launchers and propulsion systems to allow this. In fact, multiple groups are currently working on it:




    • ESA Contest

    • Vermont Technical College

    • JPL


    Cubesats have already been to Mars, as part of the InSight lander mission.



    Self Propelled



    It's not clear from your question if you are asking about a self propelled cubesat, possibly starting at LEO? If so, check this recent paper out. A lot of the necessary equations are explained within. The concept of cubesats with significant propulsion capabilities is newer, but presumably one could add modules containing enough fuel for a cubesat to get itself to the moon.



    What Do You Need To Study?



    Maybe start with the vis viva equation and the rocket equation and their respective formulations. This is a decent primer on orbital mechanics if you are starting completely from scratch.







    share|improve this answer












    share|improve this answer



    share|improve this answer










    answered 5 hours ago









    benben

    411210




    411210








    • 1




      $begingroup$
      +1 That's a really interesting review paper on cubesat electric propulsion!
      $endgroup$
      – uhoh
      4 hours ago
















    • 1




      $begingroup$
      +1 That's a really interesting review paper on cubesat electric propulsion!
      $endgroup$
      – uhoh
      4 hours ago










    1




    1




    $begingroup$
    +1 That's a really interesting review paper on cubesat electric propulsion!
    $endgroup$
    – uhoh
    4 hours ago






    $begingroup$
    +1 That's a really interesting review paper on cubesat electric propulsion!
    $endgroup$
    – uhoh
    4 hours ago













    2












    $begingroup$

    Yes, but it has not been done yet.



    NASA is currently sending three CubeSat missions I know of to the moon on EM-1 sometime in 2020 (according to current estimates of the SLS timeline). I believe they are all 6U spacecraft.
    http://exploredeepspace.com/news/the-cubesats-of-slss-em-1/



    The three missions are:




    • LunaH: http://lunahmap.asu.edu/

    • Lunar: IceCube https://en.wikipedia.org/wiki/Lunar_IceCube

    • SkyFire: https://en.wikipedia.org/wiki/SkyFire_(spacecraft)


    All three will use solar-electric propulsion to change orbits. Only LunaH and Lunar IceCube will actually establish orbits around the moon though.



    Further study of orbital mechanics will help in evaluating the trade-offs between the delta-v provided by the launch vehicle, solar power systems, and low thrust trajectory optimization.






    share|improve this answer











    $endgroup$


















      2












      $begingroup$

      Yes, but it has not been done yet.



      NASA is currently sending three CubeSat missions I know of to the moon on EM-1 sometime in 2020 (according to current estimates of the SLS timeline). I believe they are all 6U spacecraft.
      http://exploredeepspace.com/news/the-cubesats-of-slss-em-1/



      The three missions are:




      • LunaH: http://lunahmap.asu.edu/

      • Lunar: IceCube https://en.wikipedia.org/wiki/Lunar_IceCube

      • SkyFire: https://en.wikipedia.org/wiki/SkyFire_(spacecraft)


      All three will use solar-electric propulsion to change orbits. Only LunaH and Lunar IceCube will actually establish orbits around the moon though.



      Further study of orbital mechanics will help in evaluating the trade-offs between the delta-v provided by the launch vehicle, solar power systems, and low thrust trajectory optimization.






      share|improve this answer











      $endgroup$
















        2












        2








        2





        $begingroup$

        Yes, but it has not been done yet.



        NASA is currently sending three CubeSat missions I know of to the moon on EM-1 sometime in 2020 (according to current estimates of the SLS timeline). I believe they are all 6U spacecraft.
        http://exploredeepspace.com/news/the-cubesats-of-slss-em-1/



        The three missions are:




        • LunaH: http://lunahmap.asu.edu/

        • Lunar: IceCube https://en.wikipedia.org/wiki/Lunar_IceCube

        • SkyFire: https://en.wikipedia.org/wiki/SkyFire_(spacecraft)


        All three will use solar-electric propulsion to change orbits. Only LunaH and Lunar IceCube will actually establish orbits around the moon though.



        Further study of orbital mechanics will help in evaluating the trade-offs between the delta-v provided by the launch vehicle, solar power systems, and low thrust trajectory optimization.






        share|improve this answer











        $endgroup$



        Yes, but it has not been done yet.



        NASA is currently sending three CubeSat missions I know of to the moon on EM-1 sometime in 2020 (according to current estimates of the SLS timeline). I believe they are all 6U spacecraft.
        http://exploredeepspace.com/news/the-cubesats-of-slss-em-1/



        The three missions are:




        • LunaH: http://lunahmap.asu.edu/

        • Lunar: IceCube https://en.wikipedia.org/wiki/Lunar_IceCube

        • SkyFire: https://en.wikipedia.org/wiki/SkyFire_(spacecraft)


        All three will use solar-electric propulsion to change orbits. Only LunaH and Lunar IceCube will actually establish orbits around the moon though.



        Further study of orbital mechanics will help in evaluating the trade-offs between the delta-v provided by the launch vehicle, solar power systems, and low thrust trajectory optimization.







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited 3 hours ago









        uhoh

        38.1k18140487




        38.1k18140487










        answered 4 hours ago









        KnudsenKnudsen

        795




        795























            2












            $begingroup$

            Let's look at some possible examples, building on @ben's answer and @ Knudsen's answer.



            We know that the MarCo cubesats were able to navigate from Earth to Mars, with




            • attitude control via reaction wheels and cold gas thrusters

            • science data and image collection

            • communication directly with Earth via a unique pop-up flat high gain antenna

            • 70W of solar power at 1 AU via two deployable solar panels plus battery storage

            • standard 6U form factor


            for more see this answer and links therein.



            So let's adopt the MarCo design. They didn't provide their own propulsion, so let's add a propulsion system directly to MarCo's 6U, 14kg initial configuration, and call it 10U and 22 kg. The extra 4U volume is mostly for engines and extra propellant, the extra 8 kg mass budget is for engines and additional solar panels for more electric power, especially out near Mars and a whole bunch more propellant!



            Looking for at least apparently existing cubesat electric propulsion systems that you could put in a 3U cubesat today (or soon), the first one that came up in my search is the IFM Nano Thruster for CubeSats. I am sure thee are other options out there, let's just use this as an example. According to that page:



            Dynamic thrust range        10 μN to 0.5 mN
            Nominal thrust 350 μN
            Specific impulse 2,000 to 5000 s
            Propellant mass 250 g
            Total impulse more than 5,000 Ns
            Power at nominal thrust 35 W incl. neutralizer


            Our cubesat will have enough electric power for two engines at 1 AU, since we've expanded the form factor by 4 U and mass budget by 8 kg will allow for larger solar panels.



            Our two off-the-shelf engines with 250 g propellant tanks each can provide a total impulse of as much as 10,000 Newton seconds. With an average mass of about 20 kg, that only provides a delta-v of 500 m/s. But how much do we need?



            Luckily there's an existing mission that addresses this already! Answers to Going from LEO to lunar using only low-thrust ion propulsion - can it be done? say that the SMART-1 mission has done this already!



            According to that article the propulsion system used to provide a trajectory from GTO to the Moon (crash landing) demonstrated a total delta-v of about 3,900 m/s.



            Luckily we'd added 8kg to our mass budget, so if we'd added an extra 5 kg of propellant we'd have a total impulse of 100,000 Newton seconds and a delta-v of about 5,000 m/s.



            Conclusion:



            A back-of-the-envelope calculation starting with a MarCo-like cubesat with demonstrated capability of going from Earth all the way to Mars, augmented from 6U 14 kg to 10U 22 kg with two existing engine designs and another 5 kg of propellant, we can get from GTO to the Moon using solar-electric propulsion.



            The extra delta-v allows for maneuvering near the Moon and doing a bit of sight-seeing and selfie-taking.



            Alternatively you could use the extra delta-v to boost yourself from LEO to GTO, allowing for a more standard cubesat deployment option as long as the inclination were not too high. That would probably need another few kg of propellant, so it's marginal. Best way to proceed would be to piggy-back on one of the many existing launches to GTO in a similar way to how the MarCo's piggy-backed to the transfer orbit to Mars.



            MarCO: Mars Cube One piggy-backing to Mars



            Source: MarCO: Mars Cube One





            below: Source: Emily Lakdawalla's Planetary Society blogpost MarCO: CubeSats to Mars!



            Found in this answer.




            MARCO SPACECRAFT: Engineer Joel Steinkraus stands with both of the Mars Cube One (MarCO) spacecraft at NASA's Jet Propulsion Laboratory. The one on the left is folded up the way it will be stowed on its rocket; the one on the right has its solar panels fully deployed, along with its high-gain antenna on top.




            MARCO SPACECRAFT from Planetary Society blogpost





            An alternative, future propulsion system with even higher Isp and therefore needing less propellant mass:




            • http://neumannspace.com/science/

            • https://spacenews.com/more-startups-are-pursuing-cubesats-with-electric-thrusters/

            • Will the Neumann drive start testing aboard the ISS some time in 2018?

            • Which way will the Neumann drive (on the ISS) point, what will be its maximum possible thrust?




            An encouraging video:











            share|improve this answer











            $endgroup$









            • 1




              $begingroup$
              Excellent answer! I did not want to venture into the math but my guess was the required size would be much larger than 10U. Turns out this is a really attainable mission for a group with a (relatively) small grant.
              $endgroup$
              – ben
              54 mins ago










            • $begingroup$
              @ben I think it's at least a few million $US just to buy all of the parts, put them together, and do some basic tests. Maybe you can save some if you build every component from scratch, but that's not going to be so reliable. There's also significant expense in making them spaceworthy and to do all of the logistics of preparing them for launch, obtaining all of the permission. This doesn't include an actual launch, which for such a large cubesat would require special arrangements. If that's still considered (relatively) small, then you're good to go!
              $endgroup$
              – uhoh
              49 mins ago








            • 1




              $begingroup$
              Oh no doubt this is a subjective statement. No one is doing this in their garage for instance. It's just cool to think that we are at a point where for instance a small university research group could actually attain enough funding to send a mission to the moon. Of course this would also require hitching a ride (like you say, a bit complex with the size) or securing NASA or equivalent support for launch. It's cool to watch space become more accessible. Even if they are baby steps they are steps in the right direction.
              $endgroup$
              – ben
              36 mins ago








            • 1




              $begingroup$
              @ben absolutely! This answer is base on a proven design. No doubt if you started here and went back to the drawing board you cold find lower cost solutions. Comms would be easier to implement since the Moon is a lot closer than Mars. Remember that the radiation is higher than in LEO, so all of the electronics will have to be somewhat radiation resistant and tolerant to regular faults and crashes, but that's doable with redundancy which is probably cheaper than top-of-the-line rad-hard electronics. The triple-junction solar cells are really pricey, lower efficiency silicon will lower cost.
              $endgroup$
              – uhoh
              23 mins ago
















            2












            $begingroup$

            Let's look at some possible examples, building on @ben's answer and @ Knudsen's answer.



            We know that the MarCo cubesats were able to navigate from Earth to Mars, with




            • attitude control via reaction wheels and cold gas thrusters

            • science data and image collection

            • communication directly with Earth via a unique pop-up flat high gain antenna

            • 70W of solar power at 1 AU via two deployable solar panels plus battery storage

            • standard 6U form factor


            for more see this answer and links therein.



            So let's adopt the MarCo design. They didn't provide their own propulsion, so let's add a propulsion system directly to MarCo's 6U, 14kg initial configuration, and call it 10U and 22 kg. The extra 4U volume is mostly for engines and extra propellant, the extra 8 kg mass budget is for engines and additional solar panels for more electric power, especially out near Mars and a whole bunch more propellant!



            Looking for at least apparently existing cubesat electric propulsion systems that you could put in a 3U cubesat today (or soon), the first one that came up in my search is the IFM Nano Thruster for CubeSats. I am sure thee are other options out there, let's just use this as an example. According to that page:



            Dynamic thrust range        10 μN to 0.5 mN
            Nominal thrust 350 μN
            Specific impulse 2,000 to 5000 s
            Propellant mass 250 g
            Total impulse more than 5,000 Ns
            Power at nominal thrust 35 W incl. neutralizer


            Our cubesat will have enough electric power for two engines at 1 AU, since we've expanded the form factor by 4 U and mass budget by 8 kg will allow for larger solar panels.



            Our two off-the-shelf engines with 250 g propellant tanks each can provide a total impulse of as much as 10,000 Newton seconds. With an average mass of about 20 kg, that only provides a delta-v of 500 m/s. But how much do we need?



            Luckily there's an existing mission that addresses this already! Answers to Going from LEO to lunar using only low-thrust ion propulsion - can it be done? say that the SMART-1 mission has done this already!



            According to that article the propulsion system used to provide a trajectory from GTO to the Moon (crash landing) demonstrated a total delta-v of about 3,900 m/s.



            Luckily we'd added 8kg to our mass budget, so if we'd added an extra 5 kg of propellant we'd have a total impulse of 100,000 Newton seconds and a delta-v of about 5,000 m/s.



            Conclusion:



            A back-of-the-envelope calculation starting with a MarCo-like cubesat with demonstrated capability of going from Earth all the way to Mars, augmented from 6U 14 kg to 10U 22 kg with two existing engine designs and another 5 kg of propellant, we can get from GTO to the Moon using solar-electric propulsion.



            The extra delta-v allows for maneuvering near the Moon and doing a bit of sight-seeing and selfie-taking.



            Alternatively you could use the extra delta-v to boost yourself from LEO to GTO, allowing for a more standard cubesat deployment option as long as the inclination were not too high. That would probably need another few kg of propellant, so it's marginal. Best way to proceed would be to piggy-back on one of the many existing launches to GTO in a similar way to how the MarCo's piggy-backed to the transfer orbit to Mars.



            MarCO: Mars Cube One piggy-backing to Mars



            Source: MarCO: Mars Cube One





            below: Source: Emily Lakdawalla's Planetary Society blogpost MarCO: CubeSats to Mars!



            Found in this answer.




            MARCO SPACECRAFT: Engineer Joel Steinkraus stands with both of the Mars Cube One (MarCO) spacecraft at NASA's Jet Propulsion Laboratory. The one on the left is folded up the way it will be stowed on its rocket; the one on the right has its solar panels fully deployed, along with its high-gain antenna on top.




            MARCO SPACECRAFT from Planetary Society blogpost





            An alternative, future propulsion system with even higher Isp and therefore needing less propellant mass:




            • http://neumannspace.com/science/

            • https://spacenews.com/more-startups-are-pursuing-cubesats-with-electric-thrusters/

            • Will the Neumann drive start testing aboard the ISS some time in 2018?

            • Which way will the Neumann drive (on the ISS) point, what will be its maximum possible thrust?




            An encouraging video:











            share|improve this answer











            $endgroup$









            • 1




              $begingroup$
              Excellent answer! I did not want to venture into the math but my guess was the required size would be much larger than 10U. Turns out this is a really attainable mission for a group with a (relatively) small grant.
              $endgroup$
              – ben
              54 mins ago










            • $begingroup$
              @ben I think it's at least a few million $US just to buy all of the parts, put them together, and do some basic tests. Maybe you can save some if you build every component from scratch, but that's not going to be so reliable. There's also significant expense in making them spaceworthy and to do all of the logistics of preparing them for launch, obtaining all of the permission. This doesn't include an actual launch, which for such a large cubesat would require special arrangements. If that's still considered (relatively) small, then you're good to go!
              $endgroup$
              – uhoh
              49 mins ago








            • 1




              $begingroup$
              Oh no doubt this is a subjective statement. No one is doing this in their garage for instance. It's just cool to think that we are at a point where for instance a small university research group could actually attain enough funding to send a mission to the moon. Of course this would also require hitching a ride (like you say, a bit complex with the size) or securing NASA or equivalent support for launch. It's cool to watch space become more accessible. Even if they are baby steps they are steps in the right direction.
              $endgroup$
              – ben
              36 mins ago








            • 1




              $begingroup$
              @ben absolutely! This answer is base on a proven design. No doubt if you started here and went back to the drawing board you cold find lower cost solutions. Comms would be easier to implement since the Moon is a lot closer than Mars. Remember that the radiation is higher than in LEO, so all of the electronics will have to be somewhat radiation resistant and tolerant to regular faults and crashes, but that's doable with redundancy which is probably cheaper than top-of-the-line rad-hard electronics. The triple-junction solar cells are really pricey, lower efficiency silicon will lower cost.
              $endgroup$
              – uhoh
              23 mins ago














            2












            2








            2





            $begingroup$

            Let's look at some possible examples, building on @ben's answer and @ Knudsen's answer.



            We know that the MarCo cubesats were able to navigate from Earth to Mars, with




            • attitude control via reaction wheels and cold gas thrusters

            • science data and image collection

            • communication directly with Earth via a unique pop-up flat high gain antenna

            • 70W of solar power at 1 AU via two deployable solar panels plus battery storage

            • standard 6U form factor


            for more see this answer and links therein.



            So let's adopt the MarCo design. They didn't provide their own propulsion, so let's add a propulsion system directly to MarCo's 6U, 14kg initial configuration, and call it 10U and 22 kg. The extra 4U volume is mostly for engines and extra propellant, the extra 8 kg mass budget is for engines and additional solar panels for more electric power, especially out near Mars and a whole bunch more propellant!



            Looking for at least apparently existing cubesat electric propulsion systems that you could put in a 3U cubesat today (or soon), the first one that came up in my search is the IFM Nano Thruster for CubeSats. I am sure thee are other options out there, let's just use this as an example. According to that page:



            Dynamic thrust range        10 μN to 0.5 mN
            Nominal thrust 350 μN
            Specific impulse 2,000 to 5000 s
            Propellant mass 250 g
            Total impulse more than 5,000 Ns
            Power at nominal thrust 35 W incl. neutralizer


            Our cubesat will have enough electric power for two engines at 1 AU, since we've expanded the form factor by 4 U and mass budget by 8 kg will allow for larger solar panels.



            Our two off-the-shelf engines with 250 g propellant tanks each can provide a total impulse of as much as 10,000 Newton seconds. With an average mass of about 20 kg, that only provides a delta-v of 500 m/s. But how much do we need?



            Luckily there's an existing mission that addresses this already! Answers to Going from LEO to lunar using only low-thrust ion propulsion - can it be done? say that the SMART-1 mission has done this already!



            According to that article the propulsion system used to provide a trajectory from GTO to the Moon (crash landing) demonstrated a total delta-v of about 3,900 m/s.



            Luckily we'd added 8kg to our mass budget, so if we'd added an extra 5 kg of propellant we'd have a total impulse of 100,000 Newton seconds and a delta-v of about 5,000 m/s.



            Conclusion:



            A back-of-the-envelope calculation starting with a MarCo-like cubesat with demonstrated capability of going from Earth all the way to Mars, augmented from 6U 14 kg to 10U 22 kg with two existing engine designs and another 5 kg of propellant, we can get from GTO to the Moon using solar-electric propulsion.



            The extra delta-v allows for maneuvering near the Moon and doing a bit of sight-seeing and selfie-taking.



            Alternatively you could use the extra delta-v to boost yourself from LEO to GTO, allowing for a more standard cubesat deployment option as long as the inclination were not too high. That would probably need another few kg of propellant, so it's marginal. Best way to proceed would be to piggy-back on one of the many existing launches to GTO in a similar way to how the MarCo's piggy-backed to the transfer orbit to Mars.



            MarCO: Mars Cube One piggy-backing to Mars



            Source: MarCO: Mars Cube One





            below: Source: Emily Lakdawalla's Planetary Society blogpost MarCO: CubeSats to Mars!



            Found in this answer.




            MARCO SPACECRAFT: Engineer Joel Steinkraus stands with both of the Mars Cube One (MarCO) spacecraft at NASA's Jet Propulsion Laboratory. The one on the left is folded up the way it will be stowed on its rocket; the one on the right has its solar panels fully deployed, along with its high-gain antenna on top.




            MARCO SPACECRAFT from Planetary Society blogpost





            An alternative, future propulsion system with even higher Isp and therefore needing less propellant mass:




            • http://neumannspace.com/science/

            • https://spacenews.com/more-startups-are-pursuing-cubesats-with-electric-thrusters/

            • Will the Neumann drive start testing aboard the ISS some time in 2018?

            • Which way will the Neumann drive (on the ISS) point, what will be its maximum possible thrust?




            An encouraging video:











            share|improve this answer











            $endgroup$



            Let's look at some possible examples, building on @ben's answer and @ Knudsen's answer.



            We know that the MarCo cubesats were able to navigate from Earth to Mars, with




            • attitude control via reaction wheels and cold gas thrusters

            • science data and image collection

            • communication directly with Earth via a unique pop-up flat high gain antenna

            • 70W of solar power at 1 AU via two deployable solar panels plus battery storage

            • standard 6U form factor


            for more see this answer and links therein.



            So let's adopt the MarCo design. They didn't provide their own propulsion, so let's add a propulsion system directly to MarCo's 6U, 14kg initial configuration, and call it 10U and 22 kg. The extra 4U volume is mostly for engines and extra propellant, the extra 8 kg mass budget is for engines and additional solar panels for more electric power, especially out near Mars and a whole bunch more propellant!



            Looking for at least apparently existing cubesat electric propulsion systems that you could put in a 3U cubesat today (or soon), the first one that came up in my search is the IFM Nano Thruster for CubeSats. I am sure thee are other options out there, let's just use this as an example. According to that page:



            Dynamic thrust range        10 μN to 0.5 mN
            Nominal thrust 350 μN
            Specific impulse 2,000 to 5000 s
            Propellant mass 250 g
            Total impulse more than 5,000 Ns
            Power at nominal thrust 35 W incl. neutralizer


            Our cubesat will have enough electric power for two engines at 1 AU, since we've expanded the form factor by 4 U and mass budget by 8 kg will allow for larger solar panels.



            Our two off-the-shelf engines with 250 g propellant tanks each can provide a total impulse of as much as 10,000 Newton seconds. With an average mass of about 20 kg, that only provides a delta-v of 500 m/s. But how much do we need?



            Luckily there's an existing mission that addresses this already! Answers to Going from LEO to lunar using only low-thrust ion propulsion - can it be done? say that the SMART-1 mission has done this already!



            According to that article the propulsion system used to provide a trajectory from GTO to the Moon (crash landing) demonstrated a total delta-v of about 3,900 m/s.



            Luckily we'd added 8kg to our mass budget, so if we'd added an extra 5 kg of propellant we'd have a total impulse of 100,000 Newton seconds and a delta-v of about 5,000 m/s.



            Conclusion:



            A back-of-the-envelope calculation starting with a MarCo-like cubesat with demonstrated capability of going from Earth all the way to Mars, augmented from 6U 14 kg to 10U 22 kg with two existing engine designs and another 5 kg of propellant, we can get from GTO to the Moon using solar-electric propulsion.



            The extra delta-v allows for maneuvering near the Moon and doing a bit of sight-seeing and selfie-taking.



            Alternatively you could use the extra delta-v to boost yourself from LEO to GTO, allowing for a more standard cubesat deployment option as long as the inclination were not too high. That would probably need another few kg of propellant, so it's marginal. Best way to proceed would be to piggy-back on one of the many existing launches to GTO in a similar way to how the MarCo's piggy-backed to the transfer orbit to Mars.



            MarCO: Mars Cube One piggy-backing to Mars



            Source: MarCO: Mars Cube One





            below: Source: Emily Lakdawalla's Planetary Society blogpost MarCO: CubeSats to Mars!



            Found in this answer.




            MARCO SPACECRAFT: Engineer Joel Steinkraus stands with both of the Mars Cube One (MarCO) spacecraft at NASA's Jet Propulsion Laboratory. The one on the left is folded up the way it will be stowed on its rocket; the one on the right has its solar panels fully deployed, along with its high-gain antenna on top.




            MARCO SPACECRAFT from Planetary Society blogpost





            An alternative, future propulsion system with even higher Isp and therefore needing less propellant mass:




            • http://neumannspace.com/science/

            • https://spacenews.com/more-startups-are-pursuing-cubesats-with-electric-thrusters/

            • Will the Neumann drive start testing aboard the ISS some time in 2018?

            • Which way will the Neumann drive (on the ISS) point, what will be its maximum possible thrust?




            An encouraging video:




















            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited 2 hours ago

























            answered 3 hours ago









            uhohuhoh

            38.1k18140487




            38.1k18140487








            • 1




              $begingroup$
              Excellent answer! I did not want to venture into the math but my guess was the required size would be much larger than 10U. Turns out this is a really attainable mission for a group with a (relatively) small grant.
              $endgroup$
              – ben
              54 mins ago










            • $begingroup$
              @ben I think it's at least a few million $US just to buy all of the parts, put them together, and do some basic tests. Maybe you can save some if you build every component from scratch, but that's not going to be so reliable. There's also significant expense in making them spaceworthy and to do all of the logistics of preparing them for launch, obtaining all of the permission. This doesn't include an actual launch, which for such a large cubesat would require special arrangements. If that's still considered (relatively) small, then you're good to go!
              $endgroup$
              – uhoh
              49 mins ago








            • 1




              $begingroup$
              Oh no doubt this is a subjective statement. No one is doing this in their garage for instance. It's just cool to think that we are at a point where for instance a small university research group could actually attain enough funding to send a mission to the moon. Of course this would also require hitching a ride (like you say, a bit complex with the size) or securing NASA or equivalent support for launch. It's cool to watch space become more accessible. Even if they are baby steps they are steps in the right direction.
              $endgroup$
              – ben
              36 mins ago








            • 1




              $begingroup$
              @ben absolutely! This answer is base on a proven design. No doubt if you started here and went back to the drawing board you cold find lower cost solutions. Comms would be easier to implement since the Moon is a lot closer than Mars. Remember that the radiation is higher than in LEO, so all of the electronics will have to be somewhat radiation resistant and tolerant to regular faults and crashes, but that's doable with redundancy which is probably cheaper than top-of-the-line rad-hard electronics. The triple-junction solar cells are really pricey, lower efficiency silicon will lower cost.
              $endgroup$
              – uhoh
              23 mins ago














            • 1




              $begingroup$
              Excellent answer! I did not want to venture into the math but my guess was the required size would be much larger than 10U. Turns out this is a really attainable mission for a group with a (relatively) small grant.
              $endgroup$
              – ben
              54 mins ago










            • $begingroup$
              @ben I think it's at least a few million $US just to buy all of the parts, put them together, and do some basic tests. Maybe you can save some if you build every component from scratch, but that's not going to be so reliable. There's also significant expense in making them spaceworthy and to do all of the logistics of preparing them for launch, obtaining all of the permission. This doesn't include an actual launch, which for such a large cubesat would require special arrangements. If that's still considered (relatively) small, then you're good to go!
              $endgroup$
              – uhoh
              49 mins ago








            • 1




              $begingroup$
              Oh no doubt this is a subjective statement. No one is doing this in their garage for instance. It's just cool to think that we are at a point where for instance a small university research group could actually attain enough funding to send a mission to the moon. Of course this would also require hitching a ride (like you say, a bit complex with the size) or securing NASA or equivalent support for launch. It's cool to watch space become more accessible. Even if they are baby steps they are steps in the right direction.
              $endgroup$
              – ben
              36 mins ago








            • 1




              $begingroup$
              @ben absolutely! This answer is base on a proven design. No doubt if you started here and went back to the drawing board you cold find lower cost solutions. Comms would be easier to implement since the Moon is a lot closer than Mars. Remember that the radiation is higher than in LEO, so all of the electronics will have to be somewhat radiation resistant and tolerant to regular faults and crashes, but that's doable with redundancy which is probably cheaper than top-of-the-line rad-hard electronics. The triple-junction solar cells are really pricey, lower efficiency silicon will lower cost.
              $endgroup$
              – uhoh
              23 mins ago








            1




            1




            $begingroup$
            Excellent answer! I did not want to venture into the math but my guess was the required size would be much larger than 10U. Turns out this is a really attainable mission for a group with a (relatively) small grant.
            $endgroup$
            – ben
            54 mins ago




            $begingroup$
            Excellent answer! I did not want to venture into the math but my guess was the required size would be much larger than 10U. Turns out this is a really attainable mission for a group with a (relatively) small grant.
            $endgroup$
            – ben
            54 mins ago












            $begingroup$
            @ben I think it's at least a few million $US just to buy all of the parts, put them together, and do some basic tests. Maybe you can save some if you build every component from scratch, but that's not going to be so reliable. There's also significant expense in making them spaceworthy and to do all of the logistics of preparing them for launch, obtaining all of the permission. This doesn't include an actual launch, which for such a large cubesat would require special arrangements. If that's still considered (relatively) small, then you're good to go!
            $endgroup$
            – uhoh
            49 mins ago






            $begingroup$
            @ben I think it's at least a few million $US just to buy all of the parts, put them together, and do some basic tests. Maybe you can save some if you build every component from scratch, but that's not going to be so reliable. There's also significant expense in making them spaceworthy and to do all of the logistics of preparing them for launch, obtaining all of the permission. This doesn't include an actual launch, which for such a large cubesat would require special arrangements. If that's still considered (relatively) small, then you're good to go!
            $endgroup$
            – uhoh
            49 mins ago






            1




            1




            $begingroup$
            Oh no doubt this is a subjective statement. No one is doing this in their garage for instance. It's just cool to think that we are at a point where for instance a small university research group could actually attain enough funding to send a mission to the moon. Of course this would also require hitching a ride (like you say, a bit complex with the size) or securing NASA or equivalent support for launch. It's cool to watch space become more accessible. Even if they are baby steps they are steps in the right direction.
            $endgroup$
            – ben
            36 mins ago






            $begingroup$
            Oh no doubt this is a subjective statement. No one is doing this in their garage for instance. It's just cool to think that we are at a point where for instance a small university research group could actually attain enough funding to send a mission to the moon. Of course this would also require hitching a ride (like you say, a bit complex with the size) or securing NASA or equivalent support for launch. It's cool to watch space become more accessible. Even if they are baby steps they are steps in the right direction.
            $endgroup$
            – ben
            36 mins ago






            1




            1




            $begingroup$
            @ben absolutely! This answer is base on a proven design. No doubt if you started here and went back to the drawing board you cold find lower cost solutions. Comms would be easier to implement since the Moon is a lot closer than Mars. Remember that the radiation is higher than in LEO, so all of the electronics will have to be somewhat radiation resistant and tolerant to regular faults and crashes, but that's doable with redundancy which is probably cheaper than top-of-the-line rad-hard electronics. The triple-junction solar cells are really pricey, lower efficiency silicon will lower cost.
            $endgroup$
            – uhoh
            23 mins ago




            $begingroup$
            @ben absolutely! This answer is base on a proven design. No doubt if you started here and went back to the drawing board you cold find lower cost solutions. Comms would be easier to implement since the Moon is a lot closer than Mars. Remember that the radiation is higher than in LEO, so all of the electronics will have to be somewhat radiation resistant and tolerant to regular faults and crashes, but that's doable with redundancy which is probably cheaper than top-of-the-line rad-hard electronics. The triple-junction solar cells are really pricey, lower efficiency silicon will lower cost.
            $endgroup$
            – uhoh
            23 mins ago










            reason1337 is a new contributor. Be nice, and check out our Code of Conduct.










            draft saved

            draft discarded


















            reason1337 is a new contributor. Be nice, and check out our Code of Conduct.













            reason1337 is a new contributor. Be nice, and check out our Code of Conduct.












            reason1337 is a new contributor. Be nice, and check out our Code of Conduct.
















            Thanks for contributing an answer to Space Exploration Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fspace.stackexchange.com%2fquestions%2f34767%2fcould-a-cubesat-be-propelled-to-the-moon%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            Popular posts from this blog

            サソリ

            広島県道265号伴広島線

            Setup Asymptote in Texstudio