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Towards a solar sailboat-like technology for space based transportation (7/18/05)

While working on the gyroscope material I was reading "Mapping Mars" by Oliver Morton. Mr. Morton was talking about the theories of how the inner rocky planets were formed and why Earth was able to establish a liquid core and the others weren't. It is extremely interesting reading and helped me to understand just how lucky we struck it. I guess the other side of this debate would be just how hard is life?

Anyway, if you are still reading this you'll hopefully have heard of a dysonsphere, which was a theoretical concept of encasing a star in a huge shell or frame work to try to capture the energy of the star. Neat stuff, and it struck me that to get a massive amount of power in space it might be easier just to make a small "planet" and build a dysonsphere around it in the process. The liquid iron core generates a lot of stable heat in stark contrast to the cold of space and so it should be feasible to equip such a sphere with a bunch of Peltier junctions to generate electricity from the temperature differential.

So I ran some numbers. I've got an iron core 10 meters in diameter. The goal is to get this molten. Iron melts at 1811 Kelvin so by ramping up the pressure around it we can hope to reach the temperature. I do this with an outer core of compressed iron dust 1500 meters in diameter, and an outer enclosure of all of this 2000 meters in diameter. In the void we put helium ions, handily delivered by the sun to all points in the solar system via solar wind, or extracted from an He3 mining operation on the moon. But how much helium would we need? Some basic data first:

Note: All of these tables are available in an excel file. Also, I'm using Newtonian physics mainly because I couldn't find an easy way to use Einstein's and I've never been very good with Calculus. The differences shouldn't be great enough to effect the jist of this write up, though any serious look at all of this would probably want to make that change.

  Data Units
Inner core (m0)
radius 5 m
surface area (4*pi*r2) 314.1592654 m2
volume (4/3*pi*r3) 523.5987756 m3
grams of iron 411548.6376 g
kilograms of iron 411.5486376 kg
Outer core (m1)
radius 750 m
surface area (4*pi*r2) 7068583.471 m2
volume ((4/3*pi*r3) - vol(m0)) 1767145344 m3
grams of iron 1.38898E+12 g
kilograms of iron 1388976240 kg
Enclosure (m2)
radius 1000 m
surface area (4*pi*r2) 12566370.61 m2
volume (4/3*pi*r3) 4188790205 m3
volume of m3 to m2 2421644861 m3
Other stuff
gas constant (R) 8.314472 L * kPa * K1 * mol1
molar volume (V) 22.42 L/mol
universal constant of gravitation (G) 6.6742E-11 N m2 kg-2

To determine the pressure we will:

  1. Calculate the amount of acceleration (a0) caused by the inner core via a0=(G*m0)/r02 where m0 is the weight of the inner core.

      Data Units
    Acceleration caused by inner core
    a0 ((G*m0)/r02) 5.49352E-09 m/s2

  2. Calculate the amount of acceleration (a1) caused by the outer core on the helium via a1=(G*m1)/r12.

      Data Units
    Acceleration caused by outer core
    a1 ((G*m1)/r12) 1.64805E-07 m/s2

  3. Determine the force (F0) caused by a0 on the outer core (m1) and helium (m3) via F0-(m1+m3)*a0.

      Data Units
    Force caused by inner core
    F0 (m1 + m3)*a0 210992683.2 N

  4. Determine the force (F1) caused by a1 on the helium via F1=m3*a1.

      Data Units
    Force caused by outer core
    F1=m3*a1 4.557153994 N

  5. Add those forces together to determine the total force (Ftotal) acting on the inner core.

      Data Units
    Total force on inner core
    Ftotal=F0+F1 210992687.8 N

  6. Calculate the resultant pressure on the inner core by P=Ftotal/A0 where A0 is the surface area of the inner core.

      Data Units
    Pressure on inner core
    P=Ftotal/A0 671.6105844 kPa

  7. Use the Ideal Gas Law to find out the resultant temperature on the inner core, to see if it matches the 1811 Kelvin. Here we will use T=(P*V)/R, with a V of 22.42 and R of 8.314472.

      Data Units
    Resulting Temperature
    T=(Ptotal*V)/R 1811.000061 Kelvin

The end result is that we'd need to get 27651723kg of helium into the gap at 11.42g/m3. But if we were moving through space, how would we gather it?

The iron cores. They could be shaped in such a way as to create a funnel shaped magnetic field for ion collection, obviating the need for physical material and possibly allowing for a much larger collector. Near Earth a still collector 100km in diameter would receive nearly 9.8 grams of helium every day; more than enough to run the engines for the duration of the day. How do we get all of that iron? The moon's crust is 13% iron and iron bearing asteroids are quite common.

Assuming the helium collection can be placed at the front of it the ship could use pressurized helium ion engines, with the collected ions providing the fuel, or a Bussard ramjet with the heating element powered by those Peltier junctions. One might think the solar wind isn't dense enough to do so, however with the speeds the ship could operate at it would be exposed to more of the wind than a stationary object, enabling the higher ion capture rates needed. Such a ship would be limited to the environment of the solar wind unless interstellar winds prove capable of sustaining the ship. We won't know if they are till we get something out that far, which the Voyagers are close to.

The size of the structures mentioned sound daunting at first but are possible with modern inflatable technologies such as the ones used for inflatable habitats, Dr. Jay Melosh's space based mirrors for asteroid deflection, and solar sails that have already been put in space or have projects plans with solid construction proposals. Out of an abundance of caution I would also like to note that solar wind impact modeling and studies should be done before constructing such a ship. Since the ship would essentially be outputting what it takes in, less the helium in the power plant, the same amount of material would be left in the solar wind however it would flow in different directions and velocities than the untouched winds until being swept up again. This would redistribute the winds in certain parts of the solar system and the extent of those affects must be understood.

Lastly, the mass of such a object presents some interesting lines of inquiry around it's stability if the core were rotating (i.e. gyroscope) and of space-time curvature experiments. I envisign the helium stream being offset to one side of the iron core with the output to the engines in the back of the sphere. These would cause the core to rotate as the helium passed by it. I'll leave thoughts on the space-time curvature experiments to individuals more capable than I.

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