Making The Moon Into A Bernal Sphere

[CraigD]

I can across a zany idea for making the moon into a gigantic Bernal sphere in this Halfbakery page[/wiki], and wanted to work out some rough calculations about, assuming no material strength or engineering detail issues, what order of mechanical power would be involved.

 

The idea calls for the moon to be hollowed out into thin spherical shell of 2 times its original radius, the spun fast enough to produce 1 g (9.8 m/s/s) centrifugal pseudogravity at its inner equator.

 

The moment of inertia of a thin shelled sphere is about [math]I = \frac{2}{3} m r^2[/math]

m = 7.3477 x 10²² kg

r = 34742000 m

so I = 5.91248 x 10³⁷ kg m^2

 

Centripetal acceleration is [math]a = \frac{v^2}{r}[/math]

So for a= 9.8 m/s/s, v = 5836.74 m/s and angular speed w = 0.00167901 rad/s.

 

Taking away the initial speed of the hollow sphere, calculated from the change in moment of inertial and radius from the original solid one, w = .00167862 rad/s

 

So to spin the hollow sphere to this speed in 10 years, the angular acceleration must be a_w = 5.31921 x 10^-12 rad/s/s. Torque is T = a_w I = 3.14497 x 10²⁶ N m, so dividing by r, the force that must be applied to the sphere’s equator is 1.81047 x 10¹⁹ N.

 

This is a huge force, about 500,000,000,000 times the thrust of a Saturn V rocket. You couldn’t use rockets with the specific impulse of a typical chemical rocket (about 3000 m/s equivalent exhaust speed) because that would require more reaction mass than many times the Moon’s total mass. Working backward from using 0.1 m, v_e = 777593 m/s. Assuming 100% mechanical efficiency, this would require a power of 7.0390 x 10²⁴ W.

 

This is about 400,000,000,000 times the power humankind currently uses, about 2% of the total power of the Sun – pretty much type 2 civilization power.

Even for a scheme as outlandish as making the Moon into a Bernal sphere, this seems a bit much. Can somebody check my work :QuestionM:

[TomKalbfus]

You don't need to use all of the Moon's mass to build a hollow sphere, you could just mine the surface and build a hollow sphere around the Moon and spin that shell, using the mass of the Moon in the center to hold it together. Remember the Moon has 1/6th gravity. So you can build a ring around the Moon and spin it to produce gravity, at twice the radius of the Moon, the gravity would be 1/24th that of Earth, if you spin it enough to produce 1-g on the inside, you will need 24 times the mass of the spinning part in a non-spinning outer ring to balance out the centrifugal force. As you go to higher latitudes in your sphere, less gravity would become available, but the radius also becomes shorter, so you can use things like carbon-nanotubes to hold it together. You would also need to compartmentalize the habitable space within to prevent the atmosphere from rushing to the equator. Most of the Moon's mass does not get used in constructing this thing, the shell is relatively thin compared to the Mass of the Moon, the surface area within would be equivalent to Mars or all the land on Earth, Since it is artificial, you don't really need oceans. You would put in holes at the poles to let in Sunlight, make the holes the diameter of the Moon, place a statlite mirror over the Moon's North and South Poles and have them reflect sunlight through those holes to then bounce light off of mirrors on the remaining Moon's surface. Those mirrors would control the amount of sunlight the inside of the Bernal receives, you can create a 24-hour day/night cycle that way, with seasons and whatever you want.