Thursday, 26 April 2012

The Davies Sphere

I read this article on io9 about artificial gravity and was reminded of the famous 'Dyson Sphere' idea dreamed up by Freeman Dyson. The article describes the concept of building a spherical space station around an artificial (very small) black hole such that the gravitation force on the station would equal the gravitational force we feel here on Earth. Cool idea, and in some ways similar to a Dyson Sphere, except that people live on the inside of a Dyson Sphere, rather than the outside of the black hole space station. We're also talking about massively different structures in terms of scale.

So what about a combination of the two ideas? A sphere built around the Sun with a radius such that the Sun provides a gravitational force on the sphere surface that equals Earth's, so that people could live on the outside? Gravity in a normal Dyson Sphere is an open question, it doesn't provide any gravity for people to use to live on the inside surface, so it's a problem to be solved. Not so with my sphere as the Sun provides the gravity. But how big would a 'Davies Sphere' (and I hereby claim eternal dibs on the idea by naming it so ;) ) have to be for the gravity on it's external surface to be equal to Earth's?

Well, I've studied a little bit of physics and so I *think* I can work it out*. The force of gravity on the surface of the Earth is roughly 9.81ms^-2, and the equation required to work that out is this:

g = GM/R^2

where G is Newton's gravitational constant, M is the mass of the Earth and R is the radius of the Earth. I want to rearrange the equation to find R (the radius of a sphere basically) by using the mass of the Sun and keeping the same value for g:

R^2 = GM/g

R^2 = (6.67x10^-11 Nm^2kg^-2) x (1.99 x 10^30kg) / 9.81ms^-2

Work that out and you get a value for R of 3.68x10^9m. Now, that's the radius of the sphere built around the Sun that would have Earth like gravity on it's surface. But that's measured from the centre of the Sun, so I need to subtract the radius of the Sun itself to get the distance between the two:

3.68x10^9m - 6.96x10^8m = 3 x 10^9m to one s.f. - in other words the sphere's surface would be about 3 billion metres, or 3 million km from the Sun. Sounds a long way, but the orbit of Mercury at it's closest to the Sun is 46 million km! So the Davies Sphere would be reeeeeaaaallly close to the Sun! I expect it would have to be made from some new super light-weight, super heat-resistant material, but hey that's not my problem, future engineers can figure the easy bit out ;)

Other thoughts about the Davies Sphere - in contrast to the Dyson Sphere, no one will be living on the inside, so the entire inside can be coated in solar energy collectors to capture the entire EM energy output of the Sun. Apart from a few 'windows', aligned with a set of massive orbiting mirrors which, when the 'windows' in the sphere allow sunlight through, reflect it back over the outside surface of the sphere. So, if opened simultaneously, the entire surface of the sphere could have a simultaneous day/night cycle.

The surface area of the Davies Sphere works out to be 1.13x10^20m^2, which is nine orders of magnitude more than the surface of the Earth - so room to move wouldn't be a problem at all! So there it is, my idea for the future of humanity - no thanks required ;)

I should really get back to work now :)

*this may well all be totally and utterly wrong. Really quite likely.