[ExI] Extreme observational astronomy

[Anders Sandberg]

On 2013-12-11 16:29, David Lubkin wrote:
> Q: Assume Drexlerian molecular nanotechnology. If you took apart the 
> solar system for raw materials, what is the largest effective diameter 
> telescope you could create? What would its capabilities be?
>
There are two parameters: light bucket area and aperture. The resolution 
is set by the aperture, the faintness of what you can see by the area. 
So if you spread your telescope across lightyears you can see amazingly 
fine detail, even if the area is small (but then the details better be 
bright, of course).

Let's see. The mass of the solar system is around 2*10^30 kg, with 0.4% 
carbon (the most abundant element I can imagine making a telescope of). 
So that is 8*10^27 kg carbon. If we turned it all into graphene sheets 
(0.77e-6 kg/m^2) we would get 10^34 m^2. That is around 10x10 
lightyears. Now a single graphene sheet is pretty transparent (absorbs 
2.3% of light), but if we layer them at careful wavelength intervals the 
optical depth goes up a lot. So let's say we have ten layers: now we 
still have about 10 square lightyears.

Compare to Hubble (aperture 2.4 m, area 4.5 m^2, can see object of the 
31st magnitude). The solar telescope has 2*10^32 times the area, and 
would even as a single circular surface have an aperture 4*10^16 times 
wider. So it could see objects of magnitude 31+5*log10(aperture/Hubble 
aperture)=114 if I calculate right.

Hubble has a spatial resolution in visible light of 0.1 arcsec, but the 
big telescope can see 2.5e-18 arcsec objects. A one millimeter object at 
distance x meters has an angular size of 0.001/x radians, or 206/x 
arcseconds. So the big telescope can see such objects at a distance of 
8.24*10^19 meters, or 8240 lightyears. Over that distance the distance 
modulus of magnitude is just 12 magnitudes, so the telescope can still 
see objects of absolute magnitude 102. That corresponds to  around 
5*10^-13 Watts emitted by the object. This is essentially what you would 
get from very dim streetlight shining into a dark room: that telescope 
can read alien newspapers in the dark.

-- 
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University