Originally posted by twhitehead
Here you go:
If I am not mistaken about those units, one micrometer would not be the ideal wavelength.
For added interest, Sirius is actually a binary star but Sirius B is a lot fainter so won't affect total energy much. However, if your plan was anything other than theoretical, you might need to tak ...[text shortened]... le candidate depending on what exactly you are studying.
I have been fascinated by the energy reaching our solar system, which measures 9.8E-9 w/meter^2. Although totally overwhelmed by the energy of the sun, still, it means the surface of the sun gets about 15 gigawatts of energy hitting it directly from Sirius and even Jupiter gets something like 15 kilowatts on it's 'surface'.
What interests me about Sirius also is following the path of its energy away from the sun, it starts to get focused at around 80 billion Km out and stays focused in a line reaching out about the same distance as the distance to Sirius, or about 8 light years long.
Which is why I was interested in the energy there. I am trying to make a rough approximation of the amount of energy focused in that line and so I used what I call the bubble method. That is to say, a volume of space around the sun, which I arbitrarily called 1 meter cubed, would contain almost all the energy coming from Sirius per volume. So if you stretch out the circle around the sun close to the 'surface' you have a line about 4.4 million km. So if you line up those 1 meter bubbles, you get what seems like about 40 watts (where each meter^2 has its 10 nanowatts of energy) and the energy of those bubbles will come together at around 80 billion km away from the sun following the path of the light from Sirius. The path of light doesn't change after the deflection of light around the sun, that is my main MO and that means all those 1 meter sized bubbles will converge. The thing is, that is just the line closest to the 'surface' of the sun. If you look at a volume at 2 r, where the first was at a distance of 1 r, the radius of the sun, you get a total of 86 watts worth of the same bubbles but because the angle of deflection is now half and the radius is doubled, the gist of that is the place of that particular set of bubbles is now 4 times greater at about 320 billion km away from the sun.
Each radius number, say out to radius #100, means at that distance if focused, the energy will now be 4300 watts so the energy in the line goes up till it peters out at about 8 light years out. At that distance, the energy from Sirius far exceeds the energy from the sun at that distance so there would seem to be uses for that energy, for instance, it might cause an Oort cloud object to be illuminated where it shouldn't be due to interception with that focused light. Of course the chances are low but a diligent search could reveal a new way of looking for Oort cloud objects.
So you can see a continuum of those bubbles all lining up in a line stretching in this example from 80 billion km out to 320 billion km out.
Of course that is not the end of the story since the amount of deflection, although it continues to diminish going away from the sun, it never reaches zero so you can calculate the angle at any arbitrary distance just using the formula defined by Einstein, 4GM/C^2r where G is the gravitational constant times 4 and mass in kg, in this case about 2 E30 Kg divided by C squared times the radius in meters gives the angle in radians which is about 8.4 E-6 radians which is the famous 1.75 arc second number given in the press. Radians are much more useful in figuring out the distance of focus because you just invert the radian number and you get the multiplier that you multiply the radius of and you get the focus distance directly.
So now you have two competing effects, one is the variable angle of deflection vs radius number and the increasing angle of the radiation from a given star as it goes away from the line drawn center to center of the stars in question.
At some point the lowered deflection angle will be unable to deflect the increasing angle of light from the star, in this case Sirius and the focusing ends. It turns out that end point is about the same distance on the other side of the sun as the distance to Sirius so there is a line of focus staring for every distance source at about 80 billion km away from the sun and ending at whatever the distance is between the two stars, so Sirius gives a line about 8 ly long, Alpha Centauri would give a focus line extending about 4 light years long and so forth.
There are interesting implications of that line of focus which is the main area of my research.
Sorry for the lengthy reply, but it helps my writing of it to spell it out in one place, which for now has just been on tablets.....