Question about energy at one wavelength:

Originally posted by twhitehead
So combine that with the angle of incidence equation:
arctan ( r / d ) where d is the distance between the two stars (Sirius and the sun).

To find where the light will end up parallel you need to solve:
arctan ( r / d ) = GM / ( r* c ^ 2 )
Not trivial algebraically but with a computer you solve it with ease.

[b]...like I said, the distance betwee ...[text shortened]... doesn't.

As I keep saying, stop banging your head on the math, and get the logic right first.

Except that your equation does not contain the distance to the point of focus. You have d as the separation of the two stars, this isn't right it should be the distance to the point of focus. Given r is the distance of closest approach and far smaller than d we can just use the small angle approximation tan(x) ~ x, so:

4GM/rc^2 = K/r = atan(r/d) ~ r/d

=> d ~ r^2 / K

One point to note is that this formula is independent of the distance to Sirius. This is because there is a hidden approximation. Recall sonhouse's imaginary line joining Sirius to the Sun. The formula is only rigorous for incoming light travelling parallel to this. For light at a slight angle to it the point of closest approach is not on the perpendicular plane. Assuming we are looking at the part of the line of foci near to the Sun the deviation is tiny, but further out, as we get to points of focus of the order of a light year away from the Sun, the error will start being noticeable.

Originally posted by DeepThought
Except that your equation does not contain the distance to the point of focus. You have d as the separation of the two stars, this isn't right it should be the distance to the point of focus. Given r is the distance of closest approach and far smaller than d we can just use the small angle approximation tan(x) ~ x, so:

4GM/rc^2 = K/r = atan(r/d) ~ r ...[text shortened]... of focus of the order of a light year away from the Sun, the error will start being noticeable.

Are you talking about the fact the wavefront from Sirius or any star is spherical? So a line 90 degrees from theta (line between the stars) will show a deviation from 90 degrees as you go out that line? So there would be a small correction?

I looked at that myself and came to the conclusion it was a very small fraction out of vertical compared to the angle above theta Vs the convergence angle of the sun at a given altitude above the sun, the 'r' number. I believe those angles equal each other for Sirius at around the 30 r distance from the sun.

If that is what you are talking about, an 8 ly raius is a circle 4.66 E14 km around. Compared to the 30 r distance, 2 E7 km, that represents one part in 20 million as a deviation away from pure 90 degree line. Not enough to bother me as far as foci go.

For stars close in like Sirius or Alpha Centauri, the focus poops out WAY before any light year distance you are talking about. It is just negligible with stars so close to Sol.

I concentrated on the nearby stars because any focus of energy would be max from nearby stars.

A star a thousand light years away, even focused, the absolute energy would be so weak as to be unusable. On the plus side, it would have a line of foci a thousand light years long for whatever that would be worth.

I haven't even started looking at stars that far way.

Originally posted by DeepThought
Except that your equation does not contain the distance to the point of focus.

I clearly stated that my equation is to find the case where the focus is at infinity.

You have d as the separation of the two stars, this isn't right it should be the distance to the point of focus.
No, it is right for what I was calculating, not for what you imagined I was calculating.

Given r is the distance of closest approach and far smaller than d we can just use the small angle approximation tan(x) ~ x, so:
4GM/rc^2 = K/r = atan(r/d) ~ r/d
=> d ~ r^2 / K

Good point, I forgot that.

One point to note is that this formula is independent of the distance to Sirius.
That is because you changed the meaning of d.
What your formula does is assume the incoming light is parallel ie from an infinitely distant source, then ask where the focus is for a given radius. Note that my formula had one unknown to solve for: the radius, because we knew d. Yours has two unknowns as it gives the full axis of focus, and essentially proves that the axis goes from the suns shadow to infinity.

Originally posted by sonhouse
For stars close in like Sirius or Alpha Centauri, the focus poops out WAY before any light year distance you are talking about.
...
A star a thousand light years away, even focused, the absolute energy would be so weak as to be unusable.

You are nothing if not stubborn. I have shown you over and over that the focus does not 'poop out' ever.
I have also provided solid evidence that the focused energy is negligible. At best a few orders of magnitude greater than normal. Use your brain for a moment. Either:
1. The increased brightness is less than 1000 times the normal, and the overall effect would be like having 1000 Sirius like stars in the sky - which you have to admit wouldn't be pushing any spacecraft or asteroids in any significant way.
or
2. We would occasionally see stars get 1000 times (or more) brighter. We would know they were not supernovae by both the Einstein ring we would see and the timeline of the brightness (supernovae get bright suddenly then fade over time. A gravity lensing event is symmetrical.

Originally posted by twhitehead
You are nothing if not stubborn. I have shown you over and over that the focus does not 'poop out' ever.
I have also provided solid evidence that the focused energy is negligible. At best a few orders of magnitude greater than normal. Use your brain for a moment. Either:
1. The increased brightness is less than 1000 times the normal, and the overall eff ...[text shortened]... ess (supernovae get bright suddenly then fade over time. A gravity lensing event is symmetrical.

So you tell me how far the line of focus extends for that one star near us, Sirius. Do you not believe the two effects will cancel at a certain point? If a light beam, say a laser grazes the sun, it gets bent at the 1.75 arc seconds. If it grazes higher up it also gets bent less. Do you agree with that? So if a beam from a laser goes by the sun at say 100 million km out at an angle of 1 degree how do you suppose there will be a bending enough to make a focus, assuming you have two lasers on opposite sides of the sun pointing at the same angle but opposite? What do you think will happen to those laser beams, each one say a ly away pointing at an angle that would intercept a point 100 million km above and below the sun? Exactly how will that lead to a focus?

Then compare that to a couple of lasers pointing a lot closer, say 10 million km out reaching a part of the gravity field with a higher bending co-efficient. At some point the beams will be parallel to one another and pointing closer yet to the sun the beams will converge somewhere far out in space.

What is so difficult to understand about that?

I am not trying to say the convergence or diffraction of light around the sun ever ceases, of course it gets smaller and smaller as you go away from the sun and even a light year out there is still going to be a small bending and even 10 light years out the same but such a small amount that probably effects like gravity waves would be similar in amplitude.

I am just trying to make sense of what is going on around out own star lensing wise. Not so much interested in lensing that happens a billion light years away. That is for the big guys to suss out. I am just after little results here.

I never said there would be a thousand times gain but I think the amount of energy even at the first focus from Sirius far exceeds that from the sun. At 80 E9 km the energy from the sun is measured in milliwatts per square meter and I think I showed the energy from Sirius at that point is about 50 watts per meter squared, and THAT is literally thousands of times more than the sun but that is not enough to light a firecracker much less deflect an asteroid. I think, however since larger and larger discs are considered, (disc being the area above the sun where light from Sirius passes) there will be something like the energy we receive from the sun, say 1400 watts per meter squared, a few light years out, that will be the order of energy coming from Sirius. And that would not be seen because of the vastness of space and the large amount of space between any two objects and even if a beam such as that hit an asteroid or comet in the Oort, it might only last a few days and not even be in anyone's telescope view. If it hits the Oort say a half light year out, first off it would take 6 months before we COULD be aware of that hit and second, the amount of energy coming back to Earth would not be a beam like the one nicely provided by Sirius. It would spread out in a more or less half spherical shape and therefore be subject to the inverse square law so we would be lucky to see only a few photons of such a hit.

What would be the chances of seeing a light even if you knew where to look say if humans were on some asteroid in the Oort cloud literally a half light year from Earth and they shine a 10,000 watt light directly at Earth. Would we even be able to see it in say the Hubble?

So do this thought experiment: Two lasers say a half light year from the sun, we ignore such pesky details as inverse square law stuff and assume the beam is a solitron or some such where it is say 1000 watts at the emitter and 1000 watts when it passes by the sun.

So your two beams are one sun diameter apart aimed at the sun and the beam grazes by close to the surface and of course the beams will converge at about 500 AU out. So now you change the angle of the beam slowly apart so the beams now graze the sun at higher and higher altitudes. At some point the sun's diffraction effect, getting smaller and smaller and the beams now aiming higher and higher, there has to be an angle at which the two beams cannot converge and at best now only travel in a parallel path some millions of km apart wherever that would be and continue on their way forever parallel.

Do you think there is no end to where those beams converge with increasing angle applied to the lasers?

Originally posted by sonhouse
So you tell me how far the line of focus extends for that one star near us, Sirius. Do you not believe the two effects will cancel at a certain point? If a light beam, say a laser grazes the sun, it gets bent at the 1.75 arc seconds. If it grazes higher up it also gets bent less. Do you agree with that? So if a beam from a laser goes by the sun at say 100 m ...[text shortened]... think there is no end to where those beams converge with increasing angle applied to the lasers?

I'm left wondering what the "two competing effects are". One is the inward pull the Sun exerts on a ray of light - this creates the focus. What is the other effect?

Originally posted by sonhouse
So you tell me how far the line of focus extends for that one star near us, Sirius.

How many times must I say it? Infinity!

I am just trying to make sense of what is going on around out own star lensing wise. Not so much interested in lensing that happens a billion light years away.
Except that the actual effect is identical whatever the star or other object. And you cannot observe the suns lensing effect, so why not observe the ones you can? And they have been observed. And those observations prove you wrong.

I never said there would be a thousand times gain...
As I pointed out, anything less would not even be worth talking about. Add a thousand stars to the sky and see how much brighter it looks. It wouldn't even compete with the moon. The moon is about 50,000 times brighter than Sirius!
https://en.wikipedia.org/wiki/Magnitude_(astronomy)#Apparent_magnitude

but I think the amount of energy even at the first focus from Sirius far exceeds that from the sun.
At some point it does exceed that of the sun, but by that point the sun just looks like an ordinary star, so it really isn't that much.

At 80 E9 km the energy from the sun is measured in milliwatts per square meter and I think I showed the energy from Sirius at that point is about 50 watts per meter squared,
And I think your math is all wrong because you haven't yet understood the scenario.

I think, however since larger and larger discs are considered,...
You forget that as the disc gets larger it is countered by the slice getting thinner because the focal line gets longer.

....thought experiment ....
Do you think there is no end to where those beams converge with increasing angle applied to the lasers?
There is an end. That end is right after the focus gets to infinity. Work out where the beams reach an exact parallel then subtract an infinitesimal amount off the angle and there you are at infinity.
The problem is you want to move the lasers in discrete steps rather than smoothly. You are being confused by the spreadsheet math you are using and forgetting the real scenario.
Stop with the math already and draw a picture!

Originally posted by DeepThought
I'm left wondering what the "two competing effects are". One is the inward pull the Sun exerts on a ray of light - this creates the focus. What is the other effect?

The angle of the lasers.

Originally posted by twhitehead
How many times must I say it? Infinity!

[b]I am just trying to make sense of what is going on around out own star lensing wise. Not so much interested in lensing that happens a billion light years away.
Except that the actual effect is identical whatever the star or other object. And you cannot observe the suns lensing effect, so why not observe ...[text shortened]... you are using and forgetting the real scenario.
Stop with the math already and draw a picture![/b]

I am talking about real energy being focused. If you want to talk about the infintesimals associated with that tiny change of angle, maybe you are right but for all intents and purposes, the angle of light from Sirius as it goes a certain point there will be diminishing returns on the actual energy focused and that WILL poop out at the distance between the two stars. or 8 light years. After that there is little light left to converge. I don't care if a few photons gets flung to infinity, there is not much energy left to focus at that point so I don't concern myself with that, I am talking about real energy at the end of the beam not an infinitesimal number of photons on a path to infinity.

Originally posted by sonhouse
I am talking about real energy being focused. If you want to talk about the infintesimals associated with that tiny change of angle, maybe you are right but for all intents and purposes, the angle of light from Sirius as it goes a certain point there will be diminishing returns on the actual energy focused and that WILL poop out at the distance between the ...[text shortened]... real energy at the end of the beam not an infinitesimal number of photons on a path to infinity.

I will try and do a diagram later today and post it online for you to see. Of course the energy isn't infinite and it does tail off the further out you go, but it is nevertheless real and not imaginary, and it tails off a lot slower than you realise. From whatever distance Sirius can be seen, so can the focus (the Einstein ring). It also does not have a distinct end point as you earlier claimed.

I'll see if I can give you a rough formula for the energy relation too.

Originally posted by twhitehead
I will try and do a diagram later today and post it online for you to see. Of course the energy isn't infinite and it does tail off the further out you go, but it is nevertheless real and not imaginary, and it tails off a lot slower than you realise. From whatever distance Sirius can be seen, so can the focus (the Einstein ring). It also does not have a d ...[text shortened]... you earlier claimed.

I'll see if I can give you a rough formula for the energy relation too.

I didn't say it had an end point. I said it effectively ends as far as real concentration of energy goes. What use is it if it is only that tiny infinitesimal nanometer of the disk that goes by the sun that ends up streaming down the line to infinity? The energy in that part has grown to insignificance.

Don't forget, the energy dies down pretty rapidly in the original light from stars, it has a certain bandwidth. So if in that infinitesimal slice, it happens to be one nanometer in size that gets focused to infinity, the amount of energy at one nanometer is essentially zero anyway so there would not be much in that slice in the first place much less the amplified version. A wavelegth of say, 1 micron in the IR, would never have a chance to be focused because the wavelength is way to big to get involved in a slice that is one nanometer wide in that infinitesimal.

That's all I am about, the USABLE energy in the beam and THAT my fine feathered friend is what poops out at 8 light years for Sirius, 4 light years for Alpha Centauri and so forth.

Originally posted by sonhouse
That's all I am about, the USABLE energy in the beam and THAT my fine feathered friend is what poops out at 8 light years for Sirius, 4 light years for Alpha Centauri and so forth.

And you are wrong about that and still confused about the focus line.

I am afraid I haven't had the time today to do the diagram and formulas for you, I'll try and get it done tomorrow.

Originally posted by DeepThought
I'm left wondering what the "two competing effects are". One is the inward pull the Sun exerts on a ray of light - this creates the focus. What is the other effect?

The other effect is simply stars have a spherical wavefront. So you get a certain amount of energy going straight into the center of the sun from Sirius but there is also angles where the energy goes say 1 meter above r and a slightly more bent angle where that light goes by 2 meters above the sun. So that angle gets greater and greater at the same time as the angle of deflection gets smaller and smaller and at some angle, at best the only thing the suns gravity field can do is send it out parallel and maybe there is this infinitesimal that goes to infinity it is not usable like the actual energy concentrated in that 8 light year long beam.

But if you consider say just all the stars within say 20 light years from Earth, space around that 500 AU area starts to be awash with energy stabbing out from however many stars there are in that 20 ly radius which seems to be around 150 or so. So there are also 150 porcupine like shafts of light all leading away from the sun with the energy concentration starting at around 500 AU and going out to whatever the distance it is to that star but on the other side going away from the sun.

THAT is what I want to create, a representation of all those shafts of light in some kind of 3D format, I visualize a real plastic sphere, say half meter in diameter or a meter and that represents a sphere with a 20 ly radius. Then the stars inside shooting their light to our sun and the shafts of light following out on that same line between the star in question. Maybe a bunch of neon colored thin soda straws showing the effect.

Or all in software, which would have the advantage of being able to change the POV of the whole system.

I am curious whether any of those 150 shafts of light gets anywhere near another star and so forth,

I would love to have a telescope follow the line of sight on the other side of Sirius and look for anomalous bits of light that shouldn't be there, say that beam from Sirius hitting an object in the Oort cloud.

Or the same following the path of light from Alpha Centauri. I mention those two stars since they are the closest and therefore would represent probably the strongest beam that would give the best chance of seeing some encounter like that.

Then there is the neutrino situation. You could theoretically build a neutrino lab somewhere out there, 1000 AU or so and collect amplified versions of neutrinos since they also would be focused, that is the ONLY way you can focus neutrinos and maybe dark matter. Neutrinos are interesting because maybe they can penetrate partly into the sun and if so the first focus would be somewhat shorter than 500 AU. They could perhaps give us information about the sun, a probe, if you will, of the inner layers of the sun.

I heard somewhere that neutrinos cannot penetrate the sun so easily as it can say lead.

Not sure if that is true but if it isn't, it would be a great way to probe the inside of the sun, assuming a reliable source of neutrinos of some kind or other.

Originally posted by sonhouse
I heard somewhere that neutrinos cannot penetrate the sun so easily as it can say lead.

Not sure if that is true but if it isn't, it would be a great way to probe the inside of the sun, assuming a reliable source of neutrinos of some kind or other.

The sun is such a big source of neutrinos that any neutrinos from Sirius would be washed out. As for the maximum focus, I believe it would be very close to the sun if not inside it.

The sun is denser than lead, but neutrinos can still go right through it.

This site:
http://www.astronomynotes.com/starsun/s4.htm
says a neutrino could get through a light year of lead.

Originally posted by twhitehead
The sun is such a big source of neutrinos that any neutrinos from Sirius would be washed out. As for the maximum focus, I believe it would be very close to the sun if not inside it.

The sun is denser than lead, but neutrinos can still go right through it.

This site:
http://www.astronomynotes.com/starsun/s4.htm
says a neutrino could get through a light year of lead.

Yes, solid lead but I read somewhere where neutrinos made inside the sun gets whacked about bouncing around somehow and taking years to actually finding its way to the surface.

That may be totally bonkers but I think I read that somewhere.

Well I guess it's the second option, bonkers🙂

http://www.astronomynotes.com/starsun/s4.htm

It says neutrinos generated in the sun passes through in 2 seconds.

Whereas PHOTONS are what takes forever to get out, bouncing around for a million years before leaving the surface of the sun.

So that means if you had a means of detecting say a kind of neutrino NOT emitted by the sun, it could be a probe and the first focus for those neutrinos would certainly be a lot closer that the 500 AU needed for electromagnetic stuff.