Could we see Earth 75.2 years ago using light from a supermassive black hole?

[kevpatts]

Okay, say we are approx 32.6 light years from the supermassive black hole at the center of our universe. Surely then approx 75.2 years ago light left Earth traveling towards said black hole. A certain minute proportion of that light would have been sling-shotted around the black hole in just about every direction.

Using the computational power available these days it should be possibly to calculate exactly where we should have to look to see the light returning from this round trip.

Is it feasible that at some stage in the future we would be able to view this almost infinitesimally small amount of light and effectively watch Earth 75.2 years ago?

Is this far too simplistic? Am I being an idiot??

 

[phinds]

Okay, say we are approx 32.6 light years from the supermassive black hole at the center of our universe. Surely then approx 75.2 years ago light left Earth traveling towards said black hole. A certain minute proportion of that light would have been sling-shotted around the black hole in just about every direction.

Using the computational power available these days it should be possibly to calculate exactly where we should have to look to see the light returning from this round trip.

Is it feasible that at some stage in the future we would be able to view this almost infinitesimally small amount of light and effectively watch Earth 75.2 years ago?

Is this far too simplistic? Am I being an idiot??

You seem to have a serious misunderstanding of cosmology.

First, there is no center to the universe, so there is no meaning to the phrase "supermassive black hole at the center of our universe". If you mean our OBSERVABLE universe, then there IS a center, and you are at it. Are you a black hole?

If you mean the black hole at the center of our galaxy, then we are approximately 36 THOUSAND light years from it.

How you figure light waves from Earth would be sling-shot around it and come back the way the came is beyond me, but if they did, they would return to where the Earth was 72,000 years previously so, no we wouldn't see them.

 

[jarroe]

Good point. Kind of like the notion of a time traveller traveling through time from Earth in one location and in reality ending up out in cold space the next in a different time. But that doesn't work for hollywood movies unfortunaetly or HG Wells.

 

[tiny-tim]

welcome to pf!

hi kevpatts! welcome to pf!

… A certain minute proportion of that light would have been sling-shotted around the black hole in just about every direction.
…
Is it feasible that at some stage in the future we would be able to view this almost infinitesimally small amount of light and effectively watch Earth 75.2 years ago?

light approaching the black hole very close to (but outside) the photon sphere (radius 3M = 3Gm/c² = 1.5 times the schwarzschild radius) can go round it many times, before coming back out in any direction

in principle, it should be possible to detect the occasional photon from Earth returning to Earth in this way

unfortunately …

i] the photons would be far too infrequent to build up a meaningful signal in a human lifetime!
ii] how on Earth (literally) would you tell which photons had come this way from earth, and which from somewhere else? ​

 

[kevpatts]

Thanks Tiny Tim. Yes, you seemed to have understood my question. What I was thinking was that with the computational power we have these days we can predict exactly where planet Earth was relative to the centre of our galaxy at the time approx 75,200 years ago when it would have left earth, we know where the Earth is now, so could the perfect trajectory to achieve this be calculated? If so then we could focus our telescopes near the black hole where our calculations predict the light to be exiting its partial orbit.

I know there are 75,000 years in which any number of variables could be introduced to invalidate the calculations, but the fact that we can clearly see nebulae a billion light years away suggest that this is still unlikely.

I thought that the amount of photons would be an issue all right, we're not a star after all.

This was more of a theoretical question, not a practice one.

Thanks,
Kevin

 

[tiny-tim]

Hi Kevin!

If so then we could focus our telescopes near the black hole where our calculations predict the light to be exiting its partial orbit.

yes, but see my ii] above …

our calculations would also predict light with exactly the same exit direction but (infinitely many) different entry directions (none from old-earth)

(since we've no way of telling when the light approached the black hole)

 

[mfb]

Hi Kevin! yes, but see my ii] above …

our calculations would also predict light with exactly the same exit direction but (infinitely many) different entry directions (none from old-earth)

(since we've no way of telling when the light approached the black hole)

Exactly? I think this would kill information - outside a black hole.Earth is receiving ~1.4kW/m^2 * pi * (radius of earth)^2 power from the sun, and radiates approximately the same amount, partially in the visible spectrum (~1eV) and partially as infrared (~1/40eV). As an upper estimate, I will assume that all photons are infrared (this overestimates their number). This corresponds to 5*10^37 photons per second emitted from earth.

Now, we have to hit a very narrow region near the black hole to get a significant bending. Let's say it would have to come closer than 3 times the Schwarzschild radius.

The central black hole in the Milky Way has a mass of ~4 million solar masses, which corresponds to a Schwarzschild radius of ~12 million km. It is 26000 light years away.
The squared ratio shows that 2*10^(-20) of our photons come close to it, neglecting any influence of the interstellar medium.
For those photons, assume that they are scattered in all directions. The distance is the same, but if we want them to hit Earth the target is even smaller, giving a ratio of 7*10^(-28). Again, I neglect all other losses.

Multiplying all numbers, Earth receives ~7*10^(-10) photons per second "from earth", or 1 photon every ~50 years. This photon completely vanishes in all the other photons we receive. And even if the remaining universe would be completely black, the origin of the photon on Earth could not be tracked.Smaller, stellar black holes could give a slightly better number as their distance might be reduced by a factor of 1000. Their mass is smaller by a factor of ~10000 or more, but as the distance is taken to the 4th power and the mass is taken squared, the frequency can go up a bit.