Flux coupler.

Their number will increase as the cube of the distance. But the fluxes will decrease as the inverse square of the distance.

I've isolated the reverse power flux coupling.

Astronomers use magnitudes which are a logarithmic measure of flux defined by the formula written here.

The minus sign tells you that the higher the number, means the lower the flux.

In general case this will have to be integrated numerically.

Euclidean space, populated uniformly with some kind of sources.

You should really remember these numbers, because we'll constantly refer to distances and masses and luminosities using these units.

So lets now consider Hubble diagram.

For historical reasons, again, Vega which is alpha Lyrae was declared to have zero magnitude and then everything is measured relative to it.

In that case, we recover one power of one z, because the angstroms are stretched by exactly same factor or the hertz are also stretched by one of the factor.

But nevertheless the principle is the same.

And so if we had a universe populated uniformly with some sort of test particles, say, galaxies, and if we can count them as a function of redshift, or alternatively, as a function of flux, because flux would get dimmer with redshift, then we could constrain the models in which we are.

Now spectra are hard to obtin because they require long observation times.

Notice that because we're talking about logarithms of fluxes, talking about ratios of fluxes, and so it's all relative to some unit.

But in practice what we do a differential counts, how many per unit flux or other per unit magnitude.

The magnitude is 4 dB.

And because its a log, its a relative measure of flux relative to some unit flux. In log that comes as a additive constant.

It doesn't matter.

That is if we can measure the total luminosity, but, we usually measure specific flux, which is power per unit wavelength or unit frequency.

So in simple, Euclidean, non relativistic universe, the flux would be luminosity divide, divided by the area of the sphere with a radius from here to there.

That has to be compensated for, because galaxies do have different spectra, and different types will have different amount of correction.

And discovered some of them are actually quite far away, implying that given the observe flux internal power

Well don't think that the changes in Afghanistan are over not at all.

Optical and astronomers are beginning to use janskies as well although, we are typically talking about microjanskies and nanojanskies.

But not fast enough.

But not clever enough.

We'll assume that the universe is infinite and it's more or less uniformly filled with stars and it never changes, which is pretty much what people thought back in the early nineteenth century.

There's more!

We mostly observe electromagnetic radiation, although we now have forms of astronomy that are not dependent on electromagnetic radiation like cosmic rays, neutrinos and or gravitational waves.

So, it's walking in our lab this was the very first successful step.

And the younger one is

But there still be many miles to go

If we could measure distances to them then that would be all we needed, however obtaining redshifts is very expensive and instead of that we use number counts versus flux.

Until all that happens, you have to stay dead.

But darling, it's not safe.

Not yet.

But we can still be

Not yet, sir.

But is it...

Not yet,ma'am.

None so far, but they're staying on it. They have less than ten minutes left.

I'm not getting anything.

Here you see the building in its current state with blinds closed.

Not just yet.