Does anybody here really understand Ahad's constant?

I mean it lightly?

A Ahad wrote:

I mean it lightly?

Well you would wouldn't you. To what magnitude?

I think it is about the magnitude of the stars in a certain location, a part from the sun.

The formula boggles my mind.

Carol

Okay, well that's hardly surprising Marie, Carol and Shelagh.

No wonder why people are thinking "What's the big deal? It's just another mathematical puzzle like thousands of others out there! DELETE!"



Here's a very small flashlight, with a tiny beam of light cast from it:





Now imagine walking into a dark room at night with this light in your hand and projecting its beam onto a wall in front of you.

You get a circular glow of light of say 5 watts in power illuminating the wall in front of you? We assume the flashlight is rated at 5 watts.

Now imagine someone walking into the room from behind you with a second flashlight in their hand, and shining its beam onto the same area of the wall as your own flashlight. Say this second flashlight casts a beam of another 5 watts of light - being of the same power as your own light.

The total illumination of that patch on the wall will now appear much brighter, with the combined beams (5 watts + 5 watts = 10 watts) from both flashlights added together.

That sound easy enough?

Let's forget about the stars and space for one second and focus on that flashlight example above... (I want to get this from elementary level up)

Okay that's a fair point.
The second person comes up behind you, then stands next to you. You both shine the torch beams from each of your flashlights onto the same patch of wall:




Your flashlight is the one on the left, and the other persons one is on the right...

Easy?

Above is just you shining the light on your own.






Above is you plus the other person, both of you shining your lights and joining forces to get a brighter illumination on the wall.

Now let's say a third person walks into the room, and all three of you now shine your flashlights onto the same patch of wall:






With each additional contribution of light from an extra flashlight, the spot on the wall gets brighter and brighter...

Is that easy enough?

Abdul, does the angle the light strikes (and reflects) have any (e)ffect
on your constant? Two or three light sources, all from different
angles, will seemingly reflect back at different angles (to a single
observer).

No. Since the observer is standing at the receiving end of the beams of light, and stars radiate light outwards into space in all directions at the same rate, it wouldn't really make a difference.

The starlight falling on an observer from different parts of the sky is said to to be "isotropic":

http://en.wikipedia.org/wiki/Isotropic

I though tit had to do with the over all brightness you got in deep space. I also thought it also delt with how light from a star, such as Sol, deminished as it got further from the source till finally it became just part of the over all light you may get in deep space.

So far so good, Abdul. I'm understanding about the flashlight beam(s), altho it sounds as if Marie is way ahead of me in understanding your theory. If you will, please continue the explanation.

It seems to me that it wouldn't matter how many flashlights were used, or where they were in respect to the spot on the wall, there would be an area where all the flashlights would be contributing their light to(preposition w/no object), and the brightness would be a multiple of all those contributions, but that the quality of light in that spot would be the same for all observers. Does that make any sense?

Ann

Ann, I just made a post about your new avatar in Abdul's other thread, but I'll say it again - what a beautiful baby. How big, etc? And the mother's doing fine?

Brenda,

5 lbs 11 oz. born early Sat AM; this picture taken Monday morning. Yes, mother is getting better. You said something on the other thread about so many babies looking wrinkled, etc. I guess the answer is to have tinly babies by C-section when you're 40. Or maybe it's just about size. My own babies were all small, and had those perfect, tiny features, and I was in my twenties.

Sorry about getting off topic, guys.

Ann

C-sections aren't fun. My mother was a nursery nurse and when I'd visit her at the hospital, I talked with many new mothers and saw a lot of newborns, but never connected the unwrinkly babies with c-sections. Sounds logical to me.

Sorry, Adbul, for getting off-topic.

Now back to your regularly scheduled program...

That's quite alright Brenda, and I did want to tell Ann again how beautiful that child is. A miracle from God.

Back on topic. I introduced flashlights as an analogous way of visualising "starlight". The same way as if you flash the beam from a flashlight onto someone's face from a distance, the beams of light coming to us from all those pinpricks of distant stars in the sky can be thought of as "miniature flashlights".

Each star is effectively a miniature flashlight, casting a microscopically small amount of light on the Earth. It's of the order of 0.000001 watt...a tiny fraction of any light from even the smallest flashlight ever invented, and not enough to light anything up really.

The Earth is of course surrounded by such a near-infinite number of stars in every direction, as in this image:




Just as in the example I gave above with three flashlights casting their beams onto a wall inside a dark room, we can add up the contribution of light from every single star in the universe. We treat each pinprick of light as a tiny "flashlight" and do the sum:




The final value of this formula comes to a figure of -6.5 magnitudes. On a very simple level, that's it! Ahad's constant!

When we then talk about things like the Ahad's Sphere or the value of Ahad's constant at another location far away from the Earth, things can get more complicated.

I was wondering if the light of one beam is indeed weaker than the light of three beams, then I thought about those 3-way lightbulbs. The first click of the switch turns on the light at 50 watts, the second click is 100 watts and the third click is 150 watts. So, is that kind of the same?

One beam = 50 watts, two beams = 100 watts, three beams = 150 beams, etc. or am I barking up the wrong idea all the way around?

Er... no it's another way of saying the same thing. Except with starlight you don't have that kind of flexibility to step up power 50, 100, 150 watts as you would with a variable power light bulb.

The way of adding three different beams together (as in the flashlights example I gave) is more of a physics way of understanding the "additive" properties of light. This is also one of the principles behind lighting up the interior of the interstellar ark that I envisioned in my novel. But that's another story altogether...

Thanks. I thought I was on the wrong track. =) Now I'm sure of it.

I think it is the size of the variables that matter, not the fact that they differ.

Shelagh's dead right, as always. Even though you're right to say the stars are all of different sizes and brightnesses like here for example:



Even though some of these stars are way, way more powerful than the Sun, when we see them in the sky they appear very tiny. And that's only because they are so far away. And this constant is just about adding up what little light we see from Earth, without reference to the star's true (or "intrinsic") luminosity or their varying distances from us.

It's funny when people say "it's your constant"

I don't own it... I just thought of it.

Marie Pacha wrote:

So is your constant about what we see from earth, or about light that actually strikes the planet? I think this is what is confusing me.

It’s quantifying the amount of light illumination provided by stars. If I held out my hand on a moonlit night, I can see the moon's silvery light illuminating my hand and causing it to cast a shadow onto the grass.

The net illumination from starlight comes to a tiny fraction of the full moon's. Just one three-hundredth in fact. That's not bright enough for you to see your surroundings by this feeble amount of light. But it will be brighter as you get close to one particular star in space. And inside a Globular cluster or near the centre of the Milky Way galaxy, Ahad's constant will give you a very dazzling amount of illumination

I have a scene in my second novel where the Sun has dimmed so much, because it is so far away, that it looks like any other star in the sky. There on the surface of that dark planetoid, the explorers from my ship are able to experience the true meaning of Ahad's constant first hand. Seeing is believing

Ahad,

We have a gizmo called a Sky Scout. It has a GPS in it and when you point it at a star, it will tell you the name of the star. One night we were down by the lake, pointed it at a bright star and discovered it was Jupiter. Looking into the lake, Jupiter was reflected there. What this has to do with your constant is not clear, but the reflection was bright and memorable.

Carol

Carol,
Jupiter is a very bright planet in the sky, as you saw, mostly it shines brilliantly and is only superseded by Venus or Mars in its brightness.

However, the theorem of Ahad's constant is a deeply philosophical one at that than the simple explanation I provided above of adding starlight as merely a number-crunching exercise. The ground rules for its measurement from the Earth, and its deeper interpretation, assumes that the Sun has been "switched-off"!

If the Sun did stop shining, I'm afraid there will be no Jupiter visible in the night sky and we'll miss all those wonderful reflections of its image in the lake as you saw. We shall also never see a Moon in the sky, nor any of the other planets.

Jupiter (as with all the other planets and their moons) of course shine by reflected sunlight; they have no light of their own. Hence, if the Sun was turned off, we'd have only the light of the stars to see by...and the net illumination they provide will be that stipulated by my theorem. I should also like to emphasise that this "Ahad's Constant", "Ahad's Magntude" or "Ahad's Illumination"... or whatever else one likes to name it, is a theorem. I find it belittling and rude to call it a 'hypothesis' or a 'theory'. It is a theorem:

http://en.wikipedia.org/wiki/Theorem