# AnalyticBridge

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# Questions about astronomy and clustering

How do stars get a brightness score?

I've spent many hours looking at the sky over several years  with the naked eye  - in the mountains, where you can see the Milky Way and shooting stars everyday day the sky is clear -  and I have the following questions:

• Some stars appear very early in the night sky. Some other stars appear later, but eventually get brighter than the "early stars". What's the explanation?
• I've been searching intently for dual stars, without finding any. Why would that be? If you produce a chart of the top 5,000 visible stars in the sky and apply a clustering algorithm (or Monte Carlo simulations), you will find that any close proximity between two stars can be explained by probability theory, rather than dual star theory. Of course, with the naked eye, I can only see a very small sample of stars (a few hundreds), in particular, stars that are either close or very bright. But since none of the stars that I've seen have a visible companion star, either the companion star is 10 to 100 times less visible than the main star (like the sun vs. Jupiter),  or most of what is going on in the sky is not only invisible, but also very different from what is visible.
• Finally, another question about the speed of light: why is it an absolute constant? If you are on a point A moving away from a point B at the speed of the light, and you see a ray of light moving from B to A (opposite direction, at the speed of the light), of course you will see the ray of light moving faster (by a factor 2) than the supposed maximum speed allowed by Einstein's theory. How do you explain this?

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Comment by Robert Vanderbei on February 17, 2013 at 2:03pm

The constancy of the speed of light is not one of the "outputs" of the theory of relativity.   Rather, it is an input.   What I mean is that, years before Einstein came along, the speed of light was measured under various scenarios just exactly like you described and in all such cases the speed of light was found to be the same.   That was completely mystifying.  It made no sense.  Physicists struggled with it for years.   Einstein came up with his Special Theory of Relativity in which space-time is curved as a way of explaining how it could be possible for the speed of light to be constant in all frames of reference.

The fact that the speed of light is constant can be and has been demonstrated in many ways.  For example, make an instrument that measures the speed of light, use it to measure the speed of sunlight as seen at sunset and then at sunrise.  In one case we are moving away from the Sun.  In the other case we are moving toward the Sun.   Yet, the answer is the same (to many significant figures---well below what is needed to detect the speed of rotation of the Earth's surface).  The original experiment, done by Michelson and Morley, is more self-contained and therefore more elegant.   It is also more sophisticated than the simple experiment I described and maybe that's why it didn't convince you when you learned it as a student.  It is described here:

http://en.wikipedia.org/wiki/Michelson–Morley_experiment

Comment by Robert Lewis on November 3, 2011 at 8:19pm

Capri wrote: "I mean, is the speed of the light exactly the same as it was 5 billion years ago?"

It seems to me some people have tried to work with changing "constants" like that at various times in the history of physics.  I think Arthur Eddington did.  Nothing ever came of it.

Capri wrote:  "if A emitting a light ray X (in opposite direction from A) is moving away from .. B at the speed of light, people attached to B will see the light ... at a speed exactly equal to 2x the speed of the light."

No, they will measure it as c, the speed of light.  That's part of the Lorentz transform. See

http://en.wikipedia.org/wiki/Velocity-addition_formula.  If u = v = c, the sum is 2c/2 = c.

Comment by Capri on October 27, 2011 at 9:02pm

About the speed of light, is it an absolute constant regardless of referential, and regardless of time? I mean, is the speed of the light exactly the same as it was 5 billion years ago as measured in any (fast moving) referential (each referential moving from any other ones in different directions with different speeds). If yes, is it because of arbitrary, dogmatic definitions regarding time and/or distance? And why would time or distance units should be constant in the first place? One would assume that over the course of billion of years, they changed, and that their ratio (used as the definition of speed) has  probably changed as well.

I'd assume that there is no absolute referential in our universe, that all locations are relative, and thus if a referential A emitting a light ray X (in opposite direction from A) is moving away from a referential B at the speed of the light, people attached to B will see the light moving away from A at a speed exactly equal to 2x the speed of the light. How do you explain this paradox?

Comment by Robert Lewis on September 10, 2011 at 8:58pm

> it's because the basic velocity unit (meter per second) is defined as a fixed, constant

> fraction of the speed of the light. This artificial definition results in paradoxes as explained by Vincent.

I haven't studied physics in quite a few years, but this sounds very wrong.  A meter is a unit of distance.  For many years it was the length of a certain bar in Paris, then some multiple of a certain wavelength.  Meter/sec is not defined in terms of the speed of light.

There are no paradoxes in the theory of relativity, though there are parts that seem puzzling at first.

> Something very similar explains why the speed of the light is constant.

No, your analogy is wrong.  It's a deep result.  Study up on the Lorentz transform and four-dimensinal space time.

Comment by Robert Lewis on September 5, 2011 at 7:35pm

> As for the speed of light, I have attended hundreds of hours of physics courses when I was undergrad and learned that c is constant in the context of relativity theory. It does not mean that I believe in it, after all it's just a model to explain the real universe, among other models that haven't been invented yet.

Sounds like those courses weren't done right, or you would see the great beauty and unity of relativity.

Special relativity has been verified as much as any physical theory in history.  Computations with the Lorentz transform are essential in particle physics, for example.  In Quantum mechanics, Dirac incorporated relativity.  Without it, there would be no quantum theory, another extraordinarily well verified part of physics.

I've been an amateur astronomer all my life.  I really don't understand what you mean by this:

> what I observed was a change in relative brightness, with a random spatial distribution of these changes.

Comment by Vincent Granville on September 5, 2011 at 12:19pm

Robert,

I'm not an astronomer, although I spend a lot of time watching the sky. My questions are layman questions. My only exposure to celestial mechanics is a few University courses where we learned mathematical equations e.g. to compute the distance between the sun and another star, as well solving differential equations related to three-body problems (gravitation) or deflection problems etc.

As for the speed of light, I have attended hundreds of hours of physics courses when I was undergrad and learned that c is constant in the context of relativity theory. It does not mean that I believe in it, after all it's just a model to explain the real universe, among other models that haven't been invented yet.

To answer your first question, what I observed was a change in relative brightness, with a random spatial distribution of these changes.

Comment by Robert Lewis on September 5, 2011 at 11:46am

It sounds like you need to spend a some time reading up on elementary astronomy. I guess you never studied this subject in high school or college. You do not seem to understand some basic ideas.

First of all, when you say "earlier/later" are you referring to twilight conditions, or are you referring to a star rising near the horizon when it is dark, then moving slowly higher as the earth rotates?  In the first case, of course the star will appear to brighten as the sky darkens.  In the second, stars rising near the horizon appear fainter than they will later when higher in the sky because of atmospheric effects - the light passes through more air to get to our eyes. Start with some wikipedia articles.