Algol

This night looked at Beta-Persei (Algol) and was much amazed to find its
brightness altered. It now appears to be fourth magnitude... I observed it
diligently for about an hour upwards...hardly believing that it changed its
brightness, because I had never heard of any star varying so quick in its
brightness. I thought it might be perhaps owing to an optical illusion,
a defect in my eyes or bad air, but the sequel will show that its change
is true and that it was not mistaken.
(John Goodricke, journal entry November 12, 1782)

and they cannot be too eccentric or have very different masses, the orbit must be circular,

The period is circa 70 hours, and as you see from the light curve, the primary minimum is circa 10 hours.

Ok, so we put the stars closer together. We can work out how close with a little trigonometry:

In 1850, the French astronomer E. A. Roche (1820 – 1883) stated “no satellite can exist closer to a planet than 2.44x its radius or 1.44x from its surface.”

If a satellite or comet that is held together solely by its gravitational force (no tensile strength) passes within the planet’s Roche limit, it will break apart. Our two stars have no tensile strength, they are gases. The surface to surface separation is 2.56 radii. If both stars are of identical size and mass, why is one hot and the other cool?

The conclusion has to be that the binary system 'Algol' can barely exist without breaking up.

But something causes the 10 hour minimum in 70 hours, so what is it?

To answer to that question we must give up our preconceived intuition that what we see is what is there, for we know that to be false anyway. In this image, the straw is not really bent or broken, it is light itself that gives us the illusion. Mirages are well known also.

If the star has a large planet, then the star will move around a barycentre in common with the planet. This barycentre can be below the outer limb of the star since the Earth-Moon barycentre is below the surface of the Earth, but we must conclude that the star is moving.

Artist's impression of the orbit seen edge-ontcompare with:

http://www.eso.org/outreach/press-rel/pr-2006/pr-35-06.html

Here comes the awkward part. It is not only intuitive to add the velocity of light to the velocity of the source, it is mathematically correct to do so as well. Even Einstein recognises this:

"But the ray moves relatively to the initial point of k, when measured in the stationary system, with the velocity c-v..."

"Nun bewegt sich aber der Lichtstrahl relativ zum Anfangspunkt von k im ruhenden System gemessen mit der Geschwindigkeit V - v..."

Thus we are faced with two contradictory intuitions and two contradictory theories. We cannot closely examine Algol, it is much too far away, all we can see is a point of light that varies in intensity. The opposing theory to that of John Goodricke's, which is not really a theory at all but an axiom, is that the light curve of Algol is caused not by an eclipse, but by alterations in the velocity of light that we perceive. A computer program has simulated the light curve of Algol based on this axiom.

Ok, so far we have two competing theories, either of which could be correct.

Now here comes the clinch. I said above, "all we can see is a point of light that varies in intensity", but this isn't quite true. We can also observe spectral data, and if Algol is a binary system it has to be moving like a bat out of hell with an enormous doppler shift, far greater than is observed.

But never mind the amount, what about the phase? If the velocity of light is fixed relative to the space between us and Algol and independent of the motion of Algol, and the orbit is a circle, then the velocity curve should be sinusoidal.

If, on the other hand, the velocity of light is source dependent, then the velocity curve is like this:

The devil is in the details.