Double Stars - Gravity’s Ultimate Joke!


There is evidence that the deflection of light by a celestial body is significantly larger than originally predicted by Einstein. Since approximately 50% of the stars observed in the heavens appear to be double stars, we investigate the possibility that many of these double-star images are actually caused by gravitational deflection of images of distant stars.  We conclude that many, if not most, of the star images we observe are actually optical illusions, and there are far fewer stars in the heavens than previously thought. Additionally we find that the deflection of light by gravity may cause double star images to appear to be binary stars but are instead optical illusions. We further conclude that if a telescope is trained at random on a star image, the probability that image is an optical illusion is near 100%!

Deflection greater than Einstein?  Sacrilegious!

Actually it’s not.  Einstein predicted that light from a distant star that just grazed the surface of the sun would be deflected by 1.75” (0.0005 degrees).  The first experiment to verify his prediction occurred in 1919, by measuring the displacement of stars observed during a solar eclipse.  Those early results seemed to agree with Einstein’s prediction, vaulting him and his General Theory of Relativity immediately to the forefront of the scientific community

In the years that followed, this experiment has been duplicated for every solar eclipse possible.  Unfortunately, the accumulated result of these many experiments has yielded a deflection nearly 20% greater than predicted by Einstein. This discrepancy has never been satisfactorily explained.   (Studies with radio signals with the Very Large Array (VLA) seem to confirm Einstein’s value, but the closest a radio wave can come to the sun’s surface for these tests is 5 degrees because of the solar corona, so these results must be viewed with caution).  Is there a reason for the relatively large discrepancy in optical eclipse experiments?  I believe so.

Einstein’s equation for the deflection of starlight by the sun is:  Φ = 4GM/Rc2  where M is the mass of the sun, G is the gravitational constant, c is the speed of light and R is the distance the light path passes from the sun’s surface, in solar radii (called the “impact parameter”).  Note that this is a linear relationship.  That is, at 2 solar radii the deflection is just ½ that at the surface, and at 10 solar radii the deflection is just 1/10 that at the surface.  The deflection decreases according to the term 1/R.  At the sun’s surface this simple equation gives a deflection of 1.75”, although in practice no star images just grazing the surface of the sun have ever been observed because of the solar corona.

But there is another effect of the sun on light that has been verified, but virtually forgotten.  It is the Shapiro effect.   The Shapiro effect confirms that the velocity of light is reduced when in a gravitational field.  Furthermore, and very important, this effect is a logarithmic effect, and decreases with distance from the sun not by the simple term 1/R, but by the logarithmic term 1/ln(R).  For example, at a distance of 1,000 solar radii the deflection (bending) of starlight is just 1/1000 (0/001) that at the surface, but at the same distance the reduction in velocity of light is just 0.145 that at the surface, a factor 145 times greater than the deflection effect.  Clearly this is a long-range effect!

The logarithmic nature of the reduction of light velocity within a gravitational field was overlooked by Einstein.  Incorporating this effect into Einstein’s equation for the deflection of light by gravity results in substantially greater deflection at cosmological distances than previously thought. For more information, see Deflection Correction.

A Little about Double Stars

A double star is a pair of stars that appear close to each other in the sky as seen from Earth when viewed through an optical telescope. This can happen either because the pair forms a binary star, i.e. a binary system of stars in mutual orbit, gravitationally bound to each other, or because it is an optical double, a chance alignment of two stars in the sky that lie at different distances. There are three types of paired stars:

·       Optical doubles — unrelated stars which appear close together through chance alignment with Earth

·       Visual binaries — gravitationally-bound stars which are separately visible with a telescope

·       Non-visual binaries — stars whose binary status was deduced through more esoteric means.

There are many catalogs of double stars, containing data on over 125,000 double stars studied over many years.  These catalogs generally include the location and magnitude of each star as well as separation in arcseconds and position angle. Because nearly 50% of the stars we observe are doubles, numerous probability studies have been conducted to try and determine if doubles occur because of random alignments, or if something else might be the cause.  Although results of these studies vary depending on various assumptions made, in general it appears that there is only a 1-5% chance that any given double star is random.  Clearly there is some unknown factor at the cause.  We will try to show that this factor is the deflection of light by gravity. (For more information on double stars, see

Deflection of Starlight by a Celestial Object

The effect of the deflection of starlight by gravity is illustrated below:


And what you would see from earth is:


That is, three star images would be seen, even though only two stars are there.  The third image C is an optical illusion caused by gravity.  Images B and C would be considered double stars!  A few examples are shown in the following figure:



There are many catalogs of double stars, providing great details on the doubles pair B and C for over 125,000 double stars. There does not appear to be any for a trio of star images A, B and C.  The following are some observations on this three-star configuration caused by gravitational deflection:

1.     The distances between image A and B and between images B and C depends on the physical relationship between stars A and B, as well as the mass of Star B and probably on the distance from the earth to star B.  Usually A-B is much larger than B to C.

2.     Image C, while it is a duplicate image of star A, will not be identical to A.  The process of being deflected will reduce the energy of image C, which will be, in effect, redshifted.  Image C may actually appear brighter than image A if this loss of energy shifts the light of image A into a more visible spectrum, depending on the filter being used. Normally, however, image C will be dimmer than image A.  And usually they will appear to be different spectral types.

3.     If there is no difference in proper motion for stars A and B the three images will be directly aligned, as shown in the figure.  However, if there is relative proper motion between stars A and B, there will not likely be a direct alignment.  This is because each light path to earth is a different length, and the time of arrival of any light ray will not correlate to any other path.  The three images will still be related, but a straight line will not pass through all three images on a photographic plate, making it difficul to verify their relationship.

4.     If star A is variable, then optical illusion C will be as well.  If there is a notable change in the magnitude of star A, this will be duplicated in image C, and the two can be correlated.  The observation of such an event on earth will be at different times because of the different path lengths taken.  Such events have actually been observed for multiple-imaged quasars, and the time difference is months to over a year.  This would be a fruitful field for future study.  (see

5.     If star B is rotating, there may also be a visible effect due to frame-dragging of its gravitational field.

6.     The most surprising feature is that if there is relative motion between stars A and B, then Star images B and C will appear to be binary stars!  This is illustrated in the following figure, taken from my book The Deceptive Universe, published in 1982:



This amazing result means that for all but a few binary doubles which have completed a full orbit, we cannot be sure that any apparent binary double is real, or just an optical illusion caused by gravity and relative proper motion between two stars!.  But wait – there’s more!

Multiple Deflection of Multiple Stars

It’s easy to observe a double-star triple as has been described, and say yes, there is an optical illusion there!  But the space surrounding earth is like an onion—it has layers.  Suppose that far away, in a distant “layer”, an optical star image is formed as we have described.  There is now a false image out there.  Now suppose that at an inner “layer”, this star trio containing a false image is again deflected in a similar manner. We would now see 6 star images, but only 4 are real.  Now this cluster of 4 stars and two false images is again deflected, resulting in additional false images, and so on.  Or take a different look.  Suppose there is a very bright star some distance away, and there are N stars between earth and that distant star capable of deflecting its light.  We would then see 2N+1 – 1 images.  If N= 20 we would see over 2 million star images, with only 20 of them real!  Surely much of what we see in the heavens is not real. I believe that if you were to train a telescope on any randomly selected star image, the chance it would be an optical illusion would be near 100%.  Are all of the star images shown in the following figure real?  I think not!


Double stars present convincing evidence that the deflection of light by gravity is substantially larger for distant stars than predicted by Einstein’s simple equation.  As a result, many, and perhaps most, of the star images seen in the heavens are really just optical illusions, and the population of actual stars surrounding earth is far smaller than previously thought.  A surprising result is that many double stars thought to be binary systems are just optical illusions caused by proper motion between two stars, suggesting that the number of actual binary systems is far lower than currently estimated.

If the greater gravitational deflection discussed in this document is accepted, then there are many other major implications.  These are discussed in other sections of this website.


Email your comments or questions to me, Jerrold Thacker


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