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Now, Potential Solutions to Many of the Mysteries
in Astrophysics and the Universe

Over 17 answers and questions requiring
Reexamination by the Scientific Community
of the current theories of the Cosmos

Bonus: Why There Is No Need For Dark Matter Or
For The Claimed Accelerating Expansion Of The Universe

A New Hypothesis/theory that can explain many of the
decade long problems and inconsistencies
in Astrophysics


March, 26, 2003

New Views in Cosmology
Sol Aisenberg
International Technology Group
(508) 651-0140


I offer my new hypothesis/theory to explain the unusual rotation curves of the stars in the outer limits of spiral galaxies, as well as the motion of remote clusters of galaxies, both without needing to invoke dark matter. This hypothesis is that the effective gravitational constant, G, is a function of distance, r, and can be generalized to include only a first term in a Taylor series. The effective gravitational constant can be in the very simple form of G = Gn + A*r where Gn is Newton's gravitational constant (reasonably accurate in our solar system and probably in our galaxy). If the undetermined coefficient A of the additional long range gravitational term is zero, this will be determined when available data observations are used to evaluate the new coefficient A. However, data for rotation curves (rotation velocity vs. radial distance) for spiral galaxies show that the data can be explained with a positive value of A without requiring dark matter. The result is a gravitational force that includes a long-range term that decreases slower than the Newtonian inverse square function, and this new effect becomes significant at long-range galactic distances. The theory unexpectedly also predicts a red shift linear with distance for remote stars and also clarifies the meaning of the Hubble constant and questions the use of the Hubble constant and red shift data for remote stars in determining remote velocities. Surprisingly, the theory also suggests reexamination of the concepts of the expanding universe, the acceleration of the universe, the Cosmological constant, dark energy, and the Big Bang, among others. A new explanation the why the sky is dark (Olbers' paradox) is identified. Spatial gaps and temperature ripples in the microwave background are also reviewed from a new point of view. Over 17 items are identified for reconsideration based upon the new hypothesis.


We noted that the equation describing the effect of gravity involves the masses, the gravitational constant, G, and distance, r, between masses. Our hypothesis is that the gravitational constant G is almost constant but for long range galactic distances the distance term, r, becomes dominant. The almost constant G can be expressed as the start of a power series approximation, in the form G = Go + A*r where Go applies in our Galaxy and Solar system, and A can describe any long range force.

My hypothesis/theory may be unique and controversial, but it fits the available measurement data, and meets the objective of Occam's razor, which prefers the simplest alternative or solution. When theories are not consistent with the observed data, the accurate, reproducible data must be given priority over theories and the theories should be reviewed, extended, replaced, or simplified.

Although originally intended to fit rotation curves for spiral galaxies, we found many other unexpected consequences of our hypothesis. It can answer and also create many questions in cosmology.

We can show that (in addition to the real velocity), the measured red shift for remote stars is expected to increases approximately linearly with measured distance in accord with reported data, and should not be used as a true measure of velocity for large distances.

There should be a clarification of the meaning of the Hubble constant, which is commonly defined as the ratio of the velocity to the distance of stars.

When the measured optical red shift is used to compute the Hubble constant, then the Hubble constant is really an "optical Hubble constant" in terms of red shift divided by distance. When the red shift is used to compute the velocity then the corresponding Hubble constant is the "velocity Hubble constant" in terms of velocity divided by distance. We will show why the measured red shift for very remote stars will primarily depend linearly upon measured distance (in accordance with published observations) and should not be used to determine the velocity of very remote stars and galaxies.

If the red shift cannot be used to compute the velocity for stars at very large distances then others should reexamine the concepts of the expanding universe, the acceleration of the universe, and the Big Bang model.

This hypothesis when used to correct (invalidate) the velocities computed from measured red shifts will reduce the apparent acceleration of the expansion of the universe at large distances. The result also reduces the need for introducing the concept of the Cosmological constant, or of dark energy and can simplify our view of the universe. The expansion of the universe may not be accelerating as is claimed by other research.

Another result of this analysis is our prediction that the "apparent Hubble constant" or "optical Hubble constant" is not really a constant but decreases with measured distance as the inverse square of distance for close distances and asymptotically approaches a constant value for large distances and remote galaxies. Appendix A provides the derivation of the equations.

Another result is that red shifts (which really do not measure remote galactic velocities) cannot be used for determination of velocities. And cannot be used together with the measured distances of galaxies and stars to determine the life of the universe (based upon computed velocities and measured distances). This can help resolve differences in the life of the universe as determined by different means including optical measurements of radioactive decay in the oldest stars.

Also influenced could be resolution of problems in the calculations of the times needed for formation of galaxies into walls, voids, and structures in the universe. The times should be found to be shorter.

The interpretation of the microwave and infrared background will probably need to be reexamined and extended. It is reported that according to the microwave background, presumably representing the conditions in the universe going back the billions of years in traveling to us, there are ripples in the temperature spatial distribution, and that the temperature was very low. We suggest that the microwave background may consist of those photons whose energy has diminished to the values that can be detected by microwave equipment. There may be other photons that have slowed to energy below the microwave detection range, and also some photons above the microwave detection range. This idea leads to the prediction that there should be some structure in the geometric distribution of microwave energy corresponding to the structures and spatial distribution of stars that emit photons that can arrive as "tired light" and can be the cause of temperature and spatial ripples, due to star distribution in structures with consequent "ripples" in the travel distances.


A more detailed paper is in progress, which will use our equations to provide coefficients derived from analysis of available data, along with additional references. Appendix A provides some of our equations.

In general for scientific work, theories are developed to agree with observations, and the value of a theory increases when it can predict future observations. Newton's laws were based upon observations of the motion of planets. Einstein's extension of Newton's laws did not replace Newton's laws, and are based upon unusual motion of Mercury, and most important were validated by additional measurements during an eclipse.

The initial insight into the new hypotheses was based upon the problem of the rotation of spiral galaxies and the apparent need for dark matter to explain the data. The rotation characteristic of spiral galaxies were measured by Vera Ruben (1) using observation of Doppler red shift and showed that the outer stars in the galaxy has a constant velocity and was not in accord with Newton's laws unless the concept of dark matter was invoked. Fritz Zwicky and Sinclair Smith, using red shift data, measured the speed of rotation of clusters of galaxies in the mid-1930s. They determined that by a factor of about 100 the collective masses of the galaxies could not provide the gravitational forces needed to hold them together.

Zwicky and later Rubin postulated the existence of a hallo of dark matter around each galaxy that together with Newton's laws would explain the observations. This opened up the need for a number of theories involving strange hard to prove entities to explain dark matter that is estimated to be many times larger than the visible matter.

Another problem in Astrophysics is related to the measurement of distance and velocity of remote galaxies. Hubble measured the distances of nearby galaxies and their red shifts and showed that the red shifts were proportional to the near distances.

For very remote galaxies, measurements of the light intensity of Type 1a Supernova are used to determine the distances. An available plot of red shift as a function of Supernova distances was very linear as far out as could be measured.

Originally Hubble was concerned with measured distances and red shifts but later it was apparently assumed that the red shifts were caused by velocity and thus Hubble's law became a relationship between distance and velocity, although there were no direct measurements of velocity to correlate to red shift at large distances. It apparently it is not possible at present to directly measure velocity for very remote galaxies although distances can be measured. This is a case of theory without confirmation by observation.

Hubble's law and the observed red shifts (and presumably velocities) of remote galaxies showed that the universe was expanding. And even more surprising it indicated that the velocity and expansion were increasing and accelerating at larger distances if we assume that the increasing red shifts corresponded to accelerating velocity. The Hubble constant was introduced to describe the ratio of the velocity to the red shift of stars, and was then used to calculate the distance too the far galaxies. Note that at no time was the velocity of remote galaxies directly measured but were calculated based upon an assumption that related the velocity to distance by means of a Hubble constant assumed to be valid for large distances.

The increasing red shifts with distance when interpreted as measuring velocity created a need for additional theories and non-observable entities such as dark energy, dark forces, and the Cosmological constant to explain the accelerated expansion. The concept of the Big Bang was introduced to be consistent with the apparent acceleration of the universe.

The velocities of galaxies and their distances permitted calculation of the age on the Universe. However, the calculated age of the universe differed from the age of oldest stars based upon spectral analysis of the results of radioactive processes, and this identified a difficulty in the theory and calculation.

Our hypothesis generalized the gravitational force by adding an additional term that decreases with distance but not as fast as the Newtonian inverse square dependence upon distance. For large distances, the new term dominates and produces attractive forces that eliminate the need for dark matter to explain the constant rotational velocity of stars at the outer part of spiral galaxies.

We observed that, for the outer portions of the spiral galaxies, replacing the 1/(r*r) dependence in the attractive force with a 1/r term predicated a constant rotational velocity in the region where to Newtonian term was small. This agreed with the measurements reported by Rubin for spiral galaxies.

Another way of looking at this is the generalization of the gravitational constant G as a power series in r in the form: G = Gn + A*r where Gn is the Newtonian gravitational constant (apparently valid in our solar system and nearby space), and "A" is the coefficient in the first term in a series expansion depending on the distance "r". If the additional term in my hypothesis is significant at galactic distances then determination of the undetermined constant "A" by using measurement data will show if it is not zero.

Using data from rotation curves for spiral galaxies the value of "A" was determined to be greater than zero thus confirming the hypothesis.

Thus we assumed that the force F between two masses, M and m, could be expressed as an augmented relationship between the Newtonian gravitational constant Gn, the radius r, the mass m, and the galactic mass M within the radius r and in the form:

F/(M*m) = (Gn + A*r)/(r*r)

or equivalently

F/(M*m) = Gn/(r*r) + A/r

where "A" is a coefficient describing the Additional gravitational force and has been determined by curve fitting to the rotational speed data of spiral galaxies.

When the separation of masses become very small such as in the nucleus, additional nuclear forces dominate over the Newtonian gravitational forces and Coulomb forces. It is also expected that additional forces may exist when the distances become larger than that of our solar system, our laboratories, or of our galaxy.

Early, in the mid-1930s, Fritz Zwicky and Sinclair Smith, using red shift data, measured the speeds of galaxies in clusters of remote galaxies and determined that their collective masses could not provide the gravitational forces needed to hold them together. They proposed the concept of dark matter (invisible matter) to explain the rotation about the center of mass of the collection of galaxies in the galaxy cluster. The amount of dark matter needed to explain the motion was estimated by Zwicky to be about 100 times the size of the observed matter in the cluster of galaxies.

Fritz Zwicky had provided a "tired light" hypothesis for the red shift that suggested that the red shift was related to "tired light" losing energy in traveling large distances. However there is a need for an acceptable mechanism for the energy loss proportional to the distance. Our hypothesis of an additional long-range attractive force will provide a mechanism for "tired light" and will help validate the early hypotheses of Zwicky.

Mordehai Milgrom had proposed an alternative (MOND) to dark matter that modified Newtonian dynamics for large distances. He took an approach involving upon the acceleration and the masses.

The red shift measurements by Vera Rubin (ref.1) of the motion of stars in spiral galaxies showed non-Newtonian constant rotation velocity of stars at the outer edges of spiral galaxies. The important work of Rubin, added to the earlier work of Zwicky, plus the application of Newton's principals led to the amazing conclusion that over 90 percent of the matter in the universe consists of Dark Matter, or invisible mass. Just invoking the concept of dark matter to explain the data of Zwicky, and of Rubin has created a need for many complicated theories explaining dark matter.

Our hypothesis of additional attractive force effective at large distances can explain the data of Rubin and of Zwicky, and, even more interesting, without requiring dark matter.

In addition it apparently can explain additional slight attraction forces within our solar system. The Very high precision measurement within our solar system appears to support our hypothesis. Observations of Pioneer 10 and 11 probes indicated that they were slowing down faster than predicted by Einstein's general theory of relativity. "Some extra tiny force - equivalent to a ten-billionth of the gravity at Earth's surface - must be acting on the probes, braking their outward motion." Analysis by John D. Anderson (2) and his team at JPL ruled out a number of possible explanations of this extra force. (ref. 2) Our hypothesis provides a very tiny force within solar system distances, and they are too small to influence the motion of planets but can slightly influence space vehicles.

Limited available rotation curve data for spiral galaxies was used to estimate the value of the additional force coefficient, A, and the distance, ro, where additional gravitational contribution becomes equal to the Newtonian contribution. The values may be different for different galaxies.

As an unexpected result of the hypothesis we were able to predict that this additional gravitational force provides an additional mechanism for the red shift of remote stars in addition to any red shift due to real motion of the stars. Integrating the augmented gravitational force equation provides an additional term in the potential energy change and this additional potential energy term can be expanded with the distance r as the first term. This indicates that the photons (electromagnetic energy) lose energy linearly with distance for the large distances to remote galaxies.

Thus using spiral rotation data we can determine A and also derive an equation that predicts that the red shift includes a linear contribution from the travel distance r in addition to the velocity term. At distances greater than galaxy sizes, the linear second term dominates and can reduce the need for dark matter.

Our hypothesis also predicts that the "optical Hubble constant" as determined from optical red shifts should decrease inversely as the square of the distance, r, asymptotically to a constant value with increasing distance, and should be smaller at large distances. Hubble in about 1929 initially measured the Hubble constant as around 500 km/s/Mpc but this was measured for the closer distances that could be directly measured at that time. More recent measurements for very remote galaxies using advanced techniques obtained values of the Hubble constant ranging from 50 km/s/Mpc to 100 km/s/Mpc. And the differences in the "optical Hubble constant" may depend upon the location of the galaxies used for these determinations.

A major contribution of our hypothesis is to provide a mechanism and prediction that there may not be a need for dark matter. Also it shows that the red shift may be a linear function of large distances due to a long-range additional component in the gravitational force. Also, it provides a reason that large red shifts are related to large distances, and may not represent large velocities. Also the accelerating universe may not be really accelerating. The theory of the Big Bang may need reexamination if the universe expansion is not accelerating. I am currently looking for additional data on the Internet for extension and publication of my analysis. More work by others on our hypothesis is encouraged.


The hypothesis/theory of an additional long range gravitation force can:

(1) eliminate or reduce the need for dark matter,

(2) explain why photons lose energy traveling very large distances,

(3) show a red shift linear with distance for very remote galaxies,

(4) question the assumption that the red shift measures the velocity of remote galaxies rather than primarily just travel distances,

(5) show that the expansion of the universe may not be as fast as is currently believed,

(6) show that the expansion is not necessarily accelerating,

(7) explain how the differences between the measured age of the oldest stars and the age of the universe (using velocities calculated from red shifts, but not using a directly observed velocity of galaxies) may now be resolved,

(8) show that dark energy is not needed to accelerate the expansion of the universe,

(9) show that cosmological constant may not be needed to explain an apparent expansion,

(10) predict a discontinuous distribution of red shifts due to a discontinuous distribution of travel distances,

(11) predict slight irregularities in the microwave and electromagnetic background because of discontinuities in the spatial distribution of stars in the form of voids and stellar structures,

(12) show why the Hubble constant decreases with distance according to 1/(r*r) and approaches an asymptotic value for large distances, and why the Hubble constant will give different values when measured at different distances,

(13) suggests that a reexamination or modification of the Big Bang theory may be advisable,

(14) show how it may be able to explain the anomalous weak acceleration of Pioneer 10/11 probes in our solar system,

(15) explain why the sky is dark in spite of photon energy from all the stars in the sky (Olbers' paradox) - probably because of loss of photon energy below the optical values in traveling large distances according to the theory of additional long-range gravitational force,

(16) identify the source of the detected infrared and microwave background as due to the loss of light energy from the remote stars traveling large distances to earth against long-range additional attractive forces, with a consequent shift to longer wavelengths,

(17) consider if the stars distributed in structures, walls, and voids can explain the reported gaps in the measured distribution of microwave sources and also ripples in the measured temperature,

(18) revise the calculation of the times for formation of cosmic structures, walls, and voids under gravitational forces,

All that is needed in my hypothesis is the replacement of Newton's gravitational constant Gn by a generalized gravitational constant G in the form of a power series (G = Gn + A*r) as a function of distance "r". The coefficient "A" is a measure of the contribution by the linear term in the expansion. This theory is desirable from the point of view of Occam's razor, which prefers the simplest solution

Sol Aisenberg, Ph.D.
International Technology Group
Office: 508/651-0140


1. Donald Goldsmith, The Astronomers, (St. Martins Press, NY, 1991), pp. 36-44.

2. John D. Anderson, Philip A. Laing, Eunice L. Lau, Anthony S. Liu, Michael Martin Nieto, Slava G. Turyshev, Indication, from pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range acceleration, Phys.Rev.Lett. 81 (1998) 2858-2861


This provides the evolution of the equations used for the analysis based upon the theory that includes a long-range term, A*r, to Newton's gravitational constant Gn.


The forces balancing rotation of a mass "m" in an attractive gravitational field is:

(m * v * v)/r = M*m (Gn + A*r)/r*r (1)

where M is the attracting mass, m is the rotating mass, Gn is Newton's gravitational constant, r is the radius of rotation, and A is a coefficient in the first term in the series expansion of the gravitational force.

The radius "ro" is defined as the radius where the Newtonian gravitational force is equal to the additional long-range force. The values of A and ro has initially been estimated and will be determined more accurately using curve fitting of rotational velocity as a function of r for various spiral galaxies.


(v * v)/ro = M * 2 * A/ro (2)


v * v = 2 * M * A (3)

For the transition radial location, ro, where the Newton component, Gn, is equal to the Additional component, A*ro, the following is derived from equation (1):

A = Gn/ro (4)

When combined with equation (3) the following results:

v * v = 2 * M * Gn/ro (5)

The following relationship results:

v * v * ro = 2 * M * Gn (6) This shows that for cases where the mass, M, of spiral galaxies is within an almost constant range of values, the outer rotational velocity, v, increases when the radius, r, of the spiral galaxy is smaller. The radius, ro, is where the visible stars ends, where the rotational velocity is constant.

Also, this shows that for spiral galaxies either the rotational velocity and/or the radius, ro, for those spiral galaxies increase slowly with the larger mass of these spiral galaxies.


According to our hypothesis, the "optical Hubble constant", defined in terms of measured red shift and measured distance, and in units of red shift per unit of distance, can be shown to be larger for short distances and decrease for larger distances.

If one assumes that the red shift is a measure on the velocity, then one get a "velocity Hubble constant", in units of velocity per unit of distance, but for galaxies at large distances there is no experimental proof that the red shift can be used to measure velocity.

The potential energy well for a photon leaving the gravitation well of a star or galaxy and traveling a distance r is given by the integral of the attractive force to the distance r.

The gravitational force under my hypothesis is:

F = M*m (Gn/r*r + A/r) (7)

The loss of energy in moving away from the source of the gravitational force (which is a function of distance) is the force integrated over the distance of travel.

The loss of energy experienced by the photon results in a red shift that is proportional to the energy loss.

The energy loss and red shift can be described by

dE = M*m (Gn/r + A*ln r) (8)

and when the term ln r is expanded in a power series in r, the following is first term of the result:

dE = k/r + s * r (9)

where k and s are constants.

The signs of each term are positive because it takes energy to move against attractive forces.

The term k/r corresponds to the energy to move out of a potential well, and the term s*r corresponds to the energy required to move against a long-range attractive force.

The red shift is proportional to the energy loss and the "optical Hubble constant" is proportional to the red shift divided by the distance.

Optical H = b (k/r*r + s) (10)

Where "b", "k", and "s" are constants.

This analysis shows why the optical Hubble constant is large for small distances but decreases rapidly as the inverse square of the distance to an asymptotic constant value for large distances.


I expect that many experts in Astrophysics may object to my hypothesis/theory because it may call into question much of the prior work and theories that about dark matter, the accelerating universe, and the measurement of velocities of remote galaxies. The existing and future excellent astronomical measurement equipment, including the Hubble telescope, will still be valuable and useful, and their results may lead to greater insight into the universe, when my hypothesis/theory is included.

My hypothesis may take some time for acceptance and will initially be considered as completely wrong and then progress to being obvious. While my training does not include Astrophysics, my background as a scientist with a Ph.D. in Physics from M.I.T. and my experience as a multidisciplinary generalist have permitted me to take a fresh look at the available published data without preconceived opinions.

I am primarily an experimental physicist with prior part time appointments at three major educational centers in the Boston area plus years of management and technology executive responsibility (Division President) for several major conglomerates and years as principal investigator for many diverse contracts. For over the last 15 years am active as a consultant, advisor, and independent inventor in several small companies I founded or co-founded. As a multidisciplinary generalist I have over 130 publications, reports, and presentations, a number of awards and invited presentations, plus over 23 issued U.S. Patents.

When I encountered the problem of anomalous rotation curves of spiral galaxies, the solution was apparent. Because I no longer depend upon support from grants or contracts, I was able to return obsessively to the associated cosmological problems and find insights and extensions that were never anticipated.

I continue to do research, plus consult, advise, and invent, including devising inventions for companies, and advising new inventors, consultants, and others.

# # #

A short description of my education, experience, and capabilities

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