The problem of dark matter is explained ?

[Bart]

In 2011 on the link: : http://dl.dropbox.com/u/26262175/SagitariusBRprogramDescription.pdf

was presented a friendly computer program which explicitly showed that the observed the uniform orbital speed of stars in spiral galaxies, may result from the natural distribution of mass of the stars and gas halo in these galaxies. This contradicted the current claim of the existence of dark matter (non-baryonic) in these galaxies, as the dominant component of their gravitational mass, and the perpetrator of that uniform speed of stars.
It turned out that the calculations of that program have been fully confirmed in 2012 by recent discoveries of astronomers (brief reminder of these findings, below).

In light of these facts, we could conclude that the problem of dark matter has already been explained, and the case of this matter should probably be closed. Is not it so?

 

"New studies suggest lack of mysterious dark matter in the vicinity of the Sun. These conclusions emerge from the analysis of the movements of the stars in the Milky Way conducted by a team of astronomers in Chile - tells European Southern Observatory (ESO).
A team of researchers from the Universities of Chile and the European Southern Observatory has used several telescopes to investigate the movements of more than 400 stars located at distances of up to 13 000 light-years from the Sun. The largest ever study of movements of the stars in the Milky Way, on space, four times larger than the previous analysis.
The results are surprising - there is no evidence for the existence of dark matter in the immediate vicinity of the Sun in the galaxy.” ( PAP, April 2012)

 

“Astronomers have discovered a cloud of gas engulfing our Milky Way galaxy that weighs as much as all the stars inside our galactic home. If the size and mass of this cloud is confirmed, it may solve a longstanding astronomical mystery, experts say.

The cloud, called a halo, appears to be enormous, extending hundreds of thousands of light-years across. Scientists suspect it is composed mainly of hydrogen, with some oxygen and other elements. The halo's temperature, size and mass were estimated using data from NASA's Chandra X-ray Observatory, the European Space Agency's XMM-Newton space observatory and Japan's Suzaku satellite.

Researchers think the mass inside this halo could be the answer to what's called the "missing baryon problem." ” (by SPACE.com Staff, Oct. 2012)

[mathematic]

You are mxing up several different issues. Dark matter(1), dark matter in our neighborhood(2), missing baryons(3).

Current model has non-baryonic matter ~ 25%, Baryonic matter ~ 4.5 %, with dark energy the rest.

 

Since dark matter is believed to be more uniformly spread out over the galaxy, the amount in our neighborhood would be relatively small (2).

 

Although baryonic matter is ~ 4.5%, visible baryonic matter (stars and hot gas clouds) make up about 1%, so something is needed for the rest, such as cold gas clouds, brown dwarfs, etc.(3)

 

I'll leave it to others to respond to (1).

[ACG52]

"New studies suggest lack of mysterious dark matter in the vicinity of the Sun. These conclusions emerge from the analysis of the movements of the stars in the Milky Way conducted by a team of astronomers in Chile - tells European Southern Observatory (ESO).

A team of researchers from the Universities of Chile and the European Southern Observatory has used several telescopes to investigate the movements of more than 400 stars located at distances of up to 13 000 light-years from the Sun. The largest ever study of movements of the stars in the Milky Way, on space, four times larger than the previous analysis.

The results are surprising - there is no evidence for the existence of dark matter in the immediate vicinity of the Sun in the galaxy.” ( PAP, April 2012)

 

 

Biden's results have already been shown to be incorrect.

 

 

An analysis of the kinematics of 412 stars at 1-4 kpc from the Galactic mid-plane by Moni Bidin et al. (2012) has claimed to derive a local density of dark matter that is an order of magnitude below standard expectations. We show that this result is incorrect and that it arises from the assumption that the mean azimuthal velocity of the stellar tracers is independent of Galactocentric radius at all heights. We substitute the assumption, supported by data, that the circular speed is independent of radius in the mid-plane. We demonstrate that the assumption of constant mean azimuthal velocity is implausible by showing that it requires the circular velocity to drop more steeply than allowed by any plausible mass model, with or without dark matter, at large heights above the mid-plane. Using the approximation that the circular velocity curve is flat in the mid-plane, we find that the data imply a local dark-matter density of 0.008 +/- 0.003 Msun/pc^3 = 0.3 +/- 0.1 GeV/cm3, fully consistent with standard estimates of this quantity. This is the most robust direct measurement of the local dark-matter density to date.

 

http://arxiv.org/abs/1205.4033

[LaurieAG]

But the rebuttal leaves a few outstanding questions due to the assumptions given.

 

(1) ' the circular speed is independent of radius in the mid-plane'

 

(2) Moni Bidin et al. (2012) ' the mean azimuthal velocity of the stellar tracers is independent of Galactocentric radius at all heights'

 

This implies that, at large heights above the mid plane, circular speed is dependent on radius while everywhere else circular speed is independent of radius.

 

The dark matter appears to be the result of two separate 'systems', one averaged and one discrete, being conflated together.

 

http://ucsdnews.ucsd.edu/newsrel/science/mcquasar.asp

 

 

An international team of astronomers has discovered within the heart of a nearby spiral galaxy a quasar whose light spectrum indicates that it is billions of light years away. The finding poses a cosmic puzzle: How could a galaxy 300 million light years away contain a stellar object several billion light years away?

[Bart]

Mathematic :

"You are mxing up several different issues. Dark matter(1), dark matter in our neighborhood(2), missing baryons(3).

Current model has non-baryonic matter ~ 25%, Baryonic matter ~ 4.5 %, with dark energy the rest.

 

Since dark matter is believed to be more uniformly spread out over the galaxy, the amount in our neighborhood would be relatively small (2).

 

Although baryonic matter is ~ 4.5%, visible baryonic matter (stars and hot gas clouds) make up about 1%, so something is needed for the rest, such as cold gas clouds, brown dwarfs, etc.(3)

 

I'll leave it to others to respond to (1)."

 

 

According to an observation, the Milky may have at least 100 billion stars, and planetary transit observations indicate that there may be at least as many planets bound to stars as there are stars in the Milky Way. It may means that the visible matter of the Milky Way can be estimated as at least 1.0x10^11 solar masses. If we add to this the mass of the gas halo, the total baryonic mass of the Milky Way, at the low end of the estimate range, will be 2.5x10^11 solar masses.

 

If there was dark matter(non-baryonic), and it is more than five times greater amount of the baryonic matter, then the mass of the galaxy would be at least 1.25x10^12 solar masses, and the speed of rotation of the stars in the galaxy, as calculated by the program Sagitarius BR ( on the above link) , for the estimated diameter of the galaxy 200kly , would have to be about 500 km/s, and in fact, is observed only about 220 km/s . So dark matter in our galaxy does not occur.

Edited February 3, 2013 by Bart

[Spyman]

Your numbers and calculations doesn't match with estimates published on Wikipedia:


Galaxy rotation curve for the Milky Way. Vertical axis is speed of rotation about the Galactic Center. Horizontal axis is distance from the Galactic Center in kpcs. The Sun is marked with a yellow ball. The observed curve of speed of rotation is blue. The predicted curve based upon stellar mass and gas in the Milky Way is red. Scatter in observations roughly indicated by gray bars. The difference is due to dark matter.
http://en.wikipedia.org/wiki/Milky_Way#Galactic_rotation

[Bart]

Your numbers and calculations doesn't match with estimates published on Wikipedia:

 

Galaxy rotation curve for the Milky Way. Vertical axis is speed of rotation about the Galactic Center. Horizontal axis is distance from the Galactic Center in kpcs. The Sun is marked with a yellow ball. The observed curve of speed of rotation is blue. The predicted curve based upon stellar mass and gas in the Milky Way is red. Scatter in observations roughly indicated by gray bars. The difference is due to dark matter.

http://en.wikipedia.org/wiki/Milky_Way#Galactic_rotation

 

On the Internet there are many curves presented for the observed rotation speeds of spiral galaxies, including the Milky Way. Most of the curves is very similar in shape. A number of such examples is shown in the link:

http://www.google.pl/searchq=rotation+curves+of+spiral+galaxies&hl=pl&tbo=u&tbm=isch&source=univ&sa=X&ei=5bkUUfjdIqSn4ATe_4CwBA&ved=0CEoQsAQ&biw=1366&bih=600

 

The observed rotation speeds of galaxies, for example NGC 5033, NGC 801, NGC2998, NGC 2008, NGC 4157, NGC 7331 are constant or flat , similar to those of the Milky Way, with the same speed of about 220km/s across the width of the disk of the galaxy.

 

Presented on Wikipedia some fluctuation of the curve for the Milky Way, may result from the increased concentration of mass in the galaxy spiral arms in relation to the area between these arms. In the above program, Sagitarius BR, you can easily modeled yourself, one or another shape of the curve for the stellar rotational velocity by increasing and decreasing, respectively, the percentage of mass distribution along the radius of the disk of the galaxy. It is worth to check it out for yourself for the Milky Way.

 

The program Sagitarius BR in a convincing way shows that the observed rate of stars in spiral galaxies, may result from the natural distribution of mass (baryonic) in these galaxies, and the exotic dark matter or the MOND or MSTG, is not necessary to explain these rates.

 

 

 

Edited February 8, 2013 by Bart

[Spyman]

The program Sagitarius BR in a convincing way shows that the observed rate of stars in spiral galaxies, may result from the natural distribution of mass (baryonic) in these galaxies, and the exotic dark matter or the MOND or MSTG, is not necessary to explain these rates.

If the program "Sagitarius BR" has different results than mainstream science, then it must either use different methods or other estimates than what mainstream science does when they reach the consensus that the dark matter phenomen is real.

 

IMHO, I don't think random simulations made by strangers on the internet that uses conflicting methods and estimates to end up with contradicting results against conclusions made by mainstream science to be very convincing at all.

 

Claims that the consensus made by mainstream science are all wrong should be taken with a very large dose of skepticism!

 

In fact as ACG52 points out in his post#3, observations made by astronomers confirm that dark matter is fully consistent with standard estimates: "This is the most robust direct measurement of the local dark-matter density to date."

 

Observational evidence wins and it currently favors a dark matter phenomena as depicted by mainstream science.

 

[Bart]

If the program "Sagitarius BR" has different results than mainstream science, then it must either use different methods or other estimates than what mainstream science does when they reach the consensus that the dark matter phenomen is real.

 

 

The program "Sagitarius BR" is a very handy analytical tool that uses a method based on Newton's laws of motion. This method is clearly outlined in the program description (on te link in post #1) and give results consistent with observations. The assumptions adopted by mainstream science, applied probably method improper for galaxies, based on Kepler's laws (fig. from Web). Hence, the arising discrepancy between the observed speeds of the stars, and the calculations of the mainstream and which now trying to explain and justify it, for various weird ways.

 

 

 

 

IMHO, I don't think random simulations made by strangers on the internet that uses conflicting methods and estimates to end up with contradicting results against conclusions made by mainstream science to be very convincing at all.

 

Claims that the consensus made by mainstream science are all wrong should be taken with a very large dose of skepticism!

 

There is no clear consensus on this issue in mainstream science. In addition to dark matter are presented other equivalent attempts to explain the uniform speed of stars in galaxies, without dark matter (MSTG or MOND). An example of a scientific paper in this issue is the link: http://iopscience.iop.org/0004-637X/636/2/721/fulltext/63031.text.html

All of the above assumptions of mainstream science, are highly speculative and, as such, may be just conflicting to reality, as well.

 

 

In fact as ACG52 points out in his post#3, observations made by astronomers confirm that dark matter is fully consistent with standard estimates: "This is the most robust direct measurement of the local dark-matter density to date."

 

Observational evidence wins and it currently favors a dark matter phenomena as depicted by mainstream science.

 

Observations/calculations of astronomers that ACG52 points out in post # 3, are doubtful about the dark matter, in the light of later observations of a gas halo pointed in post # 1.

 

 

 

[Spyman]

The program "Sagitarius BR" is a very handy analytical tool that uses a method based on Newton's laws of motion. This method is clearly outlined in the program description (on te link in post #1) and give results consistent with observations. The assumptions adopted by mainstream science, applied probably method improper for galaxies, based on Kepler's laws (fig. from Web). Hence, the arising discrepancy between the observed speeds of the stars, and the calculations of the mainstream and which now trying to explain and justify it, for various weird ways.

Not only do you seem to claim that the consensus of mainstream science is wrong but also that professional cosmologists all over the world are unable to understand and properly use Newton's laws when they are applying them on rotating galaxies.

 

IMHO, I think it would be wise for you to at least consider the possibility that it might be you that are wrong.

 

 

 

This is a quote from the lecture your image is from:

 

Surprisingly, the rotation curves that were measured even for a wide range of galaxy sizes and luminosities exhibited a nearly flat (and even slightly increasing) region of velocities outside the galactic center. If most of the galactic mass were at the center of the galaxy (which is the source of most of the luminosity), then one would expect the velocities of the outermost stars to decrease with increasing distance. This velocity dependence would be like the Keplerian dependence observed in planetary motion. The velocity of the outermost stars orbiting with uniform circular motion can easily be determined by equating the gravitational force of attraction to the galactic core with the stellar mass times the centripetal acceleration. The velocity can then be seen to fall off as one over the square root of the orbital radius, contrary to the measured, nearly flat, rotation curves.

 

This provides further evidence for the possible existence of a large quantity of non-luminous galactic mass. Furthermore, these results suggest that much of this extra mass is farther from the galactic center than the luminous mass.

http://large.stanford.edu/courses/2007/ph210/sugarbaker2/

 

Newton's laws of motion and gravity says that orbiting velocity should decrease with the square root of the orbital radius.

 

Any "analytical tool" that uses a Newtonian method and disagrees with this is in dire need of error corrections.

 

 

There is no clear consensus on this issue in mainstream science. In addition to dark matter are presented other equivalent attempts to explain the uniform speed of stars in galaxies, without dark matter (MSTG or MOND). An example of a scientific paper in this issue is the link: http://iopscience.iop.org/0004-637X/636/2/721/fulltext/63031.text.html

All of the above assumptions of mainstream science, are highly speculative and, as such, may be just conflicting to reality, as well.

No, you are wrong - the consensus among mainstream science is very clear that the phenomenon exists and are real.

 

According to consensus among cosmologists, dark matter is composed primarily of a not yet characterized type of subatomic particle. The search for this particle, by a variety of means, is one of the major efforts in particle physics today.

 

Although the existence of dark matter is generally accepted by the mainstream scientific community, several alternative theories have been proposed to try to explain the anomalies for which dark matter is intended to account.

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

 

 

Observations/calculations of astronomers that ACG52 points out in post # 3, are doubtful about the dark matter, in the light of later observations of a gas halo pointed in post # 1.

The statement: "This is the most robust direct measurement of the local dark-matter density to date." is definitely not a doubtful comment and as has already been pointed out to you in post #2, the missing baryon problem is different from dark matter.

 

Researchers think the mass inside this halo could be the answer to what's called the "missing baryon problem."

http://www.space.com/17734-milky-way-galaxy-giant-gas-halo.html

 

Baryons are a class of subatomic particles that includes the protons and neutrons that make up the atoms inside stars and galaxies.

http://www.space.com/17734-milky-way-galaxy-giant-gas-halo.html

 

This missing matter is not to be confused with dark matter, an exotic form of matter that can only be detected by its gravitational pull.

http://www.space.com/5368-missing-cosmic-matter.html

Edited February 18, 2013 by Spyman

[Semjase]

There's another possible explanation for the missing

gravity besides dark matter is the fact that the magnetic field

of the galaxy has been mapped and the galaxy resembles a

low height large diameter cylindrical magnet with the super massive

black hole at the center of the galaxy setting up the entire magnetic

of the galaxy.This binds together all celestial objects with magnetic

fields together in the galaxy, and this could account for the missing gravity.

 

Here's a map of the magnetic field of the galaxy

 

http://www.nrl.navy.mil/media/news-releases/2012/scientists-chart-high-precision-map-of-milky-ways-magnetic-fields

[swansont]

There's another possible explanation for the missing

gravity besides dark matter is the fact that the magnetic field

of the galaxy has been mapped and the galaxy resembles a

low height large diameter cylindrical magnet with the super massive

black hole at the center of the galaxy setting up the entire magnetic

of the galaxy.This binds together all celestial objects with magnetic

fields together in the galaxy, and this could account for the missing gravity.

 

Here's a map of the magnetic field of the galaxy

 

http://www.nrl.navy.mil/media/news-releases/2012/scientists-chart-high-precision-map-of-milky-ways-magnetic-fields

 

!

Moderator Note

Responding to speculative posts with another flavor of speculation is considered thread hijacking. You can address the topic with mainstream science, or you can ask questions of the thread originator for clarification. If you want to bring up a new line of discussion, start a new thread.

[Bart]

........

 

Newton's laws of motion and gravity says that orbiting velocity should decrease with the square root of the orbital radius.

 

 

 

This is all true, but it applies only to the planetary calculations, where on the planet interact gravitational force only from one star.

 

In the calculations of orbital speed of stars in galaxies, on every single star interacts gravity of all the other stars in the galaxy (including the mass of interstellar gas halo). We must therefore take into calculations, the total resultant force of all these interactions. And that is simple and the basic principle of calculations for the orbital speed of stars in the “Sagitarius BR” program.

 

 

Newton's laws of motion and gravity says that orbiting velocity should decrease with the square root of the orbital radius.

 

Any "analytical tool" that uses a Newtonian method and disagrees with this is in dire need of error corrections

 

The calculations of the “Sagitarius BR” are based solely on Newton's laws, so these calculations are easily mathematically verifiable for anyone who may have some doubts. There are no dark tricks, no speculations, so there is no reason to correct errors of the adopted method.

 

I hope that if you carefully read the description of the program, given on the link in post # 1, and check the operation of this program, available on the link: http://dl.dropbox.com/u/26262175/SagitariusBRprogramForCalculationsOfSpeedOfStars.xlsx , then you get rid of your doubts concerning the method of calculations adopted in this program.

 

Surprising is the fact that the calculations of the “Sagitarius BR” for selected models of galaxies, show good agreement with the observed rates of stars. This is what gave rise to a critical look at the views that support the existence of dark matter (non baryonic) in galaxies , and in the amount almost five times the amount of normal matter.

 

 

 

Edited February 21, 2013 by Bart

[Bart]

Your numbers and calculations doesn't match with estimates published on Wikipedia:

 

Galaxy rotation curve for the Milky Way. Vertical axis is speed of rotation about the Galactic Center. Horizontal axis is distance from the Galactic Center in kpcs. The Sun is marked with a yellow ball. The observed curve of speed of rotation is blue. The predicted curve based upon stellar mass and gas in the Milky Way is red. Scatter in observations roughly indicated by gray bars. The difference is due to dark matter.

http://en.wikipedia.org/wiki/Milky_Way#Galactic_rotation

 

 

 

As I mention in post # 7 , some fluctuations of the speed curve for the Milky Way, presented on Wikipedia drawing, may result from the increased concentration of

mass in the galaxy spiral arms, in relation to the area between these arms.

 

You can easily model this curve by yourself in “Sagitarius BR” , by increasing and decreasing, respectively, the distribution percentage of mass along

the radius of the disk of the galaxy.

 

For instance, if you use mass distribution model like to this:

 

Ring #: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

 

Mass %: 15 2 3,5 3,47 10 2 7 8 7 5,2 5 4,95 4,30 4,10 4,6 4 3,50 2,5 2,43 2

 

you will have stellar rotational velocity curve very similar to that of Vikipedia:

 

 

 

Edited March 1, 2013 by Bart

[Bart]

Updated version (v.4.0) of the program Sagitarius BR, to calculate the rotation of stars in spiral galaxies is available on the links:

Program (8,7MB): http://dl.dropbox.com/u/26262175/SagitariusBRprogramForCalculationsOfSpeedOfStars.xlsx

Description: http://dl.dropbox.com/u/26262175/SagitariusBRprogramDescription.pdf

 

The calculations of the Sagitarius BR program, clearly show that the uniform speed of rotation of stars in galaxies, as well as higher than that required by classic calculations the speed of rotation of galaxies in clusters, are the result of natural distribution of matter in these objects and for their explanation, is not need an exotic dark matter.

 

Below some question received from the Internet regarding this program, together with an explanation.

 

Q: The observed rotation speeds of galaxies in galaxy clusters, which shapes are generally spatial and not flat like the shapes of galaxies, is higher than that calculated by the classical laws of gravity. How is this possible to explain that without the participation of dark matter, based solely on the calculations of the Sagitarius BR?

 

A: Carried out by the program Sagitarius BR, calculations of the resultant gravity g = GM/R^2, produced jointly by all the stars scattered across the galaxy disc, shows always higher gravity, for any distance in the plane of the disk, than that required by classic calculations . The difference in the gravity, greatly depends on the diameter of the dispersion of stars (diameter of the galaxy disk) and increases with the increasing dispersion. This relationship is easy to check by every skeptic in the calculation of their own, on any simple model, without participation of the Sagitarius BR.

In galaxy clusters, planes of the rotating galaxy discs, for each orbiting galaxies in the cluster (with any planes of their orbits), must lie in accordance with the laws of physics, in the planes of their orbits. The same gyroscopic effect is visible in the solar system, where the axes of rotation of the planets are arranged vertically to the plane of its orbit, with some variations resulting from the precession. Therefore the vectors of attractive forces of galaxies to the center of the cluster, always lie in the planes of rotation of the galaxy discs. As already explained, the gravity in the plane of galaxy disk is always greater than that required by the classical formula g = GM/R^2, for any distance from the disk center. Therefore, the observed rate of rotation of galaxies in clusters, will be greater than that calculated classic, which in 1933 was challenged by Fritz Zwitzky and to justify this discrepancy he introduced ad hoc the concept of dark matter, which exist to this day.

[Leif]

I think it strange that there should be an ecliptic at all unless it is based in the notion of chirality and a large scale external field of force organizing it?

[swansont]

!

Moderator Note

Threads on similar topics merged. One thread per discussion, please.

[Bart]

 

Updated version (v.4.0) of the program Sagitarius BR, to calculate the rotation of stars in spiral galaxies is available on the links:

Program (8,7MB): http://dl.dropbox.com/u/26262175/SagitariusBRprogramForCalculationsOfSpeedOfStars.xlsx

Description: http://dl.dropbox.com/u/26262175/SagitariusBRprogramDescription.pdf

 

The calculations of the Sagitarius BR program, clearly show that the uniform speed of rotation of stars in galaxies, as well as higher than that required by classic calculations the speed of rotation of galaxies in clusters, are the result of natural distribution of matter in these objects and for their explanation, is not need an exotic dark matter.

 

Below some question received from the Internet regarding this program, together with an explanation.

 

Q: The observed rotation speeds of galaxies in galaxy clusters, which shapes are generally spatial and not flat like the shapes of galaxies, is higher than that calculated by the classical laws of gravity. How is this possible to explain that without the participation of dark matter, based solely on the calculations of the Sagitarius BR?

 

A: Carried out by the program Sagitarius BR, calculations of the resultant gravity g = GM/R^2, produced jointly by all the stars scattered across the galaxy disc, shows always higher gravity, for any distance in the plane of the disk, than that required by classic calculations . The difference in the gravity, greatly depends on the diameter of the dispersion of stars (diameter of the galaxy disk) and increases with the increasing dispersion. This relationship is easy to check by every skeptic in the calculation of their own, on any simple model, without participation of the Sagitarius BR.

 

In galaxy clusters, planes of the rotating galaxy discs, for each orbiting galaxies in the cluster (with any planes of their orbits), must lie in accordance with the laws of physics, in the planes of their orbits. The same gyroscopic effect is visible in the solar system, where the axes of rotation of the planets are arranged vertically to the plane of its orbit, with some variations resulting from the precession. Therefore the vectors of attractive forces of galaxies to the center of the cluster, always lie in the planes of rotation of the galaxy discs. As already explained, the gravity in the plane of galaxy disk is always greater than that required by the classical formula g = GM/R^2, for any distance from the disk center. Therefore, the observed rate of rotation of galaxies in clusters, will be greater than that calculated classic, which in 1933 was challenged by Fritz Zwitzky and to justify this discrepancy he introduced ad hoc the concept of dark matter, which exist to this day.

 

There was another question from the internet which, together with an explanation is presented below:

 

Q. On the chart presented in the program Sagitarius BR, there is increased speed ("hill") of rotation of the stars on the edge of the galaxy disk. How to explain it?

 

A. "Hill", or "hills" in the graph occur only if the % difference of the modeled distribution of mass in the disk between successive circles is sufficiently large. At the differences of less than 1% "hills" are unnoticeable. In the case of circle #20, this is especially evident because the circle #21 and the next, have modeled mass of 0% and then may be more visualized the domination of gravity of the local equivalent star from the circle #20. It is possible to filter out that domination by the program, but deliberately it is not made, in order not to distort the image of the calculations.