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Spiral Galaxy Model

Dark matter is proposed based on the certainty of the current model for rotation of a spiral galaxy. The complexity of the spiral galaxy being predicted is interesting. This certainty cannot be justified.

from Wikipedia:
The rotation curve of a disc galaxy (also called a velocity curve) is a plot of the orbital speeds of visible stars or gas in that galaxy versus their radial distance from that galaxy's centre. It is typically rendered graphically as a plot, and the data observed from each side of a spiral galaxy are generally asymmetric, so that data from each side are averaged to create the curve. A significant discrepancy exists between the experimental curves observed, and a curve derived from theory. The theory of dark matter is currently postulated to account for the variance.
Velocities of individual stars are plotted but for nearly every spiral galaxy this discrepancy is observed so an explanation is required.

Dark matter presumes we have certainty of the motions of individual stars in the galaxy. Dark matter is the name for an excuse for a deviation. Dark matter is the result of a model that cannot deliver a correct prediction.

For reference, this is the basis for reliable predictions in our solar system:
This scheme uses Newton's force of gravity and Kepler's laws for motion in elliptical orbits. This could be called classical physics.
a) identify all bodies having a known  mass sufficient for this calculation.
b) define the orbit parameters for each body.
c) for each body identify a specific position in the orbit at a specific time.
d) The combination of (b) and (c) defines an initial state for the body, needed for the calculation for of its position at a specific time in the future.

With all these details a possible disturbance in an expected orbit could be detected when a 'random' alignment among different bodies occurs, providing a slightly stronger tug of gravity in that particular direction. Despite our certainty in these ellipses there is a small chance over time for minor random deviations.

Classical physics could be applied to a spiral galaxy rotation. This exercise could even be used to check a prediction of the model using known current conditions.

This is the basis when using classical physics for predicting the rotation of a spiral galaxy following an approach similar to our solar system, a proven approach.

a) identify all bodies in and around the galaxy having sufficient mass for this calculation
b) define the orbit parameters for each body.

c) for each body identify a specific position in the orbit at a specific time.
d) The combination of (b) and (c) defines an initial state for the body in the galaxy, needed for the calculation for of its position at a specific time in the future.

Steps (a) and (b) require resolution to individual stars.
Step (a) requires a guess at a mass when the star is not in a binary, probably based on a star's luminosity and then compared to a similar star that was in a binary where that star could have its mass estimated.
Binary pairs in step (b) require the definition of their orbit because they provide a varying force of of gravity at a specific distance dependent on their rotation axis and the orbit's timing. The universe has many binaries (perhaps half of all stars).

Step (a) is complicated by which bodies to include. Diffuse bodies of gas or dust might have a small effect. Globular clusters have substantial mass but are often outside the galactic plane. Some of these clusters appear to follow an orbit of a rough ellipse.

Steps(b) and (c) are very difficult. Our Sun is known to have a disturbed orbit that is not an ellipse.
Perhaps that is because there is no visible large mass at a focus for its ellipse. An invisible hypothetical SMBH is claimed to be there and yet the Sun does not move in an ellipse. Lab tests at Los Alamos National Laboratory using a pair of birkelund currents can generate the configuration of spiral galaxy arms so the basic shape of the spiral galaxy is apparently driven electrically not by gravity.

Step (c) must be repeated many times over months or years to determine the body's trajectory and velocity.
Step (d) after (c) establishes an expectation for an imminent change in position. In other words this is the next position with the highest probability. The next position depends on  all the simultaneous forces on that particular star, including the galactic magnetic field and both the electric and gravitational fields of stars along its path.

Classical physics has this:
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation. The three-body problem is a special case of the n-body problem. Unlike two-body problems, no closed-form solution exists for all sets of initial conditions, and numerical methods are generally required.

Those 'numerical methods' are a way to simplify the calculation. Using probabilities is one method to approximate a solution though that admits a precise prediction is impossible.

The rotation of a spiral galaxy is just too complex to predict with certainty with classical physics. A model based on probabilities cannot overcome that complexity to achieve certainty.
However cosmologists believe they have that certainty in their model.
Cosmologists do not have the necessary details for all the stars in a galaxy required to reduce the use of probabilities in their model.

Instead of the excuse of dark matter cosmologists must admit we can only approximate behaviors of  galaxies.
Certainty has no place in this context.

Dark matter has no place in a rational science.

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