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Book by David Michalets

Einstein's Mistakes

With Forces and Light

1 Physics by Newton

This is section 1 of 12 in the web-book.

By defining the initial foundation of physics, Isaac Newton defined what could be called classical physics, because the subsequent foundation, after the acceptance of relativity,  could be called modern physics.

According to Newton, absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe.

Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies: and which is vulgarly taken for immovable space ... Absolute motion is the translation of a body from one absolute place into another: and relative motion, the translation from one relative place into another ...
— Isaac Newton




In my words, absolute space is the background, has no features, and remains always immovable.

In my words, the universe has no defined limits and it has much stuff in this space.

After Newton, physicists understood absolute time and absolute space. They exist independently of any observer.

Most are aware of Euclidean geometry with its definitions of a plane, line, parallel, and point.

Most are also aware of the Cartesian coordinate system, where the point of origin defines the direction of increasing values in each axis (x,y,z).

In physics, a reference point in absolute space is identified for the origin of the coordinate system, so the measurements using the defined axis dimensions are relative to the reference point, not to the observer. Another observer can use the same reference point to share measurements, when using the same dimensions.

An observer is not limited to Cartesian coordinates.

The center of the Earth serves as the reference point for multiple coordinate systems. Among them is the geographic coordinate system, whose 2 angular dimensions are latitude and longitude. The Global Positioning system (GPS), using an array of satellites, adds a linear dimension for the observer's altitude.

Another is the celestial coordinate system, whose 2 angular dimensions are right ascension and declination. When using this system, the observer accounts for their position on the surface relative to the center so celestial measurements from different surface locations match.

These coordinate systems when using a common reference point enable measurements independent of the observer.

When using a common coordinate system and reference point, we can measure the location of any object or event and the time of each measurement to calculate its velocity and acceleration. Sometimes, many position measurements from different locations enable a distance calculation by parallax. This technique for a distance is used in our solar system and in our Milky Way.

1.1 Newton's Laws of motion

Isaac Newton defined 3 laws of motion. They are different than Kepler's laws of planetary motion.

Here is the standard explanation of Newton's laws of motion. [from reference: ]

In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

In an inertial frame of reference, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. (It is assumed here that the mass m is constant.)

When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Some also describe a fourth law which states that forces add up like vectors, that is, that forces obey the principle of superposition.

(Excerpt end)

1.2 Law of universal gravitation

Isaac Newton defined the law of universal gravitation. Spsce-time will be compared to Newton's law.

Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The publication of the theory has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.
This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newton's work PhilosophiƦ Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. In today's language, the law states that every point mass attracts every other point mass by a force acting along the line intersecting the two points. The force is proportional to the product of the two masses, and inversely proportional to the square of the distance between them.

The equation for universal gravitation thus takes the form:

F = G * (m1 * m2) / r2

where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.[ Reference:

excerpt continues below.


 Newton's force of gravity equation  has been used many times with success.

Newton's law has since been superseded by Albert Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity in most applications. Relativity is required only when there is a need for extreme accuracy, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at small distances (such as Mercury's orbit around the Sun). [same reference as above]


That mistaken claim of Newton being superseded by Einstein is one of the motivations for this web-book.

The claim that relativity is required only for "extremely massive and dense objects" suggests a black hole. this enity  exists only in the theory of relativity and does not really exist.  There is a section for a black hole.

Newton's law cannot apply to fictional objects, like a black hole..

1.3 Free Fall

In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.

In a roughly uniform gravitational field, in the absence of any other forces, gravitation acts on each part of the body roughly equally, which results in the sensation of weightlessness, a condition that also occurs when the gravitational field is weak (such as when far away from any source of gravity). [ Reference:  ]


Free fall seems to be a possible violation of Newton's force of gravity.

If a person drops two objects having different masses, they appear to fall with the same rate of acceleration. By intuition, one could expect a heavier object would fall faster.

This behavior has been demonstrated in a vacuum chamber and on the surface of the Moon.

Rather than demonstrating a possible conflict, it demonstrates the instantaneous behavior of gravity.

The experiment includes 3 masses, the two different objects, with an extremely much larger third object. In this experiment, the third is the Earth or Moon.
There is always the mutual force of gravity between the 3 objects.

A force is maintained on the two smaller objects to prevent their motion toward the larger one.

At the instant both are released, both accelerate at the same rate by the gravitational field of the much larger object.

The description  for "free fall" lacks the description of the gravitational field behavior.

There is the topic of gravitational acceleration.

Using the integral form of Gauss' Law this formula [of Newton's force] can be extended to any pair of objects of which one is extremely more massive than the other — like a planet relative to any man-scale artefact. The distances between planets and between the planets and the Sun are (by many orders of magnitude) larger than the sizes of the sun and the planets. In consequence both the sun and the planets can be considered as point masses and the same formula applied to planetary motions. (As planets and natural satellites form pairs of comparable mass, the distance 'r' is measured from the common centers of mass of each pair rather than the direct total distance between planet centers.)

If one mass is much larger than the other, it is convenient to take it as observational reference and define it as source of a gravitational field of magnitude and orientation given by:
g = - (GM / r2) * rv
Where M is the mass of the field source (larger), [r is the distance] and rv is a unit vector directed from the field source to the sample (smaller) mass. The negative sign just indicates that the force is attractive (points backward, toward the source).
Then the attraction force F vector onto a sample mass 'm' can be expressed as:

F = mg

Here g is the friction-less, free-fall acceleration sustained by the sampling mass 'm' under the attraction of the gravitational source. It is a vector oriented toward the field source, of magnitude measured in acceleration units. The gravitational acceleration vector depends only on how massive the field source 'M' is and on the distance 'r' to the sample mass 'm'. It does not depend on the magnitude of the small sample mass. [ Reference:



Just as the electric field used calculus, the gravitational field does as well.

1.4 Slingshot trajectory

When space probes follow a slingshot trajectory past a distant planet to increase the velocity of that probe, the validity of Newton's force equation is verified every time.

The site universetoday had a page titled:
How do gravitational slingshots work? [Reference:


When NASA calculates a trajectory of a space probe using another body to change the probe's velocity, it uses the force of gravity defined by Newton. Curvature of space-time is not used.

The web page noted above has a description of how NASA calculates a slingshot to execute a change in a probe's trajectory; a video is provided also. NASA has certainly demonstrated their technique with numerous successful missions.

The calculation of a slingshot involves these critical values:

a) the mass of the probe
b) the mass of the planet
c) the velocity of the probe
d) the velocity of the planet.

During the probe's approach, there is the mutual force of gravity between the two bodies where the paths of both bodies are affected simultaneously. Obviously,  the probe with a  small mass is affected much more than the planet.

These calculations are based on the simple Newton force equation.

As described above, mismatch between two bodies results in free fall acceleration of the much smaller body toward the much larger body.

Relativity is based on space-time curvature by a gravitational field. The special observer's path is assumed to curve by the other body's gravitational field.

It is impossible to know whether anyone at NASA attempted to use the tensor equations to verify the path being predicted matched the path predicted by Newton's gravity equations, one for the mutual force, and the other for possible free fall.

Curvature never involves the mass of the observer because the use of a gravitational field can ignore it, unlike the mutual force of gravity.

In relativity, the special observer has no affect on the other body, making it impossible for space-time to explain a mutual force between 2 masses

NASA never used relativity in its calculations for a slingshot trajectory.

NASA does not use space-time curvature when a precisely calculated path is required.

While not a disproof of relativity, this application just shows relativity's space-time could not enable a precise gravitational slingshot and was never used.

1.5 Other behaviors of the force of gravity

1.5.1 LaGrange Points

LaGrange points are a type of orbital resonance.


In celestial mechanics, the Lagrange points (also Lagrangian points, L-points, or libration points) are orbital points near two large co-orbiting bodies. At the Lagrange points the gravitational forces of the two large bodies cancel out in such a way that a small object placed in orbit there is in equilibrium relative to the center of mass of the large bodies.
There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies. L1, L2, and L3 are on the line through the centers of the two large bodies, while L4 and L5 each act as the third vertex of an equilateral triangle formed with the centers of the two large bodies. L1, L2, L3 are unstable equilibria, whereas L4 and L5 are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.
For each given combination of co-orbiting planetary bodies there are five Lagrange points L1 to L5 for the Sun–Earth system, and in a similar way there are five different Lagrange points for the Earth–Moon system.
Several planets have trojan satellites near their L4 and L5 points with respect to the Sun. 

Jupiter has more than a million of these trojans. 

Artificial satellites have been placed in orbits near to L1 and L2 with respect to the Sun and Earth, and with respect to the Earth and the Moon. The Lagrange points have been proposed for uses in space exploration. [Reference:  ]


LaGrange points are an orbital resonance which is straightforward for the instantaneous force of gravity, diminished by inverse-square of their mutual distance.

The equilibrium is awkward to explain with relativity where only a special observer has their path being curved, and no effect is defined for the other object, and no masses are involved.

1.5.2 Tides

Tides are a demonstration of the force of gravity. Ocean tides

Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon and the Sun, and the rotation of the Earth. [Reference:

Here is an Image from the topic.


Simplified schematic of only the lunar portion of Earth's tides, showing (exaggerated) high tides at the sublunar point and its antipode for the hypothetical case of an ocean of constant depth without land. Solar tides not shown.

] earth tides

Earth tide (also known as solid Earth tide, crustal tide, body tide, bodily tide or land tide) is the displacement of the solid earth's surface caused by the gravity of the Moon and Sun. Its main component has meter-level amplitude at periods of about 12 hours and longer. The largest body tide constituents are semi-diurnal, but there are also significant diurnal, semi-annual, and fortnightly contributions. Though the gravitational forcing causing earth tides and ocean tides is the same, the responses are quite different. [Reference:  ]


Both an ocean tide and an earth tide is a distributed force of gravity, over a wide span of either water or land.

Relativity is for only an observer whose path is being affected by a gravitational field.

That scenario does not exist with tides. The tides behave consistently, though relativity cannot explain this behavior.
Relativity involves a moving observer having their path curved. Tides do not involve a moving observer, somewhere on Earth or Moon.

Everything in the universe is in motion by forces. No objects are affected by only a gravitational field as described by  Einstein.

Tides are a good example of why relativity should be dropped by physics. There is clearly an external force involved, driven between masses.  The Moon is the moving body having an effect on the surface of the other body.

Relativity can attempt to explain only something which  affects only the moving observer. If the Moon had oceans, they would have tides due to Earth's proximity.

1.6 Kepler's Laws

n astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun.  [Reference for the 3 laws:

Here is an image from the topic.


First law

The orbit of every planet is an ellipse with the Sun at one of the two foci.

Second law

A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

The orbital radius and angular velocity of the planet in the elliptical orbit will vary.

Third law

The ratio of the square of an object's orbital period with the cube of the semi-major axis of its orbit is the same for all objects orbiting the same primary.
This captures the relationship between the distance of planets from the Sun, and their orbital periods.

Kepler enunciated in 1619 this third law in a laborious attempt to determine what he viewed as the "music of the spheres" according to precise laws, and express it in terms of musical notation. So it was known as the harmonic law.


Kepler described the orbits with the Sun at a focus of the ellipse. That assumption is a mistake of simplification.

That focus is the instantaneous center of gravity (COG) in the solar system.

Often, the center of gravity  of our solar system is within the diameter of the solar sphere. However, that is not always the case, and most of the time, THE COG is not at the center of the Sun. The Sun has 1047 times the mass of Jupiter, but the gas giants do affect the COG.


A motion around a system's center of gravity is described by using Newton's force.
1.7 Mechanism for Gravity

The mechanism driving Newton's force of gravity id not critical to this book's conclusions. This web-book must identifty the problems introduced by the acceptance of Einstein's mistakes. The mechanism for Newton's force was not fully developed before 1905.

However I found how the simple change to the attributes of the electron and proton to include a field for mass enables all the behaviors defined for the instantaneous electric force to apply to the instantaneous force of gravity. That solution enabled me to sole the atomic mass defect problem in the Standard Model. That solution is in the book Practical Particle Physics, and in the Atomic Mass Defect Alternative free pdf.

In my book Redefining Gravity, I proposed a mechanism for the force of gravity. This mechanism is based on Maxwell's mechanism for charge, where protons and electrons create a charge field, but with an opposing polarity. Just as the electric force is instantaneous, because the fields exerted by the proton and electron are always present. When a particle's field encounters the correct field of another particle, they immediately interact.

The pdf Return to Classical Physics has the same section as in Redefining Gravity. The section My Other Publications will enable finding the book if desired.
Otherwise, here is the link to the  Return to Classics pdf

1.8 Summary of section

This is a description of classical  physics

Isaac Newton defined his laws of motion and several equations, including one for the force of gravity between 2 masses.

This force is mutual but diminishes by inverse-square of their mutual distance.

Maxwell defined the electric force between 2 charges. This electric force force is also mutual and also diminishes by the inverse-square of their mutual distance.

Relativity describes no mutual forces and ignores forces that affect charges.

This is important because our Sun, considered an average star, has a measured,  positive,  charge.

Classical physics, with its forces defined by Newton and Maxwell, enable our understanding of physics in the real universe.

Relativity handles only a limited subset of behaviors. Relativity also has 2 important false assumptions, like the velocity of matter cannot exceed c. and forces cannot be instantaneous but must act at the velocity of c.

Go to Table of Contents, to read a specific section.

last change 01/25/2022