Discussion
Started 19th Mar, 2019

# The 2nd Newton law test for small accelerations and BIG masses

Dear Sirs,
I would like to find out more precisely whether the 2nd Newton law is valid or not in wide range of masses, accelerations, forces. Particulary I have a question whether the inertial property of body (inertial mass) is able to stop the body for small external forces or not. I have found in the Internet the fresh articles with tests of the 2nd Newton law for small accelerations (10^-10), small forces (10^-13) and SMALL masses (about 1 kg). The articles deal with the question of dark matter and MOND theory in astrophysics.
But I am interested in BIG masses. Could the test be carried out in planetary scale? Maybe for the Moon or asteroids? Or for masses like 1000 kg? Thank you very much for any references.

You may always apply the Newtonian 2nd-law for any kind of body extensively if and only if you compromise with the following:
(1) Point mass approximation
(2) Non-curved geometry
(3) Non-inertial relativistic effects

## All replies (16)

As long as the discussion remains within the validity limit of the acceleration of constant mass, Newtonian Law-2 should be applicable.
- The Deep Impact mission to Tempel 1 comet: "...The change in the comet's orbit is miniscule. We can't really measure it..." https://www.nasa.gov/mission_pages/deepimpact/launch/event_transcript5.html - One may consider the pressure of light as a small force, however, the conclusions in the particular case of the solar sail employment may occur ambiguous and highly dependable of the model and interpretation. https://www.youtube.com/watch?v=QYhpAmCOH9I
- This topic is best known to those who are engaged in ephemeris models.
If you want to move a tank with your finger, can you? The quick answer is no. But if we hold the tank with a rope, then we can move it with a finger,
b.What does Madun pressure constant (MPC) mean? Madun pressure constant means that each Madun pressure unit causes an acceleration of (0.837) of the part of 1,000,000,000 parts of a meter. In simple terms, each Madun pressure unit causes acceleration less than a part of a billion parts of a meter.
"A new alternative theory of gravity where gravity is particles behave as a fluid forming two types of swirls Annular swirls and oval swirls ".
It's not clear what test you are proposing but lunar ranging has been used to show that the Nordtvedt Effect is null to a high degree of accuracy so perhaps the same data would be of use to you:
Dear George, to my point of view, a lot of researchers, testing modified gravitation theories, come across a generall blunder, that radar experiments (of any kind and range) may help them to verify the effect.
Howvever, in most cases they are ignoring the need to take in account the contribution by the additional gravitation potential to Shapiro delay (due to decrease of the speed of light in the additional gravitational field) and miss corresponding encrease of the measured distance of the same order.
In most cases, mainstrem scientists defend the Keplerian dynamics referring to the Bertrand theorem. However, the initial condition in this case is the statement that the trajectory of the body is a conic section (ellipse), as confirmed by the radar measurements ... However, when using modifications of the Newtonian dynamics, and taking into account the corresponding Shapiro delay, we no more can assert that we deal with a conic section... the Bertrand theorem is not applicable.. In fact, instead of an ellipse, we are have ovoid, but the radar ranging method do not allow it to be measured.
There is no other body between us and the moon so the Shapiro delay is not relevant to the observations I suggested you could use.
In relation to say radar measurements of Venus with the line of sight passing close to the Sun, while the Shapiro delay affects the round trip radar signal, the planet is still in an orbit that is an ellipse (and with very low eccentricity) in the Sun-centred frame. The planet doesn't have a kink in its orbit, it is only the radar signal that shows the delay.
Dear George, your comments are completely valid in the framework of the classical model. However, the author of the question consider possible violations of the 2nd Newton's Law, which is the subject for verification.
Speaking about the inertial mass of celestial bodies, we can hardly get rid of the gravity law, which controls motion of these bodies. My comment concerns possible violation of Newton’s gravity law, and the impossibility of using radar methods to test it.
For the modified law of gravitation, one should take into account the change in the speed of light in the (modified) gravitational field. That is what Shapiro’s delay is doing. The third body is not required, since we are talking about changing the law of Newton's gravity and the corresponding need for alternative mathematics when calculating the measured distance over the signal propagation time.
As far as we know nothing about the modified gravity law, we also cannot use the correct Shapiro delay values for radar ranging in the modified gravitation.
The most distant radar ranging for orbital elements refinement has been employed for Saturn.
1 Recommendation
Ivan, my comment was that laser ranging of the Moon would be a good way to test for possible violations of GR (Newton's Law has long been superseded) and the Shapiro delay could only interfere with that if there were a third body between us and the Moon. That's not the case so any departure from GR should show up as a discrepancy between the measurement and the GR prediction, that deviation could not be ascribed to a Shapiro delay because that from the Earth and Moon would already be accounted for in the prediction.
- When calculating ephemeris in the most accurate models of EPM and in some DE models, only miserable corrections are obtained from the PPN formalism. The Newtonian gravitation remains in the basement of celestial mechanics and of the GR. To my point of view, and stem from the fact, that geodetic lines in the presence of masses get bent, the Newton’s gravitation law suffers from a fundamental flaw due to violation of the inverse square law, underlying it. Let's try to go down from generalizations to specifics.
For example, discussing the modification of the law of Newton, I will argue that the mass is not an invariant, and the APPARENT gravitational mass depends on the distance to the observer Ma = M (1+ KR), where, for particular body, K = const. To verify the validity of the modified law, one will have to a) recalculate the masses of all celestial bodies in accordance with modified law, and b) get the Shapiro amendment, which will also depend on the (apparent) mass. As a result, using appropriate Shapiro delay values, we may get confirmation of the modified law.
1 Recommendation
Dear Ivan,
IK: The Newtonian gravitation remains in the basement of celestial mechanics and of the GR.
For the bending of starlight passing the Sun, Newton's Law gives a value half of what is observed while GR gives the correct value. That was first determined by Eddington a century ago and has been confirmed with much better accuracy by the Hipparcos Mission and presumably by GAIA since. As such the current theory is GR, not Newton.
However, that isn't relevant to the original question. What Anatoly asked was: "Could the test be carried out in planetary scale? Maybe for the Moon or asteroids?"
The answer I gave is that he can use laser ranging data from the Moon as a sensitive test. Using the Newton approximation for that would be appropriate but there is no object between so Shapiro Delay is not relevant to what was asked.
I Agree With Ivan Krasnyj
Dear Anatoly,
Refer the site may be quite useful for you.
(very good example in c no. picture)
Ashish
As per the Newtonian inverse square law, it is applicable only for point objects;
This law, as an extreme case, is therefore applicable for objects of any geometric kinetic property
The discovery of gravitational waves provides a new way for us to reveal the universe, but the speed of gravitational waves cannot represent the speed of gravitational ﬁelds. The speed of action of gravitational ﬁelds will be much greater than the speed of gravitational waves. Just like Newton said: Gravitation is acting force at a distance. Gravitational waves caused by the revolution of the sun will aﬀect the orbits of planets and provide some planetary precession data. The chasing eﬀect of gravitational waves will also cause the planetary orbital mechanical energy to continue to increase slowly until the planet escapes from the solar system. Gravitational waves are real, and the gravitational model under the inﬂuence of gravitational waves we constructed is a physical model. Through the calculation of planetary orbital precession, the correctness of the gravitational equation under the inﬂuence of gravitational waves is veriﬁed.
You may always apply the Newtonian 2nd-law for any kind of body extensively if and only if you compromise with the following:
(1) Point mass approximation
(2) Non-curved geometry
(3) Non-inertial relativistic effects

## Similar questions and discussions

What is time, t or ct?
Question
• Ziaedin Shafiei
One of the consequences of relativistic physics is the rejection of the well-known concepts of space and time in science, and replacing them with the new concept of Minkowski space-time or simply space-time.
In classical mechanics, the three spatial dimensions in Cartesian coordinates are usually denoted by x, y and z. The dimensional symbol of each is L. Time is represented by t with the dimensional symbol of T.
In relativistic physics x, y and z are still intactly used for the three spatial dimensions, but time is replaced by ct. It means its dimension has changed from T to L. Therefore, this new time is yet another spatial dimension. One thus wonders where and what is time in space-time?
Probably, due to this awkwardness, ct is not commonly used by physicists as the notion for time after more than a century since its introduction and despite the fact that it applies to any object at any speed.
The root of this manipulation of time comes directly from Lorentz transformations equations. But what are the consequences of this change?
We are told that an observer in any inertial reference frame is allowed to consider its own frame to be stationary. However, the space-time concept tells us that if the same observer does not move at all in the same frame, he or she still moves at the new so-called time dimension with the speed of light! In fact, every object which is apparently moving at a constant speed through space is actually moving with the speed of light in space-time, divided partially in time and partially in spatial directions. The difference is that going at the speed of light in the time direction is disassociated with momentum energy but going at the fraction of that speed in the other three dimensions accumulates substantial momentum energy, reaching infinity when approaching the speed of light.
Are Dr. Hans-Otto Carmesin Models supported by the Supernova Observations?
Discussion
4 replies
• Marco Pereira
Dr. Hans-Otto Carmesin is a prolific theoretician who wrote among other things, these two books:
Modeling SN1a data:
That said, he leads a field where a lot of unsupported claims are tossed around without anything to support it. That is why they are unsupported..:)
As Dr. Carmesin professed, scientists should follow the teachings of Aristotle and always use the simplest possible model that is consistent with Reality.
Dr. Carmesin's model has nonlocality, dimensional transitions, the usual suspects (Dark Matter and Dark Energy), and an epoch-dependent Dark Energy (figure 8.15 on the first book above).
It is a fantastic work and from my point of view, unnecessary and incorrect.
Unnecessary because there is HU which is capable to explain everything Dr. Carmesin explained without the need for a Big Bang, Dark Energy, Dark Matter, epoch-dependent Dark Matter, Polychromatic Vacuum. Because of that, Aristotle and Occam's Razor would support HU and rebut Dr. Carmesin's work.
Attached is my summary of the problems I found on Dr. Carmesin's claims that SN1a distances support his work.
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This is an ongoing discussion.
Dr. Carmesin provided a reply to my objections and confirmed that he is not sure if his model can predict the SN1a distances.
In fact, he said: "My theory does not fail to predict these distances. I just did not calculate these distances yet for a good reason: I tested my full theory by calculating the measured Hubble constants of the Hubble tension."
First, that is not a good reason. Second, I calculated the distances according to his model and the model failed. See the plot and the attached python script.
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My plot of his model showcases that the model fails to predict the observed distances.
I also drive home the fact that Dr. Carmesin's model modifies the meaning of H0 (the Hubble Constant). Because of that comparison of results are not straightforward and seems to not have been considered before.
The plots also show that HU model predicts the observed distances without any parameters.

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