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

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,

Please, see

2.2.3Madun pressure constant (MPC)

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.

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.

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.

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.

1. https://www.khanacademy.org/science/ap-physics-1/ap-forces-newtons-laws/newtons-second-law-ap/e/newton-s-second-law9with example of big dog.photo .try to understand)

2. https://courses.lumenlearning.com/physics/chapter/4-3-newtons-second-law-of-motion-concept-of-a-system/

(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