Start when the distance between m and M is r.$$t$$ is the elapsed time since when?
This is basic physics knowledge. If you lack basic physics knowledge, it is difficult to understand this paper.
Start when the distance between m and M is r.$$t$$ is the elapsed time since when?
No mate. This is you using terms and not bothering to define them properly.This is basic physics knowledge.
Yes.So ppp in your equation 1 is supposed to be the impulse provided by gravity as the object moves from altitude rrr to altitude r+vTr+vTr+vT?
Ha ha ha. I agree with your final summary there but the initial part is a bit unfair imo. For that initially static arrangement scenario he specifies the v to be strictly radial in which case the impulse expression is correct. BUT he then goes on to derive in some contorted fashion I don't care to investigate, a quasi-Newtonian not actually Newtonian gravity theory that ostensibly accounts for the anomalous perihelion advance of Venus. Which is passing strange given Mercury's advance is much greater than that of Venus but presumably he has no disagreement with the value for Mercury! Given Newtonian gravity predicts zero advance for any co-orbiting spherically symmetric masses, proclaiming Newtonian gravity will 'resume it's rightful place' is a non-starter.Read the first paragraph of section 2 of his paper. He states his equation for gravitational force: $$F(t)=\frac{GMm}{(r+vt)^2}$$. The $$vt$$ term grows without bound and his gravitational force falls towards zero over time. He then uses some bizarre process to get rid of the time dependence (not make it implicit, get rid of it). That must be illegitimate because the force is either time dependent or it's not, but he has it being both. And the model is inconsistent in other ways. He claims that his "gravitational waves" propagate at c, but has his gravitational force point through the ellipse focus. That is the gravitational force is directed at where the Sun currently is and not where it was when the "gravitational waves" now arriving at Mercury left the Sun. So he's assuming a finite speed in order to get his "Doppler" factor and simultaneously assuming an infinite speed to get his force direction.
That's all I bothered to read. So what do you think the comments of anyone who knew what they were talking about were?
I bet he used an Euler integrator in his simulation too.
Bonus: he could correct the inconsistent propagation speeds so that the force points at where the Sun was and not where it is. If he does he'll run into the same problem real physicists ran into when they tried this kind of fix to Newtonian gravity over a century ago. Orbits are unstable on time scales of a century or so and the solar system shouldn't exist (https://arxiv.org/abs/gr-qc/9909087).
But in your calculation for \(p\) you treat \(v\) as constant so you are not considering a body in free fall. Why is this relevant to planetary motion?Yes.
Not for a body in free fall it's not. If the mass \(m\) passes radius \(r\) at velocity \(v\) and it arrives at \(r+vT\) with a velocity I'll call \(u\) then conservation of energy says\[\frac 12mv^2-\frac{GMm}{r}=\frac 12mu^2-\frac{GMm}{r+vT}\]The change in radial momentum moving from \(r\) to \(r+vT\) is \(\Delta p=mv-mu\) and you can use the conservation of energy expression to find \(u\) and get \[\Delta p=mv-mv\sqrt{1-\frac{2GMT}{rv(r+vT)}}\]You can Taylor expand the square root to recover his expression for \(p\) as a leading order approximation to the exact \(\Delta p\) but to neglect the next term in the series is to say that\[\frac{GM}{2vr}\frac{T}{r+vT}\ll 1\]Do you notice anything about that statement when \(v=0\)? That happens twice per orbit.he specifies the v to be strictly radial in which case the impulse expression is correct.
What we care about is the effect of gravity on an object, and what we care about is the change in the momentum of the object. So we set m to keep the speed constant. (You can think of m as a powered object that keeps v unchanged).But in your calculation for ppp you treat vvv as constant so you are not considering a body in free fall. Why is this relevant to planetary motion?
Q-reeus said: he specifies the v to be strictly radial in which case the impulse expression is correct.
Err yes you are correct assuming free fall applies. I've read enough further to now understand he has been trying to develop a theory where relative velocity changes big G! All the time relying on Newtonian gravity to 'prove' it! A conflict of logical interest.Not for a body in free fall it's not...
But a planet isn't powered so why would you care what a powered object does? A free falling object moves at a different speed to a powered one so it won't move from \(r\) to \(r+vT\) in time \(T\) so your integration limits in your calculation for \(p\) are wrong for a free falling object even if you're happy to ignore that you're counting momentum that comes from a rocket that Mercury doesn't have.What we care about is the effect of gravity on an object, and what we care about is the change in the momentum of the object. So we set m to keep the speed constant. (You can think of m as a powered object that keeps v unchanged).
That is a way of saying that the difference between your approximation and my accurate calculation is negligible. I proved that wrong in the post you quoted.For a short time T, the speed of m can also be approximately regarded as constant.
What we care about is the effect of gravity on an object, and what we care about is the change in the momentum of the object. So we set m to keep the speed constant.But a planet isn't powered so why would you care what a powered object does? A free falling object moves at a different speed to a powered one so it won't move from \(r\) to \(r+vT\) in time \(T\) so your integration limits in your calculation for \(p\) are wrong for a free falling object even if you're happy to ignore that you're counting momentum that comes from a rocket that Mercury doesn't have.
That is a way of saying that the difference between your approximation and my accurate calculation is negligible. I proved that wrong in the post you quoted.
So you agree that you are adding momentum from a rocket and including it in your calculation.So we set m to keep the speed constant.
They don't have to be planets but they do have to be unpowered if you want to study gravity separate from the influence of a power source. You are mixing up the gravity and the power source.M and m are two objects, you don’t need to regard them as planetary models
So you're not going to acknowledge that your maths is wrong just post a rant and a picture of your made up field around a moving Earth and an embedding of GR's spatial plane around a stationary Earth and say they look alike.You see, the space-time warping model established by GR is so similar to the gravitational model under the Doppler effect of gravitational wave, but GR is static, and GR's space warping model is symmetrical relative to the center of the ball, but our gravitational model is a dynamic gravitational model, which is axisymmetric relative to the direction of the planet's motion, which is the real physical essence.
Last year, some scholars have done data verification for my mathematical derivation, which is completely correct in the end. If you are interested, you can also use the data to verify.So you're not going to acknowledge that your maths is wrong just post a rant and a picture of your made up field around a moving Earth and an embedding of GR's spatial plane around a stationary Earth and say they look alike.
Right.
I also saw their article on academia.edu, from India, and their data also came from the fitting of GR. I wrote to the author, but I didn't get a responseFurther confirmation Venus anomalous precession conforms to GR prediction:
https://arxiv.org/abs/0802.0176
As table 2 in first linked article in #36 shows, the observed perihelion advances of Earth, Mars, and especially Saturn, are much greater than for Venus. Which makes sense given the first three's relative orbital proximities to that of massive Jupiter. These values match detailed Newtonian gravity predictions except for the slight GR corrections.Russian astronomers claimed that they had accurately observed the orbits precession deviation of the planets in the solar system. I wrote to ask. Finally, they told me that their data were not from their observations, but from other conturies.
As for my question, the author keeps alert. Later, I also consulted Professor Richard, who told me that Newton's gravitational calculation of planetary precession itself is an approximate calculation, which is crazy for those scholars who publicize accurate observation of planetary precession deviation.
Due to the special orbit of Venus, it is more vulnerable to external interference, so its precession deviation will be greater....
From that you seem to infer they were massively fudging their published results. Yet without any sign of a backlash from the wider GR/astronomical community. As in published rebuttal articles. How reasonable would that conclusion be?I also saw their article on academia.edu, from India, and their data also came from the fitting of GR. I wrote to the author, but I didn't get a response
So you are saying that you don't stand by it anymore?I haven't revised my paper for a long time.
A neat way of avoiding having to waste time commenting on your ideas.I once asked a famous physics professor: If there is no GR, what would you think of my theory? He replied : Unfortunately, GR already exists.