CONCEPT OF RELATIVE MOTION- How Can We Say That Planets revolve around Sun?

[Billy T]

Billy, orbiting objects are considered to be in an eternal free fall. This is easily verified by any number of online sources

I went to your link, and made a quick scan for "free fall" If it is defined there, I missed it. For me "free fall" in a gravity field is without any detectable force inside a box that is "free falling", until it hits the gravity source. How, other than that, do you define "free fall" ?

 

[RJBeery]

I went to your link, and made a quick scan for "free fall" If it is defined there, I missed it. For me "free fall" in a gravity field is without any detectable force inside a box that is "free falling", until it hits the gravity source. How, other than that, do you define "free fall" ?

I define a free fall as being a geodesic as mentioned earlier.

In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational force, is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.

 

[Billy T]

I define a free fall as being a geodesic as mentioned earlier.

As is always the case, definitions are conventions, that often change with time and different meaning for the same words do exit, especially when one person, like me, still is using an older version. I can't do the complex math that is required for defining the geodesic, or any other part of general relativity, so I prefer to consider gravity a force and stick with the concept that falling (in the context of gravity) is to move to more negative gravitational potential (and rising is the reverse).

Thus as a comet falls from apogee to perigee (point closet to the sun) it gains kinetic energy while doing so to keep total energy constant. For me “free fall” is when this transformation of PE to KE is most rapid possible. – I. e. direct or “free fall” on the radial line to the gravitational source. Free falling is a form of falling that always end with impact of the gravity source.

I am aware that this older POV is not quite as accurate as the general relativity POV that there is no gravity force – only mass distorted space. That my POV has slight error when careful measurement of Venus' orbit are made but I can use it to compute and not general relativity, so stick with idea gravity is an inverse square law force.
As they say: “Physics advances a little with the death of each old physicist.”

It not just that I can't compute with general relativity's complex tensor equations, it is also such a mathematical form of physic that it does not interest me as for me, at least, there is no understanding available with it, only proofs.

 

[RJBeery]

As is always the case, definitions are conventions, that often change with time and different meaning for the same words do exit, especially when one person, like me, still is using an older version. I can't do the complex math that is required for defining the geodesic, or any other part of general relativity, so I prefer to consider gravity a force and stick with the concept that falling (in the context of gravity) is to move to more negative gravitational potential (and rising is the reverse).

Thus as a comet falls from apogee to perigee (point closet to the sun) it gains kinetic energy while doing so to keep total energy constant. For me “free fall” is when this transformation of PE to KE is most rapid possible. – I. e. direct or “free fall” on the radial line to the gravitational source. Free falling is a form of falling that always end with impact of the gravity source.

I am aware that this older POV is not quite as accurate as the general relativity POV that there is no gravity force – only mass distorted space. That my POV has slight error when careful measurement of Venus' orbit are made but I can use it to compute and not general relativity, so stick with idea gravity is an inverse square law force.
As they say: “Physics advances a little with the death of each old physicist.”

It not just that I can't compute with general relativity's complex tensor equations, it is also such a mathematical form of physic that it does not interest me as for me, at least, there is no understanding available with it, only proofs.

I understand your position. My personal definition of acceleration is determined by simply asking whether a body would "feel" anything under ideal circumstances (with perfect measurement, etc). This also happens to be basically something close to the definition of geodesics.

 

[hansda]

Yes. I know that.

If you knew that, in the case of "Relative Motion" one of the objects can be chosen as reference frame and in the case of "Acceleration" no such reference frame is necessary.

 

[brucep]

I went to your link, and made a quick scan for "free fall" If it is defined there, I missed it. For me "free fall" in a gravity field is without any detectable force inside a box that is "free falling", until it hits the gravity source. How, other than that, do you define "free fall" ?

Free fall is the natural motion [inertial motion] of an object, described by a geodesic path, thru the gravitational field. This includes light following a natural path described by the null geodesic. Most everything in GR is about the natural path. Orbits are geodesic paths. This is a derivation of the natural path for Einstein orbits including the prediction for Mercury's natural precession. This derivation is from the Schwarzschild geometry. Newton's Law of Gravity predicts there is no natural precession and the rate of radial oscillation, w^2_r, and the rate of angular velocity, w^2_phi, is M/r^3. No natural precession. This is what Einstein predicts for w^2_r and w^2_phi including the weak field calculation for the natural precession.


Derive the natural precession rate of Einstein orbits. All Einstein orbits naturally precess.

Start with the Schwarzschild metric, in geometric units, setting theta at 0.

dTau^2 = (1-2M/r)dt^2 - dr^2/(1-2M/r) - r^2(dphi)^2

Substituting constants of geodesic motion E/m and L/m for dt and dphi

dt = [(E/m)/(1-2M/r)]dTau

dphi = [(L/m)/r^2]dTau

The solution relates squared values for radial motion (dr/dTau)^2, energy per unit mass (E/m)^2, and the effective potential per unit mass
(V/m)^2 = (1-2M/r)(1+[(L/m)^2/r^2]).

(dr/dTau)^2 = +/- (E/m)^2 - (1-2M/r)(1+[(L/m)^2/r^2])

Taking some license for the weak field and multiplying through by 1/2 after multiplying out the squared effective potential

1/2(dr/dTau)^2 = 1/2(E/m)^2 - [1/2 - M/r + (L/m)^2/2r^2 - M(L/m)^2/r^3]

setting (V/m)^2 = U/m

U/m = 1/2 - M/r + (L/m)^2/2r^2 - M(L/m)^2/r^3

1st derivative

d(U/m)/dr = M/r^2 - (L/m)^2/r^3 + 3M(L/m)^2/r^4

2nd derivative d'2(U/m)/dr'2 = rate of radial oscillation = w^2_r

w^2_r = M(r-6M)/r^3(r-3M)

Without writing down details the rate of angular velocity becomes

w^2_phi ~ (dphi/dTau)^2 = M/r^2(r-3M)


The difference.

w^2_phi - w^2_r = 6M^2/r^3(r-3M)

We can find a factor * M/r^3 which closely approximates
6M^2/r^3(r-3M)

That factor is 6M/r

(6M/r)(M/r^3) = 6M^2/r^4

The last step is further weak field approximation

(6M/r)^1/2 ~ 1/2(6M/r) = 3M/r

So a very close approximation for the rate of orbital precession, in the weak field, is 3M/r. You can plug in numbers and get an answer that matches observation.

3M_Sun = 4431m
r_mean Mercury = 5.8x10^10 meters
415.1539069 times Mercury orbits the Sun in 100 Earth years
360 degrees per year
3600 arcseconds per degree
etc...

 

[brucep]

If you knew that, in the case of "Relative Motion" one of the objects can be chosen as reference frame and in the case of "Acceleration" no such reference frame is necessary.

The science of relativity theory, GR & SR, is frame independent. Coordinate independent. We us coordinate systems as a helpful tool for evaluating the physics. Force and acceleration are frame independent. You can't measure force or acceleration from remote frame dependent coordinates. You measure force and acceleration where it occurs. When you use a coordinate system to describe the place where the direct measurement is made it's the local proper frame where the acceleration occurs. No coordinate systems are required for doing relativistic physics but I couldn't do it without coordinate systems. LOL.

 

[chinglu]

The science of relativity theory, GR & SR, is frame independent. Coordinate independent. We us coordinate systems as a helpful tool for evaluating the physics. Force and acceleration are frame independent. You can't measure force or acceleration from remote frame dependent coordinates. You measure force and acceleration where it occurs. When you use a coordinate system to describe the place where the direct measurement is made it's the local proper frame where the acceleration occurs. No coordinate systems are required for doing relativistic physics but I couldn't do it without coordinate systems. LOL.

I am confused.

If frame independence is logical fact, why in GPS does the ECEF frame agree with the ECI frame conclusions? ECEF should only agree with its own conclusions under SR/GR.

Can you explain this?

 

[Tach]

I am confused.

If frame independence is logical fact, why in GPS does the ECEF frame agree with the ECI frame conclusions? ECEF should only agree with its own conclusions under SR/GR.

Can you explain this?

Because a coordinate transformation (from ECI to ECEF) is applied in order to account for the Sagnac effect. Still trying (in vain) to disprove relativity, chinglu?

 

[ash64449]

Really. You're going to insist [assert] that acceleration is frame dependent? Your assertion is wrong whether you're going for it or not. Have at it.

brucep. Sorry!!! i completely AGREE that my assertion is wrong...

 

[ash64449]

Because a coordinate transformation (from ECI to ECEF) is applied in order to account for the Sagnac effect. Still trying (in vain) to disprove relativity, chinglu?

Sure that will not work! Relativity is a verified one. No experiment disproved relativity.

One feels like disproving relativity is due to the fact that understanding relativity is tough.

 

[wellwisher]

The laws of physics are the same in all references. But since references can be different in terms of space and time (this is part of all equations) we need to mathematically transform what you see in one reference to quantify in another reference.

Say we have the two twins, each in separate references ,with one twin in a relativistic reference. Both bounce a rubber ball off the wall, since this relaxes the twins. Within each reference, the bouncing ball will appear to act with the same force, acceleration, velocity and momentum in that reference. If we switched the twins they would not notice any change in the ball and bounce. But since one twin is aging slower, we would need to use a math transform to compensate for the reference of the other twin.

This is special relativity but not true for GR, because gravity creates pressure within the reference, while SR does not. For example, the iron in the center of the earth is solid at temperatures it would be a gas on the surface of the earth. There is a significant phase change between the surface and the core that goes beyond aging slower. In the core reference, you can't bounce the ball because pressure alters the references. In special relativity the twins do not suffer pressure transformation at velocity but transformation only in space-time.

In low GR one twin can dance ballet but in the high GR reference, he can't do anything due to pressure. The laws of physics don't change but you need a second transform for pressure as a function of phase. At the GR induced mass pressures of the earth's core water becomes a metal and good conductor of electricity but on the surface it does not conduct well. This change can be modelled by math after the fact but can't predict ahead.

 

[Tach]

In low GR one twin can dance ballet but in the high GR reference, he can't do anything due to pressure. The laws of physics don't change but you need a second transform for pressure as a function of phase. At the GR induced mass pressures of the earth's core water becomes a metal and good conductor of electricity but on the surface it does not conduct well. This change can be modelled by math after the fact but can't predict ahead.

what possesses you to post such rubbish?

 

[chinglu]

Because a coordinate transformation (from ECI to ECEF) is applied in order to account for the Sagnac effect. Still trying (in vain) to disprove relativity, chinglu?

Sure, there is a coordinate transformation in GPS.

Both ECI and ECEF must translate to ECI in order to be correct.

Is that how SR/GR works?

Further, in ECEF does the equation d/c = t hold, where d is in ECEF coordinates?

 

[Tach]

Sure, there is a coordinate transformation in GPS.

Both ECI and ECEF must translate to ECI in order to be correct.

Wrong, the equations are correct in any frame. I know that this is frustrating to you but this is how things are.

Is that how SR/GR works?

You aren't really interested in how SR/GR work, you are interested only in your kooky ideas of "disproving" SR/GR. You are wasting your life away on a fool's errand.

 

[chinglu]

Wrong, the equations are correct in any frame. I know that this is frustrating to you but this is how things are.



You aren't really interested in how SR/GR work, you are interested only in your kooky ideas of "disproving" SR/GR. You are wasting your life away on a fool's errand.

Let's try it again.

Sure, there is a coordinate transformation in GPS.

Both ECI and ECEF must translate to ECI in order to be correct.

Is that how SR/GR works?

Further, in ECEF does the equation d/c = t hold, where d is in ECEF coordinates?

 

[Tach]

Let's try it again.

Why? You already received the explanation.
Too bad that the answers contradict your prejudices. Tough.

 

[chinglu]

Why? You already received the explanation.
Too bad that the answers contradict your prejudices. Tough.

Uh, here is how GPS works.

t = d/c does not hold true in the ECEF frame. The sagnac correction is required.

However, t = d/c is true in ECI.

SR claims t=d/c holds true in any frame.

Is this correct?

 

[OnlyMe]

Uh, here is how GPS works.

t = d/c does not hold true in the ECEF frame. The sagnac correction is required.

However, t = d/c is true in ECI.

SR claims t=d/c holds true in any frame.

Is this correct?

Special Relativity only holds that the laws of physics are equivalent in inertial frames.

While both ECEF and ECI frames use the Earth's center of mass, as an origin, only the ECI frame is inertial, in the sense suggested, within the context of Special Relativity.

 

[chinglu]

Special Relativity only holds that the laws of physics are equivalent in inertial frames.

While both ECEF and ECI frames use the Earth's center of mass, as an origin, only the ECI frame is inertial, in the sense suggested, within the context of Special Relativity.

Well, Neil Ashby states the following,

The Sagnac effect can be regarded as arising from the relativity of simultaneity in a Lorentz transformation to a sequence of local inertial frames co-moving with points on the rotating earth.

Chapter 2
http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=node1.html

So, Neil Ashby claims the sagnac effect in GPS is SR oriented.

Now what?