Only a bot could substitute the area, which uses the R1 and R2 radii, for the area which is calculated using r1 and r2.

A total disaster.

But for a bot thereis no problem.

In the real world, however, it really is a problem.

You cannot substitute an area involving r2 and r1 into a formula which features R2 and R1.

θo = angle subtended by the two radii, R2 and R1 = orbital angle

s2 = R2 x θo

s1 = R1 x θo

θr = angle subtended by the two radii, r2 and r1 = rotational angle

s2 = r2 x θr

s1 = r1 x θr

R2 - R1 = r2 - r1

r2 x θr = R2 x θo

r1 x θr = R1 x θo

r2/r1 = R2/R1

(r2 x R1) = (r1 x R2)

Since the two areas must be equal,

r1/R1 = (r2 + r1)/(R2 + R1)

Right away, one runs into huge problems with this scenario.

R2 = r2 - r1 + R1

(r2 x R1) = r1r2 - r12 + (R1 x r1)

r2(R1 - r1) = r1(R1 - r1)

So we end up with: r2 = r1, which is impossible.

The best astrophysicists from NASA and ESA proved that the orbital Sagnac is much larger than the rotational Sagnac.

Here is the demonstration.

LISA: Light Interferometer Space Antenna

https://lisa.nasa.gov/https://www.elisascience.org/http://sci.esa.int/lisa/The orbital calculations for the LISA project were performed by some of the very best astrophysicists in the world.

http://tycho.usno.navy.mil/ptti/2003papers/paper34.pdfDr. Massimo Tinto, Jet Propulsion Laboratory, Principal Scientist

In the SSB frame, the differences between back-forth delay times

**are very much larger than has been previously recognized.** The reason is in the aberration due to motion and changes of orientation in the SSB frame.

**With a velocity V=30 km/s**, the light-transit times of light signals in opposing directions (Li, and L’i) will differ by as much as 2VL (a few thousands km).

SSB = solar system barycenter

Published in the Physical Review D

http://tycho.usno.navy.mil/ is the U.S. Naval Observatory website

https://arxiv.org/pdf/gr-qc/0310017.pdfWithin this frame, which we can assume to be Solar System Barycentric (SSB), the differences between back-forth delay times that occur are in fact thousands of kilometers, very much larger than has been previously recognized by us or others. The problem is not rotation per se, but rather aberration due to motion and changes of orientation in the SSB frame.

The kinematics of the LISA orbit brings in the effects of motion at several orders of magnitude larger than any previous papers on TDI have addressed.

**The instantaneous rotation axis of LISA swings about the Sun at 30 km/sec, and on any leg the transit times of light signals in opposing directions can differ by as much as 1000 km.****Aberration due to LISA’s orbit about the Sun dominates its instantaneous rotation.**The formula is 2VL/c.

V = RΩ

THIS IS THE ORBITAL SAGNAC EFFECT.

Its magnitude is much larger than the rotational Sagnac effect.

Actually, there is no difference in the path lengths: the light signals take different times around the path, amounting to two different speeds c + v and c - v, which of course would be equivalent to admitting that STR is false.

Therefore, the papers have to mention the difference in path lengths to avoid admitting that STR is false.

The formula for the difference in path lengths is:

dp = 2ΩA/c (p = path length)

Then, the difference in time will be:

dt = 2dp/c

The ORBITAL SAGNAC calculated at the Jet Propulsion Laboratory amounts to an admitted difference in path lengths of 1,000 kilometers.

The difference in path lengths for the rotational Sagnac is 14.4 kilometers:

https://arxiv.org/pdf/gr-qc/0306125.pdf (Dr. Daniel Shaddock, Jet Propulsion Laboratory)

https://gwic.ligo.org/thesisprize/2011/yu_thesis.pdf (pg. 63)

Therefore the difference in path lengths for the ORBITAL SAGNAC is some 60 times greater than the difference in path lengths for the rotational Sagnac, according to these calculations.

The formula used for the ORBITAL SAGNAC (difference in path lengths) is 2VL/c, V = RΩ.

R = Earth - Sun distance

Ω = orbital angular velocity

Algebraic approach to time-delay data analysis: orbiting case

K Rajesh Nayak and J-Y Vinet

https://www.cosmos.esa.int/documents/946106/1027345/TDI_FOR_.PDF/2bb32fba-1b8a-438d-9e95-bc40c32debbeThis is an IOP article, published by the prestigious journal Classic and Quantum Gravity:

http://iopscience.iop.org/article/10.1088/0264-9381/22/10/040/metaIn this work, we estimate the effects due to the Sagnac phase by taking the realistic model for LISA orbital motion.

This work is organized as follows: in section 2, we make an estimate of Sagnac phase

for individual laser beams of LISA by taking realistic orbital motion. Here we show that, in general, the residual laser noise because of Sagnac phase is much larger than earlier estimates.

**For the LISA geometry, R⊙/L is of the order 30 and the orbital contribution to the Sagnac phase is larger by this factor.**The computations carried out by Dr. R.K. Nayak (over ten papers published on the subject) and Dr. J.Y. Vinet (Member of the LISA International Science Team),

**and published by prestigious scientific journals and by ESA, show that the orbital Sagnac is 30 times greater than the rotational Sagnac for LISA.**"In reality the motion of LISA is much more complex and our study shows that the main term for Sagnac effect comes from orbital motion."

ORBITAL SAGNAC/ROTATIONAL SAGNAC =~ R/L = 30

This fact is true for each and every satellite orbiting above the surface of the Earth, especially the GPS satellites.

But the orbital Sagnac is not being recorded/registered by the GPS satellites even though is much larger than the rotational Sagnac effect.

As has been proven above, the calculations of Dr. R.K. Nayak (over ten papers published on the subject) and Dr. J.Y. Vinet (Member of the LISA International Science Team), published by prestigious scientific journals and by ESA, show that the orbital Sagnac is 30 times greater than the rotational Sagnac for LISA.

Algebraic approach to time-delay data analysis: orbiting case

K Rajesh Nayak and J-Y Vinet

https://www.cosmos.esa.int/documents/946106/1027345/TDI_FOR_.PDF/2bb32fba-1b8a-438d-9e95-bc40c32debbeThis is an IOP article, published by the prestigious journal Classic and Quantum Gravity:

http://iopscience.iop.org/article/10.1088/0264-9381/22/10/040/metaSee also: Algebraic approach to time-delay data analysis for orbiting LISA

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.70.102003"In this work, we estimate the effects due to the Sagnac phase by taking the realistic model for LISA orbital motion."

"Earlier results assume a simple module in which LISA rotates only about its own axis!!

In reality the motion of LISA is much more complex and our study shows that the main term for Sagnac effect comes from orbital motion."

Conclusions:

The contribution from the Sagnac effect is much larger than earlier predicted.

Full calculations comparing the rotational Sagnac with the orbital Sagnac lead to the final result:

The original arm length for LISA: 5,000,000 km (L)

Earth - Sun radius: 150,000,000 km (R)

ORBITAL SAGNAC/ROTATIONAL SAGNAC =~ R/L = 30

http://qem.ee.nthu.edu.tw/f1b.pdfThis is an IOP article.

The author recognizes the earth's orbital Sagnac is missing whereas the earth's rotational Sagnac is not.

He uses GPS and a link between Japan and the US to prove this.

In GPS the actual magnitude of the Sagnac correction

due to earth’s rotation depends on the positions of

satellites and receiver and a typical value is 30 m, as the

propagation time is about 0.1s and the linear speed due

to earth’s rotation is about 464 m/s at the equator.

**The**

GPS provides an accuracy of about 10 m or better in positioning.

Thus the precision of GPS will be degraded significantly,

if the Sagnac correction due to earth’s rotation

is not taken into account. On the other hand, the orbital

motion of the earth around the sun has a linear speed of

about 30 km/s which is about 100 times that of earth’s

rotation. Thus the present high-precision GPS would be

entirely impossible if the omitted correction due to orbital

motion is really necessary.

In an intercontinental microwave link between Japan and

the USA via a geostationary satellite as relay, the influence

of earth’s rotation is also demonstrated in a high-precision

time comparison between the atomic clocks at two remote

ground stations.

In this transpacific-link experiment, a synchronization

error of as large as about 0.3 µs was observed unexpectedly.

Meanwhile, as in GPS,

**no effects of earth’s orbital motion**

are reported in these links, although they would be

easier to observe if they are in existence. Thereby, it is evident

that the wave propagation in GPS or the intercontinental

microwave link depends on the earth’s rotation, but

is entirely independent of earth’s orbital motion around

the sun or whatever. As a consequence, the propagation

mechanism in GPS or intercontinental link can be viewed

as classical in conjunction with an ECI frame, rather than

the ECEF or any other frame, being selected as the unique

propagation frame. In other words, the wave in GPS or the

intercontinental microwave link can be viewed as propagating

via a classical medium stationary in a geocentric

inertial frame.

The GPS on your phone works because the MISSING ORBITAL SAGNAC EFFECT does not show up.

But according to the calculations referenced above by some of the very best astrophysicists in the world, this orbital effect is tens of times larger than the rotational effect.