## Foucault’s Pendulum

- The oldest method you can do yourself for a small budget is Foucault’s Pendulum, or you can see these at many museums. I’ve seen the one at the Chicago Science museum myself.
- The pendulum rotates while swinging. The rotation is about once a day at the North Pole and decreases as the latitude is farther south until you get to the equator where it doesn’t turn. Then, south of the equator it rotates the other direction increasing in speed as it goes farther south. The amount of time the pendulum takes to rotate one full revolution is just under 24 hours divided by the sine of the latitude.
- This observed behavior is predicted by a rotating spherical earth. This confirms the spinning earth hypothesis.
- There are some flat earth ideas on what causes this.
- One popular idea is that the flat earth sun swishes through the aether causing the pendulum to move. Unfortunately, the same idea about the sun suggests the sun travels in wider and narrower concentric circles. If this were the case, the amount of rotation would vary as the sun got closer or farther away. Additionally, the place where the rotation stopped would vary with the sun’s movement instead of always being on the equator.
- There are further problems should some otherwise never-heard-of-before force causing the rotation. Firstly, why would it vary with the sine of the latitude? Sine and cosine functions strongly suggest a uniformly curving ellipsoid surface.
- The flat earth idea does not match observations, therefore it is wrong.

- If you take issue with this information, I want to hear about it. Please email me: mctoon@mctoon.net

## Eötvös Effect

- Weight changes based on latitude and movement
- The downward acceleration, typically called gravity, can be directly measured. If the earth is spinning about once per day this force should vary with latitude. However, this acceleration is also affected by the distance from the center of the earth’s mass. This mingled change can be controlled by measuring at similar elevations. We can also travel at a sufficiently high enough speed to greatly diminish or increase the net lateral speed.
- We can create a hypothesis for this effect:
- If the earth is spinning about one revolution per day, objects weigh less because of centrifugal force in proportion to their lateral speed while at rest in relation to the surface of the earth. If an object is moving against the direction of the earth’s spin the net lateral speed will be reduced then the centrifugal force will be reduced causing an increase in the object’s weight. If an object is moving with the direction of the earth’s spin the net lateral speed will be increased then the centrifugal force will be increased causing a decrease in the object’s weight.

- Wolfie6020 did this with a 500 gram mass and a scale that measures to hundredths of a gram
- https://www.youtube.com/watch?v=3ushpbbP2H8
- Original video from Wolfie6020: https://youtu.be/CkhxPm15PFo?t=425
- The mass averaged over 4 grams lighter when traveling eastward which increases the lateral speed, thus the centrifugal force. This supports the hypothesis.

- If you take issue with this information, I want to hear about it. Please email me: mctoon@mctoon.net

## Optical Gyroscopes

#### Airplane Inertial Reference Systems

- An airplane Inertial Reference System (IRS) or Inertial Reference Unit (IRU) uses three gyroscopes, each oriented in a different plane, to measure all three dimensions of the airplane’s rotation. Large airplanes have multiple IRS’s for measurement confirmation and fail-over.
- The airplane IRS measures the different rotation in each of these three planes. The ability of the IRS to accurately and precisely measure rotation is critically important for pilots to safely fly their planes. Optical gyroscopes have been in use for decades in airplanes and work very reliably.
- On the poles, the gyroscope set tangent to the surface of the earth measures the highest amount of rotation. At 30 degrees north or south the rotation is 45 degrees to the tangent so measures half what it did at the pole. At the equator, this rotation is 90 degrees to the tangent so it measures no rotation. This means that a single, leveled gyroscope measures in proportion to the sine function of the latitude. This is the same pattern as a Foucault’s pendulum.
- Gyroscopes stood vertical to the surface of the earth at the poles measure no spin. A gyroscope vertical to the surface with its axis pointing north-sound will not measure rotation and a gyroscope set with its axis pointing east-west measures spin according to the cosine of the latitude.
- This observed behavior is predicted by a rotating spherical earth. This confirms the spinning earth hypothesis.
- This topic can get very complicated, rather than summarize more, I recommend reading this article: https://www.theairlinepilots.com/forum/viewtopic.php?f=35&t=902
- This angular difference causes each gyroscope to measure a different amount of the whole rotation. The sum of the rotation in all three planes is 15 degrees per hour.
- This measurement is what IRSs use to measure an airplane’s latitude.
- This video shows a pilot in a large commercial airplane covering many aspects of an airplane’s IRS. He even forces incorrect latitude information and the IRS knows this doesn’t match its measured value so puts itself into an error state: https://youtu.be/tUwHc_wUykk
- Information on IRSs
- Initializing the ADIRU | Training | Honeywell
- Understanding the ADIRU | Training | Honeywell
- Honeywell User Manual:
- Lockheed-Martin article:

## Peer-reviewed publications measuring the rotation of the earth

### Optical gyroscopes

- How to Detect the Chandler and the Annual Wobble of the Earth with a Large Ring Laser Gyroscope
- “The sensitivity and stability of large ring laser gyroscopes has improved so dramatically that we are now able to directly measure the combined effect of the Chandler and the annual wobble of the freely rotating Earth.”
- Link to publication: https://www.ncbi.nlm.nih.gov/pubmed/22107520
- Direct PDF Download: How to Detect the Chandler and the Annual Wobble of the Earth with a Large Ring Laser Gyroscope

- Deep underground rotation measurements: GINGERino ring laser gyroscope in Gran Sasso
- “The system provides Earth rotation rate measurements as well as seismic rotational data thanks to a dedicated architecture for laser remote control, data acquisition and data transfer.”
- Link to published PDF: https://arxiv.org/pdf/1702.02789.pdf

- Direct measurement of diurnal polar motion by ring laser gyroscopes
- Analyses results from multiple earth rotation measurements.
- Link to publication: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2003JB002803
- Link to PDF: https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2003JB002803

- Sensing earth’s rotation with a helium–neon ring laser operating at 1.15 μm
- “In summary, we have successfully obtained unlocked rotation sensing of a large HeNe ring laser gyroscope in the infrared regime rate biased by the earth’s rotation alone.”
- Link to published PDF: https://pdfs.semanticscholar.org/22f2/3ca364929ee96aa054b19fcaf2c83d0fd87d.pdf

- Experiment to Internally Measure the Earth’s Rotating Speed and the Calculation Comparison with the Relativistic Treatment
- “In this paper it was clearly shown that it is possible to internally detect the rotation of Earth using the One Way interferometer where the one arm of the interferometer is built in an optically dense medium.”
- Link to published PDF: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.907.6458&rep=rep1&type=pdf

### Measurements not based on optical gyroscopes

- Detection of the Earth’s rotation using superfluid phase coherence
- “Using this device, we determine the Earth’s rotation rate to be a precision os 0.5% with the measurement time of one hour”
- Link to publication in Nature: https://www.nature.com/articles/386585a0
- Link to PDF: http://physics.berkeley.edu/sites/default/files/_/detectionnature386585a0.pdf
- Direct PDF download: Detection of the Earth’s rotation using superfluid phase coherence

- Measuring the Earth’s Rotation Rate Using a Low-Cost MEMS Gyroscope
- “This paper presents an improved method of computing the Earth’s rotation rate using a MEMS gyroscope.”
- Link to publication: https://www.semanticscholar.org/paper/Measuring-the-Earth’s-Rotation-Rate-Using-a-MEMS-Iozan-Collin/275e267727763fcbb74b991a6e60c20290634dca
- Link to PDF download: https://pdfs.semanticscholar.org/275e/267727763fcbb74b991a6e60c20290634dca.pdf

- Earth rotation measurement with micromechanical yaw-rate gyro
- Link to publication: https://iopscience.iop.org/article/10.1088/0957-0233/16/11/024/meta

- Transcontinental Baselines and the Rotation of the Earth Measured by Radio Interferometry
- Link to publication: https://science.sciencemag.org/content/186/4167/920.long
- Direct PDF Download: Transcontinental Baselines and the Rotation of the Earth Measured by Radio Interferometry

- An Apparatus for Measuring the Speed of Rotation of the Earth
- This uses two 50cm spinning disks each with a mass of 30kg spinning around 2,400rpm. This is suspended by a wire and allowed to rotate freely.
- “…an agreement within 2 per cent was found to exist between the angular speed of the rotation of the earth as derived from these terrestrial motion phenomena and the astronomical earth rotation…”
- Link to Publication: https://www.jstor.org/stable/10.2307/24998181
- Direct PDF Download: AN APPARATUS FOR MEASURING THE SPEED OF ROTATION OF THE EARTH 1905

- Earth rotation prevents exact solid-body rotation of fluids in the laboratory
- “These results show that setting a fluid in a perfect solid body rotation in a laboratory experiment is impossible — unless tilting the rotation axis of the experiment parallel to the Earth rotation axis.”
- Link to published PDF: https://arxiv.org/pdf/1205.4555.pdf

## Organizations dedicated to measuring Earth’s Rotation

- International Earth Rotation and Reference System Service: https://www.iers.org
- Paris Observatory IERS Center: http://hpiers.obspm.fr/

## Government Documents

There are many government documents confirming the rotation of the earth. Very notably are the corrections to artillery firing angles due to the rotation of the earth, otherwise called the “Coriolis Force”.

- “THE PRODUCTION OF FIRING TABLES FOR CANNON ARTILLERY”
- https://apps.dtic.mil/dtic/tr/fulltext/u2/826735.pdf
- Page 101 (PDF page 103): Table H “CORRECTIONS TO RANGE, IN METERS. TO COMPENSATE FOR THE ROTATION OF THE EARTH”
- Page 102 (PDF page 104): Table I “CORRECTIONS TO AZIMUTH IN MILS TO COMPENSATE FOR THE ROTATION OF THE EARTH”

- “Field Artillery Manual Cannon Gunnery”
- https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/tc3_09x81.pdf
- Page 194: Table H “CORRECTIONS TO RANGE, IN METERS. TO COMPENSATE FOR THE ROTATION OF THE EARTH”
- Page 195: Table I “CORRECTIONS TO AZIMUTH IN MILS TO COMPENSATE FOR THE ROTATION OF THE EARTH”

- “Tactics, Techniques, and Procedures for the Field Artillery Manual Cannon Gunnery”
- https://www.marines.mil/Portals/1/Publications/mcwp3_16_4.pdf
- Page 209: Table H “CORRECTIONS TO RANGE, IN METERS. TO COMPENSATE FOR THE ROTATION OF THE EARTH”
- Page 210: Table I “CORRECTIONS TO AZIMUTH IN MILS TO COMPENSATE FOR THE ROTATION OF THE EARTH”