Math 2.0

Geophysics Definition

Length of day variations

Builds on Earth's rotationAngular velocity

Definition

Let UT1 be the time scale defined by the rotation of the Earth, and let TAI be atomic time measured in SI seconds. The length of day LOD(t)\mathrm{LOD}(t) near time tt is the interval of atomic time, in SI seconds, during which UT1 advances by 8640086400 seconds. The excess length of day is ΔLOD(t)=LOD(t)−86400 s,\Delta\mathrm{LOD}(t) = \mathrm{LOD}(t) - 86400\ \mathrm{s}, and length of day variations are the changes of ΔLOD\Delta\mathrm{LOD} with time.

Remarks

To first order, ΔLOD/86400 s=−Δω/Ω\Delta\mathrm{LOD}/86400\ \mathrm{s} = -\Delta\omega/\Omega, where Ω\Omega is the nominal rate of rotation and Δω=ω−Ω\Delta\omega = \omega - \Omega the deviation of the angular velocity about the polar axis. Example: ΔLOD=1\Delta\mathrm{LOD} = 1 ms corresponds to Δω/Ω≈−1.16⋅10−8\Delta\omega/\Omega \approx -1.16 \cdot 10^{-8}; if it lasts for a year, UT1 falls behind atomic time by about 0.370.37 s. Non-example: the solar day of 8640086400 s is longer than the sidereal day of about 8616486164 s, but this difference is not a length of day variation. It comes from the orbital motion of the Earth, not from a change of its rotation.

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Cross product, concept, no evidence levelCross productconceptDerivative, concept, no evidence levelDerivativeconceptEarth's rotation, concept, no evidence levelEarth's rotationconceptEuclidean vector, concept, no evidence levelEuclidean vectorconceptIdentity matrix, object, no evidence levelIdentity matrixobjectMatrix, definition, no evidence levelMatrixdefinitionVector space, definition, no evidence levelVector spacedefinitionVelocity, concept, no evidence levelVelocityconceptSquare matrix, definition, no evidence levelSquare matrixdefinitionTranspose, definition, no evidence levelTransposedefinitionLinear map, definition, no evidence levelLinear mapdefinitionMultilinear map, definition, no evidence levelMultilinear mapdefinitionOrthogonal matrix, definition, no evidence levelOrthogonal matrixdefinitionAlternating multilinear map, definition, no evidence levelAlternating multiline…definitionOrthogonal group, object, no evidence levelOrthogonal groupobjectDeterminant, definition, no evidence levelDeterminantdefinitionSpecial orthogonal group, object, no evidence levelSpecial orthogonal gr…objectAngular velocity, concept, no evidence levelAngular velocityconceptLength of day variations, definition, no evidence levelLength of day variati…definition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Cross product concept
  2. Derivative concept
  3. Earth's rotation concept
  4. Euclidean vector concept
  5. Identity matrix object
  6. Matrix definition
  7. Vector space definition
  8. Velocity concept
  9. Square matrix definition
  10. Transpose definition
  11. Linear map definition
  12. Multilinear map definition
  13. Orthogonal matrix definition
  14. Alternating multilinear map definition
  15. Orthogonal group object
  16. Determinant definition
  17. Special orthogonal group object
  18. Angular velocity concept
  19. Length of day variations definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Day_length_fluctuations
About this page
TagRXB61H2G55
URIm2://RXB61H2G55
Kinddefinition
WritingW0 stub
MSC86A30, 86A04
DefinesLength of day variations
UsesEarth's rotation, Angular velocity
Changed3 November 2026

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