Transformations between Time Systems - Revision history

Gema.Cueto: /* UT0, UT1, UT2 */

2025-01-27T08:03:19Z

UT0, UT1, UT2

← Older revision		Revision as of 08:03, 27 January 2025
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	:<math>		:<math>
	\Delta S=0^s_{\cdot}022\; \sin{2\pi t}-0^s_{\cdot}~~120~~\; \cos{2\pi t}-0^s_{\cdot}0060\sin{4\pi t}+0^s_{\cdot}0070\; \cos{4\pi t}		\Delta S=0^s_{\cdot}022\; \sin{2\pi t}-0^s_{\cdot}012\; \cos{2\pi t}-0^s_{\cdot}0060\sin{4\pi t}+0^s_{\cdot}0070\; \cos{4\pi t}
	\qquad \mbox{(15)}		\qquad \mbox{(15)}
	</math>		</math>
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	\qquad \mbox{(16)}		\qquad \mbox{(16)}
	</math>		</math>



	== TAI - TDT, TCG, TT ==		== TAI - TDT, TCG, TT ==

Claudia.Prajanu at 21:15, 23 September 2018

2018-09-23T21:15:54Z

← Older revision		Revision as of 21:15, 23 September 2018
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	where UT1R is an smoothed a priory measurement of the earth's orientation for which the short period (<math>t< 35</math> days) tidal effects have been removed before smoothing [Webb and Zumberge, 1993] <ref> [Webb and Zumberge, 1993] Webb, F. and Zumberge, J., 1993. An Introduction to GIPSY/OASIS-II. Jet Propulsion Laboratory, JPL, 4800 Oak Grove Drive, Pasadena, CA 91109.</ref>.		where UT1R is an smoothed a priory measurement of the earth's orientation for which the short period (<math>t< 35</math> days) tidal effects have been removed before smoothing [Webb and Zumberge, 1993] <ref> [Webb and Zumberge, 1993] Webb, F. and Zumberge, J., 1993. An Introduction to GIPSY/OASIS-II. Jet Propulsion Laboratory, JPL, 4800 Oak Grove Drive, Pasadena, CA 91109.</ref>.

	The TAI-UT1R or UTC-UT1R is provided in the Earth's Rotation Parameters files <ref group="footnotes"> Earth orientation parameters and time information are provided in different servers and with different format files: "erp" files, the GIPSY format "TPNML" and "tpeo.nml" files. See ~~ftp://igscb.jpl.nasa.gov/pub/product/iers/ or~~ http://acc.igs.org/, or the JPL sites: ftp://sideshow.jpl.nasa.gov/pub/gipsy_products/2009/orbits/, ftp://sideshow.jpl.nasa.gov/pub/gipsy_products/RapidService/orbits/.</ref>.		The TAI-UT1R or UTC-UT1R is provided in the Earth's Rotation Parameters files <ref group="footnotes"> Earth orientation parameters and time information are provided in different servers and with different format files: "erp" files, the GIPSY format "TPNML" and "tpeo.nml" files. See http://acc.igs.org/, or the JPL sites: ftp://sideshow.jpl.nasa.gov/pub/gipsy_products/2009/orbits/, ftp://sideshow.jpl.nasa.gov/pub/gipsy_products/RapidService/orbits/.</ref>.

	According to [Yoder et al., 1981] <ref> [Yoder et al., 1981] Yoder, C., Williams, J. and Parke, M., 1981. Tidal Variations of Earth Rotation. Journal of Geophysical Research. pp. 881-891.</ref> the periodic variations of UT1 due to the tidal deformations of the polar moment of inertia can be given by:		According to [Yoder et al., 1981] <ref> [Yoder et al., 1981] Yoder, C., Williams, J. and Parke, M., 1981. Tidal Variations of Earth Rotation. Journal of Geophysical Research. pp. 881-891.</ref> the periodic variations of UT1 due to the tidal deformations of the polar moment of inertia can be given by:

Jaume.Sanz at 20:05, 4 February 2013

2013-02-04T20:05:10Z

← Older revision		Revision as of 20:05, 4 February 2013
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	:<math>		:<math>
	\begin{array}{c}		\begin{array}{c}
	TCB-~~TDT~~=L_B\;(MJD-43\,144.0)\; 86\,400\,s+P_0\\		TCB-TDB=L_B\;(MJD-43\,144.0)\; 86\,400\,s+P_0\\
	\mbox{with}\\		\mbox{with}\\
	L_B=1.55051976772\;10^{-8},\mbox{ and }P_0\simeq 6.55\, 10^{-5}s.		L_B=1.55051976772\;10^{-8},\mbox{ and }P_0\simeq 6.55\, 10^{-5}s.

Carlos.Lopez at 11:42, 23 February 2012

2012-02-23T11:42:04Z

← Older revision		Revision as of 11:42, 23 February 2012
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	\|Level=Intermediate		\|Level=Intermediate
	\|YearOfPublication=2011		\|YearOfPublication=2011
	~~\|Logo=gAGE~~
	\|Title={{PAGENAME}}		\|Title={{PAGENAME}}
	}}		}}

Jaume.Sanz at 09:43, 30 January 2012

2012-01-30T09:43:00Z

← Older revision		Revision as of 09:43, 30 January 2012
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	::[[File: Transf_between_Time_Systems_Fig_1.png \|none\|thumb\|520px\|'''''Figure 1:''''' Time flowing (from [Seeber, 1993] <ref>[Seeber, 1993] Seeber, G., 1993. Satellite Geodesy: Foundations, Methods, and Applications. Walter de Gruyter & Co., Berlin, Germany. </ref>.]]		::[[File: Transf_between_Time_Systems_Fig_1.png \|none\|thumb\|520px\|'''''Figure 1:''''' Time flowing (from [Seeber, 1993] <ref>[Seeber, 1993] Seeber, G., 1993. Satellite Geodesy: Foundations, Methods, and Applications. Walter de Gruyter & Co., Berlin, Germany. </ref>).]]

Jaume.Sanz at 12:35, 26 January 2012

2012-01-26T12:35:16Z

← Older revision		Revision as of 12:35, 26 January 2012
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	:<math>		:<math>
	TDT\equiv TT=TAI+32.184\ seconds		TDT\equiv TT=TAI+32.184\ seconds
	\qquad \mbox{(17}		\qquad \mbox{(17)}
	</math>		</math>

Jaume.Sanz at 12:34, 26 January 2012

2012-01-26T12:34:37Z

← Older revision		Revision as of 12:34, 26 January 2012
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	:<math>		:<math>
	\alpha_2=l^{\prime }=1\,287\,099_{\cdot}^{\prime \prime}804+(99^r+1\,292\,581_{\cdot}^{\prime \prime}224)\; T-0_{\cdot}^{\prime \prime}577\; T^2-0_{\cdot}^{\prime \prime}012\; T^3		\alpha_2=l^{\prime }=1\,287\,099_{\cdot}^{\prime \prime}804+(99^r+1\,292\,581_{\cdot}^{\prime \prime}224)\; T-0_{\cdot}^{\prime \prime}577\; T^2-0_{\cdot}^{\prime \prime}012\; T^3
	\qquad \mbox{(7)}		\qquad \mbox{(8)}
	</math>		</math>

	:<math>		:<math>
	\alpha_3=F=335\,778_{\cdot}^{\prime \prime}877+(1342^r+295\,263_{\cdot}^{\prime \prime}137)\; T-13_{\cdot}^{\prime \prime}257\; T^2+0_{\cdot}^{\prime \prime}011\; T^3		\alpha_3=F=335\,778_{\cdot}^{\prime \prime}877+(1342^r+295\,263_{\cdot}^{\prime \prime}137)\; T-13_{\cdot}^{\prime \prime}257\; T^2+0_{\cdot}^{\prime \prime}011\; T^3
	\qquad \mbox{(8)}		\qquad \mbox{(9)}
	</math>		</math>

	:<math>		:<math>
	\alpha_4=D=1\,072\,261_{\cdot}^{\prime \prime}307+(1\,236^r+1\,105\,601_{\cdot}^{\prime \prime}328)\; T-6_{\cdot}^{\prime \prime}891\; T^2+0_{\cdot}^{\prime \prime}019\; T^3		\alpha_4=D=1\,072\,261_{\cdot}^{\prime \prime}307+(1\,236^r+1\,105\,601_{\cdot}^{\prime \prime}328)\; T-6_{\cdot}^{\prime \prime}891\; T^2+0_{\cdot}^{\prime \prime}019\; T^3
	\qquad \mbox{(9)}		\qquad \mbox{(10)}
	</math>		</math>

	:<math>		:<math>
	\alpha_5=\Omega =450\,160_{\cdot}^{\prime \prime}280-(5^r+482\,890_{\cdot}^{\prime \prime}539)\; T+7_{\cdot}^{\prime \prime}455\; T^2+0_{\cdot}^{\prime \prime}008\; T^3		\alpha_5=\Omega =450\,160_{\cdot}^{\prime \prime}280-(5^r+482\,890_{\cdot}^{\prime \prime}539)\; T+7_{\cdot}^{\prime \prime}455\; T^2+0_{\cdot}^{\prime \prime}008\; T^3
	\qquad \mbox{(8)}		\qquad \mbox{(11)}
	</math>		</math>

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	UT1=UT0+\Delta l		UT1=UT0+\Delta l
	\end{array}		\end{array}
	\qquad \mbox{(9)}		\qquad \mbox{(12)}
	</math>		</math>

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	\Delta l=\frac{1^{s}}{15}\;(x_p\; \sin \lambda -y_p\; \cos \lambda)\; \tan \varphi		\Delta l=\frac{1^{s}}{15}\;(x_p\; \sin \lambda -y_p\; \cos \lambda)\; \tan \varphi
	\end{array}		\end{array}
	\qquad \mbox{(10)}		\qquad \mbox{(13)}
	</math>		</math>

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	:<math>		:<math>
	UT2=UT1+\Delta S		UT2=UT1+\Delta S
	\qquad \mbox{(11)}		\qquad \mbox{(14)}
	</math>		</math>

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	:<math>		:<math>
	\Delta S=0^s_{\cdot}022\; \sin{2\pi t}-0^s_{\cdot}120\; \cos{2\pi t}-0^s_{\cdot}0060\sin{4\pi t}+0^s_{\cdot}0070\; \cos{4\pi t}		\Delta S=0^s_{\cdot}022\; \sin{2\pi t}-0^s_{\cdot}120\; \cos{2\pi t}-0^s_{\cdot}0060\sin{4\pi t}+0^s_{\cdot}0070\; \cos{4\pi t}
	\qquad \mbox{(12)}		\qquad \mbox{(15)}
	</math>		</math>

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	:<math>		:<math>
	t=2000.00+\frac{MJD-51\,544.03}{365.2422}		t=2000.00+\frac{MJD-51\,544.03}{365.2422}
	\qquad \mbox{(13)}		\qquad \mbox{(16)}
	</math>		</math>

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	:<math>		:<math>
	TDT\equiv TT=TAI+32.184\ seconds		TDT\equiv TT=TAI+32.184\ seconds
	\qquad \mbox{(~~14)~~}		\qquad \mbox{(17}
	</math>		</math>

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	L_G=6.969290134\;10^{-10}		L_G=6.969290134\;10^{-10}
	\end{array}		\end{array}
	\qquad \mbox{(15)}		\qquad \mbox{(18)}
	</math>		</math>

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	g=\displaystyle{\frac{2 \; \pi \; (357^o_{\cdot}528+35\,999^o_{\cdot}050 \; T)}{360^{o}}}		g=\displaystyle{\frac{2 \; \pi \; (357^o_{\cdot}528+35\,999^o_{\cdot}050 \; T)}{360^{o}}}
	\end{array}		\end{array}
	\qquad \mbox{(16)}		\qquad \mbox{(19)}
	</math>		</math>

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	:<math>		:<math>
	Centuries=\frac{Julian\ date-2\,451\,545.0}{36\,525}		Centuries=\frac{Julian\ date-2\,451\,545.0}{36\,525}
	\qquad \mbox{(17)}		\qquad \mbox{(20)}
	</math>		</math>

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	L_B=1.55051976772\;10^{-8},\mbox{ and }P_0\simeq 6.55\, 10^{-5}s.		L_B=1.55051976772\;10^{-8},\mbox{ and }P_0\simeq 6.55\, 10^{-5}s.
	\end{array}		\end{array}
	\qquad \mbox{(18)}		\qquad \mbox{(21)}
	</math>		</math>

Jaume.Sanz at 12:33, 26 January 2012

2012-01-26T12:33:05Z

← Older revision		Revision as of 12:33, 26 January 2012
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	The number <math>N</math> is chosen to include all terms with a period less than <math>35</math> days. The <math>\alpha _j</math> are the functions of time given by equations (6) ~~and~~ (7) ~~(see~~ [[ICRF to CEP]]).		The number <math>N</math> is chosen to include all terms with a period less than <math>35</math> days. The <math>\alpha _j</math> are the functions of time given by equations (6) to (10) in [[ICRF to CEP]].

	:<math>		:<math>
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	</math>		</math>

			:<math>
			\alpha_2=l^{\prime }=1\,287\,099_{\cdot}^{\prime \prime}804+(99^r+1\,292\,581_{\cdot}^{\prime \prime}224)\; T-0_{\cdot}^{\prime \prime}577\; T^2-0_{\cdot}^{\prime \prime}012\; T^3
			\qquad \mbox{(7)}
			</math>

			:<math>
			\alpha_3=F=335\,778_{\cdot}^{\prime \prime}877+(1342^r+295\,263_{\cdot}^{\prime \prime}137)\; T-13_{\cdot}^{\prime \prime}257\; T^2+0_{\cdot}^{\prime \prime}011\; T^3
			\qquad \mbox{(8)}
			</math>

			:<math>
			\alpha_4=D=1\,072\,261_{\cdot}^{\prime \prime}307+(1\,236^r+1\,105\,601_{\cdot}^{\prime \prime}328)\; T-6_{\cdot}^{\prime \prime}891\; T^2+0_{\cdot}^{\prime \prime}019\; T^3
			\qquad \mbox{(9)}
			</math>

	:<math>		:<math>

Jaume.Sanz at 08:19, 26 January 2012

2012-01-26T08:19:14Z

← Older revision		Revision as of 08:19, 26 January 2012
Line 119:		Line 119:
	: <math>		: <math>
	\begin{array}{c}		\begin{array}{c}
	\Delta l= \frac{1^{s}}{15}\;(x_p\; \sin \lambda -y_p\; \cos \lambda)\; \tan \varphi		\Delta l=\frac{1^{s}}{15}\;(x_p\; \sin \lambda -y_p\; \cos \lambda)\; \tan \varphi
	\end{array}		\end{array}
	\qquad \mbox{(10)}		\qquad \mbox{(10)}

Jaume.Sanz at 08:05, 26 January 2012

2012-01-26T08:05:40Z

← Older revision		Revision as of 08:05, 26 January 2012
Line 74:		Line 74:
	where UT1R is an smoothed a priory measurement of the earth's orientation for which the short period (<math>t< 35</math> days) tidal effects have been removed before smoothing [Webb and Zumberge, 1993] <ref> [Webb and Zumberge, 1993] Webb, F. and Zumberge, J., 1993. An Introduction to GIPSY/OASIS-II. Jet Propulsion Laboratory, JPL, 4800 Oak Grove Drive, Pasadena, CA 91109.</ref>.		where UT1R is an smoothed a priory measurement of the earth's orientation for which the short period (<math>t< 35</math> days) tidal effects have been removed before smoothing [Webb and Zumberge, 1993] <ref> [Webb and Zumberge, 1993] Webb, F. and Zumberge, J., 1993. An Introduction to GIPSY/OASIS-II. Jet Propulsion Laboratory, JPL, 4800 Oak Grove Drive, Pasadena, CA 91109.</ref>.

	The TAI-UT1R or UTC-UT1R is provided in the Earth's Rotation Parameters files <ref group="footnotes"> Earth orientation parameters and time information are provided in different servers and with different format files: "erp" files, the GIPSY format "TPNML" and "tpeo.nml" files. See ftp://igscb.jpl.nasa.gov/pub/product/iers/ or http://acc.igs.org/, or the JPL sites: ftp://sideshow.jpl.nasa.gov/pub/~~gipsy\_products~~/2009/orbits/, ftp://sideshow.jpl.nasa.gov/pub/~~gipsy\_products~~/RapidService/orbits/.</ref>.		The TAI-UT1R or UTC-UT1R is provided in the Earth's Rotation Parameters files <ref group="footnotes"> Earth orientation parameters and time information are provided in different servers and with different format files: "erp" files, the GIPSY format "TPNML" and "tpeo.nml" files. See ftp://igscb.jpl.nasa.gov/pub/product/iers/ or http://acc.igs.org/, or the JPL sites: ftp://sideshow.jpl.nasa.gov/pub/gipsy_products/2009/orbits/, ftp://sideshow.jpl.nasa.gov/pub/gipsy_products/RapidService/orbits/.</ref>.

	According to [Yoder et al., 1981] <ref> [Yoder et al., 1981] Yoder, C., Williams, J. and Parke, M., 1981. Tidal Variations of Earth Rotation. Journal of Geophysical Research. pp. 881-891.</ref> the periodic variations of UT1 due to the tidal deformations of the polar moment of inertia can be given by:		According to [Yoder et al., 1981] <ref> [Yoder et al., 1981] Yoder, C., Williams, J. and Parke, M., 1981. Tidal Variations of Earth Rotation. Journal of Geophysical Research. pp. 881-891.</ref> the periodic variations of UT1 due to the tidal deformations of the polar moment of inertia can be given by:
Line 98:		Line 98:


	The parameters <math>A_i</math>, <math>k_{ij}</math> are given in Table 1 of article [[ICRF to CEP]] for periods up to <math>41</math> days. A table with periods up to <math>18.6</math> years (<math>62</math> terms) based on [Yoder et al., 1981] is available in http://hpiers.obspm.fr/eop-pc/models/UT1/UT1R_tab.html. An extended model with "<math>\sin</math>" and "<math>\cos</math>" terms is given in the IERS03 conventions, (see [Denis et al., 2004]<ref>[Denis et al., 2004] Denis, D., McCarthy and Petit, G., 2004. IERS Conventions (2003). IERS Technical Note 32.. IERS Convention Center., Frankfurt am Main.</ref>, page 92) with the associated table of coefficients.		The parameters <math>A_i</math>, <math>k_{ij}</math> are given in Table 1 of article [[ICRF to CEP]] for periods up to <math>41</math> days. A table with periods up to <math>18.6</math> years (<math>62</math> terms) based on [Yoder et al., 1981] is available in http://hpiers.obspm.fr/eop-pc/models/UT1/UT1R_tab.html. An extended model with "<math>\sin</math>" and "<math>\cos</math>" terms is given in the IERS03 conventions, (see [Denis et al., 2004]<ref>[Denis et al., 2004] Denis, D., McCarthy and Petit, G., 2004. IERS Conventions (2003). IERS Technical Note 32. IERS Convention Center, Frankfurt am Main.</ref>, page 92) with the associated table of coefficients.