Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.gao.spb.ru/english/as/j2014/presentations/tang.pdf Дата изменения: Wed Oct 8 08:34:24 2014 Дата индексирования: Sun Apr 10 01:07:02 2016 Кодировка: Поисковые слова: р п р п р п р п р п р п р п р п р п р п р п

Motivation

Long-term precession

Relativistic Effects

Conclusions

.

Relativistic precession model of the Earth
.

for long time interval
Kai Tang, Michael H. Soffel, Jin-He Tao, Zheng-Hong Tang

2014-09-22

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2014-09-22

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Motivation

Long-term precession

Relativistic Effects

Conclusions

. 1

Motivation

. 2

Long-term precession

. 3

Relativistic Effects

. 4

Conclusions

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Motivation

Long-term precession

Relativistic Effects

Conclusions

Contents

. 1

Motivation

. 2

Long-term precession

. 3

Relativistic Effects

. 4

Conclusions

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Motivation

Long-term precession

Relativistic Effects

Conclusions

Vondrak's long-term precession

an extension of IAU 2006 model of precession (Vondrak et al., 2011) the precession of the ecliptic: PA , Q (Mercury 6 package) the precession of the equator: XA , Y
A A

(La93 (Laskar et al., 1993), additional corrections due to IAU2006) a cubic polynomial plus 8 to 14 periodic terms ±200 millennia from J2000.0 . points . consistent with the IAU 2006 precession (differences are less than a few arcseconds in the vicinity of J2000.0) . no effects from General Relativity
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Motivation

Long-term precession

Relativistic Effects

Conclusions

Goals

. a relativistic theory of Earth's rotation . Klioner, Gerlach and Soffel (2010) . consistent with General relativity

(1) the Earth's long-term precession in a relativistic framework the precession of the ecliptic: integrated numerically as in most previous works. the precession of the equator: based on the 1PN model of Earth's rotation (Klioner et al., 2010) (2) the relativistic effects on the precession

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Motivation

Long-term precession

Relativistic Effects

Conclusions

Contents

. 1

Motivation

. 2

Long-term precession

. 3

Relativistic Effects

. 4

Conclusions

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Motivation

Long-term precession

Relativistic Effects

Conclusions

the Precession of the Ecliptic

Dynamical model (Laskar et al., 2010): the Sun, all 8 planets of the solar system and Pluto the Moon is treated as a separate object the quadruple moment of the Sun and the Earth the tidal dissipation in the Earth-Moon System the solar mass loss . Relativistic effect . The 1PN correction due to the Sun . Numerical integration: BCRS the symplectic SABA4 scheme (Laskar et al., 2001) ±1 Myr, 1-day step
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Motivation

Long-term precession

Relativistic Effects

Conclusions

the Precession of the Ecliptic

The approximations for the precession of the ecliptic PA and QA : PA = 5440 - 1 .98 в 10-4 T + QA = -1608 - 2 .06 в 10
-4 26 i=1

Ci cos(2 T/Pi ) + Si sin(2 T/Pi ), Ci cos(2 T/Pi ) + Si sin(2 T/Pi ) (1)

T+

26 i=1

where T is in TDB from J2000.0.
Table 1: The Main Periodic Terms in PA , QA .
Term -s3 -s1 -s4 -s2 -s6 Ci [ ] -3720 657 -2068 -855 438 PA Si [ ] 1259 -2586 -302 -570 338 Ci [ ] -1290 2508 288 548 -334 QA Si [ ] -3698 736 -2056 -838 435 P[yr] 68975 235535 72488 192342 49178 fi [ /yr] 18.789505 5.502369 17.878769 6.7377991 26.35311

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Motivation

Long-term precession

Relativistic Effects

Conclusions

the Precession of the Ecliptic

15000 10000 PA (") 5000 0 -5000 -1 1 0.5 QA (") 0 -0.5 -1 -1.5 -1 -0.5 0 time (Myr)
Journess2014

our solution Vondrak

-0.5
4

0

0.5

1

x 10

0.5

1

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Motivation

Long-term precession

Relativistic Effects

Conclusions

the Precession of the Equator

Dynamical model: . Relativistic effects . Geodetic precession the post-Newtonian inertial torque several relativistic reference systems with corresponding time scales and relativistic scaling of parameters . (Klioner, Gerlach, Soffel (2010))

Numerical integration: GCRS, BCRS, TRS 8th-order Runge-Kutta ±1 Myr, 0.1-day step
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Motivation

Long-term precession

Relativistic Effects

Conclusions

the Precession of the Equator

The approximations for the precession of the equator XA and YA : XA = 5128 - 1 .054 в 10-3 T +
25 i=1

Ci cos(2 T/Pi ) + Si sin(2 T/Pi ), Ci cos(2 T/Pi ) + Si sin(2 T/Pi ) (2)

YA = -74120 - 2 .86 в 10-5 T + where T is in TT from J2000.0.

25 i=1

Table 2: The Main Periodic Terms in XA , YA .
Term -p -s 3 -s 1 -s 6 Ci [ ] -25597 -68282 227568 48758 PA Si [ ] 1608 -4561 488 583 Ci [ ] 59383 2390 -1639 520 QA Si [ ] 55590 2218 -1553 434 P[yr] -857 4238 -503 -499 fi [ /yr] 50.63 18.98 5.695 26.58

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Motivation

Long-term precession

Relativistic Effects

Conclusions

the Precession of the Equator

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Motivation

Long-term precession

Relativistic Effects

Conclusions

Contents

. 1

Motivation

. 2

Long-term precession

. 3

Relativistic Effects

. 4

Conclusions

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Motivation

Long-term precession

Relativistic Effects

Conclusions

Relatvistic Effect on PA ,Q
1500

A

1500

1000

1000

500

500

(")

A

-500

Q
-500 -1000 -1000 -1500 -1 -0.5 0 0.5 1 -1500 -1

P

A

0

(")

0

-0.5

0

0.5

1

time (Myr)

time (Myr)

the 1PN effect of the Sun the relativistic effect reach about 1300" in ±1 Myr the main period is about 195 000 yr in ±0.2 Myr, this influence is smaller than 10
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Motivation

Long-term precession

Relativistic Effects

Conclusions

Relatvistic Effect of geodetic precession on XA ,Y
8000 6000 4000 2000
XA (")

A

8000 6000 4000 2000
YA (")

0 -2000 -4000 -6000 -8000 -1

0 -2000 -4000 -6000 -8000 -1

-0.5

0 time (Myr)

0.5

1

-0.5

0 time (Myr)

0.5

1

the most important relativistic effect in Earth's rotation the influence is about 8000 in ±1 Myr

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Motivation

Long-term precession

Relativistic Effects

Conclusions

Other relatvistic Effects on XA ,Y
1 0.8 0.6 0.4 0.2
XA (")

A

0.8 0.6 0.4 0.2
YA (")

0 -0.2 -0.4 -0.6 -0.8

0 -0.2 -0.4 -0.6 -0.8 -1 -1 -0.5 0 time (Myr) 0.5 1

-1 -1

-0.5

0 time (Myr)

0.5

1

accumulate with time the amplitude of these effects is less than 1 arcsecond within ±1 Myr too small to be considered in most cases over this time span

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Motivation

Long-term precession

Relativistic Effects

Conclusions

Contents

. 1

Motivation

. 2

Long-term precession

. 3

Relativistic Effects

. 4

Conclusions

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Motivation

Long-term precession

Relativistic Effects

Conclusions

Conclusions

1

. Relativistic precession model of the Earth for long time interval (1)the difference to P03 is only several arcseconds in the interval ±2000 years around J2000.0 (2)consistent with other long-term precession theories (3)consistent with general relativity . Relativistic features 1 the 1PN effects related with the Sun 2 the geodetic precession/nutation 3 the post-Newtonian torque 4 several relativistic reference systems with corresponding time scales and relativistic scaling of parameters.

2

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Motivation

Long-term precession

Relativistic Effects

Conclusions

Thank you!

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