l. iorio- lense-thirring effect on two-body range in solar system scenarios

8/3/2019 L. Iorio- Lense-Thirring effect on two-body range in solar system scenarios

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Lense-Thirringeffect ontwo-body

range in solarsystem

L. Iorio

Motivationsand Overviewof thePlanetaryScenario

Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta

Trans-NeptunionObjects

Planet X?

Conclusions

Lense-Thirring effect on two-body range insolar system scenarios

L. Iorio

Ministero dellIstruzione, dellUniversit e della Ricerca, Fellow of the RoyalAstronomical Society

38th COSPAR Scientific Assembly, Bremen, Germany,July 18-25, 2010
http://goforward/http://find/http://goback/


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions

Outline

1 Motivations and Overview of the Planetary Scenario

2 Lense-Thirring

3 Schwarzschild

4 Solar Oblateness

5 Minor Asteroids

6 Ceres, Pallas, Vesta

7 Trans-Neptunion Objects

8 Planet X?

9 Conclusions


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions

For a long time since its prediction in 1918 within

general relativity [Lense & Thirring 1918], the

Lense-Thirring effect has been retained too small to be

detected with planetary motions. Nowadays, the

situation is becoming more favorable.

At present, some attempts to measure it in the

gravitational fields of the Earth and Mars have been

performed with the LAGEOS [Ciufolini et al. 2009] and

Mars Global Surveyor [Iorio 2006] artificial satellites.Their status is somewhat uncertain, and the realistic

evaluation of the accuracy reached in such tests is

matter of controversy

[Krogh 2007, Iorio 2009, Iorio 2010a]

The data analysis of the GP-B mission, aimed todirectly measure another gravitomagnetic effect in a

dedicatedspacecraft-based experimentorbiting the

Earth, is still ongoing [Everitt et al. 2009]. Anyway, it

will notbe possible to repeatsuch an experiment in a

foreseeable future.


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions

















foreseeable future.


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions

















foreseeable future.


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions

The non-gravitational perturbations do notaffect the

motion of the planets

The gravitational perturbations are well-known and

relativelyeasy to model

Only oneeven zonal J2 has to be taken into account inmodeling the non-spherical field of the Sun

The Earth-planet range || is a direct, unambiguousobservable

Present-day 1-way range residuals to Mercury fromradar-ranging spanning 30 yr are at a few-km level

The future approved Bepi-Colombo mission to Mercury

will allow to reach a 4.510 cm accuracy in measuringits range over t 2 yr [Milani et al. 2010].

Plans for implementing Planetary Laser Ranging (PLR),accurate to a cm-level, exist [Smith et al. 2006]. First

attempts with Mercury have already been performed by

GGAO with the non-optimized MLA onboard the

Messenger spacecraft with a formalerror of 20 cm

[Neumann et al. 2006].


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions
















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Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions
















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Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions
















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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions
















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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions







Present-day 1-way range residuals to Mercury from

radar-ranging spanning 30 yr are at a few-km level









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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions

Numerically integrated range:

Lense-Thirring

0 0.5 1 1.5 2

t y

7.5

5

2.5

0

2.5

5

7.5

10

m

EMBMercury range: SSB numerical calculation

Figure: Difference|| between the numerically integratedEMB-Mercury ranges with and without the solar Lense-Thirring effect

over t= 2 yr. The same initial conditions, retrieved from the NASA JPL

Horizons system in the ICRF/J2000.0 frame, have been used for both theintegrations.


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions


Schwarzschild

0 0.5 1 1.5 2

t y

200000

100000

0

100000

m


Figure: Difference|| between the numerically integratedEMB-Mercury ranges with and without the perturbation due to the Suns

Schwarzschild field over t= 2 yr. The same initial conditions, retrieved

from the NASA JPL Horizons system in the ICRF/J2000.0 frame, havebeen used for both the integrations.

L Thi i


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions


J2

0 0.5 1 1.5 2

t y

150

100

50

0

50

100

150

m


Figure: Difference|| between the numerically integratedEMB-Mercury ranges with and without the solar J2 effect over t= 2 yr.

The same initial conditions, retrieved from the NASA JPL Horizons

system in the ICRF/J2000.0 frame, have been used for both theintegrations.

L Thi i


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions


minor asteroids

0 0.5 1 1.5 2t y

2

1

0

1

2

m

EMB

Mercury range: SSB numerical calculation

Figure: Difference || between the numerically integrated EMB-Mercury ranges with and without thenominal perturbation due to the ring of minor asteroids with mring = 1 10

10M [Fienga et al. 2010] andRring = 3.14 au [Fienga et al. 2010] over t = 2 yr. The same initial conditions, retrieved from the NASAJPL Horizons system in the ICRF/J2000.0 frame, have been used for both the integrations.

Lense Thirring


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions


Ceres, Pallas, Vesta

0 0.5 1 1.5 2

t y

40

20

0

20

40

m

EMB

Mercury range: SSB numericalcalculation

Figure: Difference || between the numerically integrated EMB-Mercury ranges with and without thenominal perturbation due to Ceres, Pallas, Vesta [Pitjeva & Standish 2009] over t = 2 yr. The same initialconditions, retrieved from the NASA JPL Horizons system in the ICRF/J2000.0 frame, have been used forboth the integrations.

Lense Thirring


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions


TNOs

0 0.5 1 1.5 2t y

0.4

0.2

0

0.2

0.4

m

EMB


Figure: Difference || between the numerically integrated EMB-Mercury ranges with and without thenominal perturbation due to the ring of Trans-Neptunian Objects with mring = 5.26 10

8M [Pitjeva 2010]and Rring = 43 au [Pitjeva 2010] over t = 2 yr. The same initial conditions, retrieved from the NASA JPLHorizons system in the ICRF/J2000.0 frame, have been used for both the integrations.

Lense-Thirring


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L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions


planet X?

0 0.5 1 1.5 2t y

1.5

1

0.5

0

0.5

1

1.5

m

EMB


Figure: Difference || between the numerically integrated EMB-Mercury ranges with and without theperturbation due to a hypothetical remote planet X lying almost in the ecliptic with maximum tidal parameter

KX = 2.7 1026 s2 [Iorio 2010b] over t = 2 yr. The same initial conditions, retrieved from the NASA

JPL Horizons system in the ICRF/J2000.0 frame, have been used for both the integrations.

Lense-Thirring


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Lense Thirringeffect ontwo-body


L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions

Summary

The Lense-Thirring range signal does fall well within the

expected level of measurability, so that it may be

detected with a 0.20.5% accuracy over t= 2 yr.

Several competing range signals induced by other

dynamical effects act as systematic errors. Anyway,

their temporal patterns are, in general, different from

that of the Lense-Thirring signal. The most insidiousone is the solar J2 , presently known with an uncertainty

of 10%. However, its more accurate measurement is

just one of the goals of the Bepi-Colombo mission. The

masses of Ceres, Pallas, Vesta are known with at a

102 103 level, while the mass of the ring of theminor asteroids is uncertain at a 30% level.

The Lense-Thirring effect, if not modeled, may act as

source of systematic bias in other high-accuracy

proposed tests of general relativity.

Lense-Thirring


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Lense Thirringeffect ontwo-body


L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions

Summary















Lense-Thirring


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geffect ontwo-body


L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions

Summary















Lense-Thirring


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geffect ontwo-body


L. Iorio


Lense-Thirring

Schwarzschild

SolarOblateness

MinorAsteroids

Ceres, Pallas,Vesta


Planet X?

Conclusions

Table: Maximum peak-to-peak nominalamplitudes, in m, of the Earth-planet range signals over t = 2yr due to the dynamical effects listed for Mercury. We adopted the standard value J

2= 2.0 107

[Fienga et al. 2010] for the quadrupole mass moment of the Sun. It is presently known at a 10% level of

accuracy. For its proper angular momentum we used S = 190.0 1039 kg m2 s1 [Pijpers 1998] from

helioseismology. For the ring of the minor asteroids we used mring = (1 0.3) 1010M, Rring = 3.14au [Fienga et al. 2010], while for the TNOs, modeled as massive ring as well, we adopted

mring = 5.26 108M, Rring = 43 au [Pitjeva 2010]. The masses of the major asteroids Ceres Pallas,

Vesta, accurate to 102 103 level, have been retrieved from [Pitjeva & Standish 2009]. For the tidal

parameter of X we used GMX/r3X = (2.1 0.6) 10

26 s2 [Iorio 2010b], obtained from the perihelionprecession of Saturn [Fienga et al. 2010, Pitjeva 2008].

Dynamical effect Peak-to-peak amplitude (m)Solar Schwarzschild 4 105

Solar J2 300

Ceres, Pallas, Vesta 80

Solar Lense-Thirring 17.5Ring of minor Asteroids 4

Planet X? 1.5 3TNOs 0.8

Lense-Thirring


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AppendixReferences

References I

I. Ciufolini et al.,

Space Science Reviews,148

, 71, 2009C.W.F. Everitt et al.,

Space Science Reviews, 148, 53, 2009

A. Fienga et al.

Proc. IAU symposium 261 Relativity in FundamentalAstronomy: Dynamics, Reference Frames and Data

analysis, 5, 159-169, 2010

L. Iorio,

Classical Quantum Gravity,23

, 5451, 2006L. Iorio,

Space Science Reviews, 148, 363, 2009

L. Iorio,

Central European Journal of Physics, 8, 509, 2010a

Lense-Thirringff


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AppendixReferences

References II

L. Iorio,

The Open Astronomy Journal, 3, 1, 2010b

K. Krogh,

Classical Quantum Gravity, 24, 5709, 2007

J. Lense, H. Thirring

Phys. Z., 19, 156, 1918

A. Milani et al.,

Proc. IAU symposium 261 Relativity in Fundamental

Astronomy: Dynamics, Reference Frames and Data

analysis, 5, 356-365, 2010

G. Neumann et al.,

Proc. 15-th International Workshop on Laser Ranging,

Canberra, Australia, 2006

Lense-Thirringff t


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effect ontwo-body


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AppendixReferences

References III

F.P. Pijpers,

Mon. Not. R. Astron. Soc., 297, L76, 1998

E.V. Pitjeva,

Journes 2008 Systmes de rfrence

spatio-temporels and X. Lohrmann-Kolloquium 22-24

September 2008 - Dresden, Germany

E.V. Pitjeva, E.M. Standish,

Celestial Mechanics and Dynamical Astronomy, 103,

365, 2009

E.V. Pitjeva,Proc. IAU symposium 261 Relativity in Fundamental

Astronomy: Dynamics, Reference Frames and Data

analysis, 5, 170-178, 2010

Lense-Thirringeffect on


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L. Iorio

AppendixReferences

References IV

D.E. Smith et al.,Science, 311, 53, 2006

l. iorio- lense-thirring effect on two-body range in solar system scenarios

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