of 27
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1/27
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
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2/27
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
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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3/27
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
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.
http://goforward/http://find/http://goback/8/3/2019 L. Iorio- Lense-Thirring effect on two-body range in solar system scenarios
4/27
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
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.
http://goforward/http://find/http://goback/8/3/2019 L. Iorio- Lense-Thirring effect on two-body range in solar system scenarios
5/27
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
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.
http://goforward/http://find/http://goback/8/3/2019 L. Iorio- Lense-Thirring effect on two-body range in solar system scenarios
6/27
8/3/2019 L. Iorio- Lense-Thirring effect on two-body range in solar system scenarios
7/27
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
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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8/27
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
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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9/27
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
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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10/27
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
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].
http://goforward/http://find/http://goback/8/3/2019 L. Iorio- Lense-Thirring effect on two-body range in solar system scenarios
11/27
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
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].
http://goforward/http://find/http://goback/8/3/2019 L. Iorio- Lense-Thirring effect on two-body range in solar system scenarios
12/27
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
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 from
radar-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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13/27
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
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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14/27
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
Numerically integrated range:
Schwarzschild
0 0.5 1 1.5 2
t y
200000
100000
0
100000
m
EMBMercury range: SSB numerical calculation
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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15/27
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
Numerically integrated range:
J2
0 0.5 1 1.5 2
t y
150
100
50
0
50
100
150
m
EMBMercury range: SSB numerical calculation
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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16/27
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
Numerically integrated range:
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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17/27
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
Numerically integrated range:
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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18/27
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
Numerically integrated range:
TNOs
0 0.5 1 1.5 2t y
0.4
0.2
0
0.2
0.4
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 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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19/27
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
Numerically integrated range:
planet X?
0 0.5 1 1.5 2t y
1.5
1
0.5
0
0.5
1
1.5
m
EMB
Mercury range: SSB numerical calculation
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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20/27
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
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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21/27
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
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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22/27
geffect ontwo-body
range in solarsystem
L. Iorio
Motivationsand Overviewof thePlanetaryScenario
Lense-Thirring
Schwarzschild
SolarOblateness
MinorAsteroids
Ceres, Pallas,Vesta
Trans-NeptunionObjects
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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23/27
geffect ontwo-body
range in solarsystem
L. Iorio
Motivationsand Overviewof thePlanetaryScenario
Lense-Thirring
Schwarzschild
SolarOblateness
MinorAsteroids
Ceres, Pallas,Vesta
Trans-NeptunionObjects
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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effect ontwo-body
range in solarsystem
L. Iorio
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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effect ontwo-body
range in solarsystem
L. Iorio
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
range in solarsystem
L. Iorio
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