The post-Keplerian orbital representations of the relativistic two-body problem

Klioner, S. A.; Kopeikin, Sergei M.

doi:10.1086/174201

Cited by 44 publications

(57 citation statements)

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“…of a, e do not even agree each other. Indeed, by using Equation (58) and Equations (66)-(67), Equation (30) of Klioner & Kopeikin (1994), which, in general relativity, reads…”

Section: A Comparison With Other Workmentioning

confidence: 99%

“…Sometimes, they may wonder which numerical values of the parameters of the system under consideration out of those recorded in the literature have to be inserted in the equations. For a recent discussion on some aspects of the approaches followed in the literature so far, see Tucker & Will (2019); see also Klioner & Kopeikin (1994) for a comparison of some of the parameterizations used in the literature to the 1PN level.…”

Section: Introductionmentioning

confidence: 99%

“…with the aid of Equation (14) and Equation (16) of Klioner & Kopeikin (1994), whose general relativistic expressions are…”

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confidence: 99%

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Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements

Iorio

2020

Universe

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At the second post-Newtonian (2PN) order, the secular pericentre precessionω 2PN of either a full two-body system made of well detached non-rotating monopole masses of comparable size and a restricted two-body system composed of a point particle orbiting a fixed central mass have been analytically computed so far with a variety of approaches. We offer our contribution by analytically computingω 2PN in a perturbative way with the method of variation of elliptical elements by explicitly calculating both the direct contribution due to the 2PN acceleration A 2PN , and also an indirect part arising from the self-interaction of the 1PN acceleration A 1PN in the orbital average accounting for the instantaneous shifts induced by A 1PN itself. Explicit formulas are straightforwardly obtained for both the point particle and full two-body cases without recurring to simplifying assumptions on the eccentricity e. Two different numerical integrations of the equations of motion confirm our analytical results for both the direct and indirect precessions. The values of the resulting effects for Mercury and some binary pulsars are confronted with the present-day level of experimental accuracies in measuring/constraining their pericentre precessions. The supermassive binary black hole in the BL Lac object OJ 287 is considered as well. A comparison with some of the results appeared in the literature is made.

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“…of a, e do not even agree each other. Indeed, by using Equation (58) and Equations (66)-(67), Equation (30) of Klioner & Kopeikin (1994), which, in general relativity, reads…”

Section: A Comparison With Other Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements

Iorio

2020

Universe

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“…Figure 5 depicts their differences; they are well below the expected experimental accuracy level since they amount to about |∆ρ anal − ∆ρ num | 5 × 10 −5 m, |∆ρ anal − ∆ρ num | 1 × 10 −4 cm s −1 , respectively. Furthermore, Figure 5 demonstrates pragmatically and effectively that using the osculating Keplerian orbital elements to perform our analytical gravitomagnetic calculation as in Section 3.2 did not introduce any spurious, unphysical harmonics, contrary to what could, in principle, be argued on the basis of what happened in the literature for the post-Newtonian gravitoelectric field in the case of the two-body problem and its different orbital parameterizations (Klioner & Kopeikin 1994). Moreover, to the best of the author's knowledge, no other orbital parameterizations than the osculating elements have been used so far in the case of the Lense-Thirring effect; see, e.g., Damour & Schafer (1988) and references therein.…”

Section: The Bepicolombo Range and Range-rate Perturbationsmentioning

confidence: 84%

Analytically calculated post-Keplerian range and range-rate perturbations: the solar Lense–Thirring effect and BepiColombo

Iorio

2018

Monthly Notices of the Royal Astronomical Society

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We analytically calculate the time series for the perturbations ∆ρ (t) , ∆ρ (t) induced by a general disturbing acceleration A on the mutual range ρ and range-rateρ of two test particles A, B orbiting the same spinning body. We apply it to the general relativistic Lense-Thirring effect, due to the primary's spin S, and the classical perturbation arising from its quadrupole mass moment J 2 for arbitrary orbital geometries and orientation of the source's symmetry axisŜ. The Earth-Mercury range and range-rate are nominally affected by the Sun's gravitomagnetic field to the 10 m, 10 −3 cm s −1 level, respectively, during the extended phase (2026-2028) of the forthcoming Bepi-Colombo mission to Mercury whose expected tracking accuracy is of the order of ≃ 0.1 m, 2 × 10 −4 cm s −1 . The competing signatures due to the solar quadrupole J ⊙ 2 , if modelled at the σ J ⊙ 2 ≃ 10 −9 level of the latest planetary ephemerides INPOP17a, are nearly 10 times smaller than the relativistic gravitomagnetic effects. The position and velocity vectors r, v of Mercury and Earth are changed by the solar Lense-Thirring effect by about 10 m, 1.5 m and 10 −3 cm s −1 , 10 −5 cm s −1 , respectively, over 2 yr; neglecting such shifts may have an impact on long-term integrations of the inner solar system dynamics over ∼ Gyr timescales.

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“…The formulas for g and h will become identical to those for the two-body system in general relativity given by Klioner and Kopeikin [17], when the source's charge are dropped in the former and the limit of extreme mass ratio is taken in the latter. It can be seen that the formula for the E ′ -period given in Eq.…”

Section: The Epstein-haugan Representationmentioning

confidence: 93%

Post-Keplerian motion in Reissner–Nordström spacetime

Yang

Lin

2019

Gen Relativ Gravit

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We present the analytical post-Newtonian solutions for the test particle's motion in the Reissner-Nordström spacetime. The solutions are formulated in the Wagoner-Will representation, the Epstein-Haugan representation, the Brumberg representation, and the Damour-Deruelle representation, respectively. The relations between the (post-)Keplerian parameters in different representations, as well as their relations to the orbital energy and angular momentum are also provided.

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The post-Keplerian orbital representations of the relativistic two-body problem

Cited by 44 publications

References 0 publications

Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements

Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements

Analytically calculated post-Keplerian range and range-rate perturbations: the solar Lense–Thirring effect and BepiColombo

Post-Keplerian motion in Reissner–Nordström spacetime

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