The recently approved Juno mission will orbit Jupiter for one year in a highly eccentric (r_min=1.06R_Jup, r_max=39R_Jup) polar orbit (i=90 deg) to accurately map, among other things, the jovian magnetic and gravitational fields. Such an orbital configuration yields an ideal situation, in principle, to attempt a measurement of the general relativistic Lense-Thirring effect through the Juno's node Omega which would be displaced by about 570 m over the mission's duration. Conversely, by assuming the validity of general relativity, the proposed test can be viewed as a direct, dynamical measurement of the Jupiter's angular momentum S which would give important information concerning the internal structure and formation of the giant planet. The long-period orbital perturbations due to the zonal harmonic coefficients J_L, L=2,3,4,6 of the multipolar expansion of the jovian gravitational potential accounting for its departures from spherical symmetry are a major source of systematic bias. While the Lense-Thirring node rate is independent of the inclination i, the node zonal perturbations vanish for i=90. In reality, the orbit injection errors will induce departures δi from the ideal polar geometry, so that the zonal perturbations will come into play at an unacceptably high level, in spite of the expected improvements in the low-degree zonals by Juno. A linear combination of Omega, the periJove omega and the mean anomaly M cancels out the impact of J_2 and J_6. A two orders of magnitude improvement in the uncanceled J_3 and J_4 would be needed to reduce their bias on the relativistic signal to the percent level; it does not seem unrealistic because the expected level of improvement in such zonals is three orders of magnitude.
An assessment of the measurement of the Lense-Thirring effect in the Earth gravity field, in reply to: ``On the measurement of the Lense-Thirring effect using the nodes of the LAGEOS satellites, in reply to ``On the reliability of the so far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites'' by L. Iorio,'' by I. Ciufolini and E. Pavlis
Some comments on the recent results about the measurement of the Lense-Thirring effect in the gravitational field of the Earth with the LAGEOS and LAGEOS II satellites
On the Measurement of the Lense-Thirring effect Using the Nodes of the LAGEOS Satellites in reply to "On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites" by L. Iorio
Reply to "The meaning of systematic errors, a comment to "Reply to On the Systematic Errors in the Detection of the Lense-Thirring Effect with a Mars Orbiter", by Lorenzo Iorio'', by G. Felici
The impact of the new CHAMP and GRACE Earth gravity models on the measurement of the general relativistic Lense--Thirring effect with the LAGEOS and LAGEOS II satellites
Some comments about a recent paper on the measurement of the general relativistic Lense-Thirring effect in the gravitational field of the Earth with the laser-ranged LAGEOS and LAGEOS II satellites
We investigate the Hamilton-Jacobi equation of a probe particle moving on d-dimensional generalized Lense-Thirring metric. This space-time is different from the slowly rotating Myers-Perry black hole at second order in rotation parameters. We show that the dynamics of the probe particle along the time-like geodesic of the generalized Lense-Thirring space-time is super-integrable and has more constants of motion with respect to the same dynamics on Myers-Perry black hole. We also discuss the second rank Killing tensors associated with the generalized Lense-Thirring metric.
Reply to ``On the Systematic Errors in the Detection of the Lense-Thirring Effect with a Mars Orbiter '', by Giampiero Sindoni, Claudio Paris and Paolo Ialongo
The geodesics of bound spherical orbits i.e. of orbits performing Lense-Thirring precession, are obtained in the case of the $Λ$-term within gravito-electromagnetic formalism. It is shown that the presence of the $Λ$-term in the equations of gravity leads to both relativistic and non-relativistic corrections in the equations of motion. The contribution of the $Λ$-term in the Lense-Thirring precession is interpreted as an additional relativistic correction and the gravito-gyromagnetic ratio is defined.
The meaning of systematic errors, a comment to "Reply to On the Systematic Errors in the Detection of the Lense-Thirring Effect with a Mars Orbiter", by Lorenzo Iorio
Advances in the measurement of the Lense-Thirring effect with planetary motions in the field of the Sun
E. V. Pitjeva通过使用EPM 2006星历表的动力学模型处理超过400，000个不同类型的行星观测数据，最近估计了对牛顿-爱因斯坦金星近日点进动的修正为每世纪-0.0004 +/- 0.0001弧秒。根据广义相对论的预测，金星近日点的Lense-Thirring岁差为每世纪-0.0003角秒。事实证明，无论是其他错误建模/未建模的标准牛顿/爱因斯坦效应，还是外来效应，假设，例如，解释先锋异常，可能导致了确定的额外岁差的金星轨道，因此，可以合理地归因于太阳的重力磁场，而不是在EPM 2006星历的例程建模。然而，必须指出的是，引用的错误是正式的，统计的一个;现实的不确定性可能更大。未来对内行星星历表的改进，包括信使号和金星快车号的跟踪数据，应该会进一步提高这种广义相对论测试的准确性和一致性，这也将有利于其他天文学家团队对近日点（和节点）的额外岁差的独立估计。
The standard Lense-Thirring metric is a century-old slow-rotation large-distance approximation to the gravitational field outside a rotating massive body, depending only on the total mass and angular momentum of the source. Although it is not an exact solution to the vacuum Einstein equations, asymptotically the Lense-Thirring metric approaches the Kerr metric at large distances. Herein we shall discuss a specific variant of the standard Lense-Thirring metric, carefully chosen for simplicity, clarity, and various forms of "improved" behaviour, (to be more carefully defined in the body of the a…
The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $Λ$. It is shown that according to the current accuracy of satellite measurements the obtained error limits for $Λ$ is self-consistent with cosmological observations. The corrections of $Λ$ term are derived for the strong field Lense-Thirring precession i.e. the frame dragging effect and for the nutation. As a result, in the context of recently proposed $Λ$-gravity we obtain constraints for $Λ$ in both relativistic and weak-field limits. Namely…
In this paper, we investigate the properties of the Lense-Thirring precession frequency and periastron precession of the relativistic bound orbits in slowly rotating naked singularity spacetimes. We show that the precession frequencies of a stationary test gyroscope are quite unique in slowly rotating naked singularity spacetimes, and therefore, one can easily distinguish them from the slowly rotating Kerr black hole spacetime. On the other hand, we also show that in slowly rotating Joshi-Malafarina-Narayan (JMN1) naked singularity spacetime, negative precession of the timelike bound orbits is…
We make use of the absence of Lense-Thirring precession of the innermost megamaser clumps around black holes in order to place upper limits on the spin amplitude of seven black holes at the center of megamaser galaxies: NGC 4258, NGC 2273, UGC 3789, NGC 3393, NGC 5495, NGC 5765b, and UGC 6093. The constraints are derived by requiring that the associated precession time-scale be longer than the age of the megamaser clumps, in order to preserve the single-plane geometry of the megamasers.
The Lense--Thirring spacetime describes a 4-dimensional slowly rotating approximate solution of vacuum Einstein equations valid to a linear order in rotation parameter. It is fully characterized by a single metric function of the corresponding static (Schwarzschild) solution. In this paper, we introduce a generalization of the Lense--Thirring spacetimes to the higher-dimensional multiply-spinning case, with an ansatz that is not necessarily fully characterized by a single (static) metric function. This generalization lets us study slowly rotating spacetimes in various higher curvature gravitie…
