Modified double-averaged Hamiltonian in hierarchical triple systems

In this work, we introduce a modified double-averaging approach by considering the shortterm effects and formulate a more accurate double-averaged Hamiltonian (in comparison to the classical octupole-level Hamiltonian) for hierarchial triple systems. The Hamiltonian is expressed as a power series in the ratio of the semi-major axes of the inner and outer binaries. Both the Delaunay's elements and the classical orbit elements are adopted to describe the motion. To derive the secular Hamiltonian, the short-term oscillations in the Hamiltonian are averaged out by means of a double-averaging approach. In particular, during the average over the orbital period of the outer binary, the periodic corrections to the secular motion are taken into account. Based on the double-averaged Hamiltonian, we provide two versions of equations of secular motion, given in the form of canonic relations and Lagrange planetary equations. The resulting secular evolution equations can be utilized to reproduce the long-term behaviours for those physical systems where the perturbations coming from the disturbing bodies are relatively strong. To test the approach, we use the averaged Hamiltonian to predict the longterm motions of a planet in a stellar binary system and natural satellites in Sun-planet systems. Simulation results show that the modified Hamiltonian can reproduce secular behaviours with high accuracy. Additionally, the comparison of dynamical models truncated at different orders indicates that the secular Hamiltonian with inclusion of higher order terms has better accuracy in predicting long-term evolution

Comparison of LARES 1 and LARES 2 Missions - One Year After the Launch

With the successful launch of LARES 2, the constellation of laser ranged satellites to be used for the accurate measurement of frame-dragging of the theory of general relativity has improved significantly. The lift-off was from the European spaceport in French Guyana by the inaugural flight of VEGA C the 13th of July 2022. This launch occurred 10 years after the other maiden flight of VEGA that was carrying as main payload LARES satellite. Both launch vehicles are developed, financed and managed by ESA, Avio and ASI, with Arianespace commercialising them. The two orbits are quite special because are neither sun-synchronous nor equatorial. Particularly the LARES 2 orbit needed to be quite high compared to the classical LEO orbits. In the paper it will be explained in detail the reason for this particular orbit. Differently from LARES satellite this time the orbit did not have large tolerances in the orbit parameters. The injection accuracy for LARES was very high, though as mentioned not required, but with LARES 2 the accuracy was spectacular because it matched the orbit 10 times better than required. This will allow to improve the accuracy of the frame-dragging (also known as Lense-Thirring effect) measurement by one order of magnitude with respect to what obtained with LARES satellite thus allowing to reach an accuracy of at least a few parts in a thousand. Frame-dragging is measured by observing the node of the satellite orbit that is shifted by the dragging of spacetime induced by the Earth rotation. In fact in general relativity spacetime is deformed not only by mass but also by energy, so that also currents of mass, such as the Earth rotation, will affect gravity. The laser ranging technique will provide the most accurate ranging measurement achievable today and is thus capable to provide the necessary data for the goal of the LARES missions. However the main problem of the measurement is due to the classical gravitational and non-gravitational perturbations whose effects on the node are huge with respect to frame-dragging. To achieve this tremendous task of extracting frame-dragging to the node shift, a combination of the data of the two LARES satellites and the two LAGEOS satellites is required. Furthermore very accurate knowledge of the gravitational field of Earth is necessary, so that during the data analysis the gravitational field from GRACE and GRACE Follow On missions are used. In this work some engineering aspects of the two missions are compared along with the results obtained with the LARES mission and the expected ones from LARES 2

First results of the LARES 2 space experiment to test the general theory of relativity

The LAGEOS 3 (today LARES 2) space experiment was proposed in the eighties by the Physics Department and by the Center of Space Research (CSR) of the University of Texas (UT) at Austin and by the Italian Space Agency (ASI) to test and accurately measure frame-dragging, with the strong support of John Archibald Wheeler, director of the Center for Theoretical Physics of UT Austin. Frame-dragging is an intriguing phenomenon predicted by Einstein’s theory of general relativity which has fundamental implications in high-energy astrophysics and in the generation of gravitational waves by spinning black holes. LAGEOS 3 was reproposed in 2016 to the Italian Space Agency and to the European Space Agency as a technologically much improved version of LAGEOS 3 under the name LARES 2 (LAres RElativity Satellite 2) and then successfully launched in 2022 with the new launch vehicle VEGA C of ASI, ESA and AVIO. Today, after almost 40 years since the original proposal, we report the first results of the LARES 2 space experiment to test general relativity. The results are in complete agreement with the predictions of Einstein’s gravitational theory. Whereas previous results already confirmed the frame-dragging prediction, the conceptual relative simplicity of the LARES 2 experiment with respect to the previous tests with the LARES and LAGEOS satellites provides a significant advance in the field of tests of general relativity

First results of the LARES 2 space experiment to test the general theory of relativity

The LAGEOS 3 (today LARES 2) space experiment was proposed in the eighties by the Physics Department and by the Center of Space Research (CSR) of the University of Texas (UT) at Austin and by the Italian Space Agency (ASI) to test and accurately measure frame-dragging, with the strong support of John Archibald Wheeler, director of the Center for Theoretical Physics of UT Austin. Frame-dragging is an intriguing phenomenon predicted by Einstein's theory of general relativity which has fundamental implications in high energy astrophysics and in the generation of gravitational waves by spinning black holes. LAGEOS 3 was reproposed in 2016 to the Italian Space Agency and to the European Space Agency as a technologically much improved version of LAGEOS 3 under the name LARES 2 (LAres RElativity Satellite 2) and then successfully launched in 2022 with the new launch vehicle VEGA C of ASI, ESA and AVIO. Today, after almost forty years since the original proposal, we report the first results of the LARES 2 space experiment to test general relativity. The results are in complete agreement with the predictions of Einstein's gravitational theory. Whereas previous results already confirmed the frame-dragging prediction, the conceptual relative simplicity of the LARES 2 experiment with respect to the previous tests with the LARES and LAGEOS satellites provides a significant advance in the field of tests of general relativity.Comment: 11 page

On the high accuracy to test dragging of inertial frames with the LARES 2 space experiment

In this paper we treat some aspects of the LARES 2 space experiment to test the general relativistic phenomenon of dragging of inertial frames, or frame-dragging, in particular we discuss some aspects of its relative accuracy which can approach one part in a thousand. We then, once again respond to the criticisms of the author of a recent paper about the accuracy in the measurement of frame-dragging with LARES 2. The claims of such a paper are not reproducible in any independent analyses. Indeed, it claims that the accuracy in the test of frame-dragging, which can be reached by the LARES 2 space experiment, is several orders of magnitude larger than previously estimated in a number of papers. Here we show that such a paper is based on a number of significant misunderstandings and conceptual mistakes. Furthermore, it is puzzling to observe that previous papers by the same author contained completely opposite statements about the accuracy which can be reached using two satellites with supplementary inclinations, such as in the LARES 2 space experiment, and in general with laser-ranged satellites

Long dwell time orbits for lander-based Mars missions

This paper deals with the possibility of retrieving orbits around Mars able to provide long dwell times over a given area of the planet, without needing expensive orbital corrective manoeuvres. After a general description of the fundamental principles associated with the obtainment of the repeating ground track orbits which satisfy the aforesaid requirement, the concepts have been applied to Mars to gain trajectories which make it possible to maximise the daily contact time between a probe orbiting around the planet and a lander on the surface. The lander has been considered as equipped with an antenna of 0.5 m of diameter, working in the bands C, X, Ku, and the cases of both fixed and mobile antennas have been taken into account

On the aerosols monitoring by satellite observations

Particulate matter is the general term used to identify a complex mixture of organic and inorganic particles (aerosols) that can be found suspended in the atmosphere in solid, liquid or both physical states. The presence of particulate of non-natural origin is linked to important climatic and environmental effects. The interactions of these particles with the solar radiation, the Earth and the atmospheric gases, can modify the atmosphere physical and chemical characteristics, the temperature vertical profile and other thermodynamic variables, as well as the Earth surface characteristics and its temperature. Studies on the particles have furthermore demonstrated the existence of a link between the presence of fine and ultra-fine particulate of non-natural origin and some effects on the health of human and other living being. The aerosols can contaminate a wide area of the region surrounding the source of particulate. Based upon all these reasons it is considered the utmost importance to develop a satellite-based system capable of monitoring the presence of particulate on very large areas. This paper provides methodologies to identify atmospheric particles by means of satellite-based sensors operating both in the reflective and in the thermal infrared part of the electromagnetic spectrum. © 2008 Springer-Verlag