The impact of the new Earth gravity models on the measurement of the Lense–Thirring effect with a new satellite

Abstract

In this paper we investigate the opportunities offered by the new Earth gravity models from the dedicated CHAMP and, especially, GRACE missions to the project of measuring the general relativistic Lense-Thirring effect with a new Earth's artificial satellite. It turns out that it would be possible to abandon the stringent, and expensive, requirements on the orbital geometry of the originally prosed LARES mission (same semimajor axis a = 12270 km of the existing LAGEOS and inclination i = 70 deg) by inserting the new spacecraft in a relatively low, and cheaper, orbit (a = 7500 − 8000 km, i ∼ 70 deg) and suitably combining its node Ω with those of LAGEOS and LAGEOS II in order to cancel out the first even zonal harmonic coefficients of the multipolar expansion of the terrestrial gravitational potential J 2 , J 4 along with their temporal variations. The total systematic error due to the mismodelling in the remaining even zonal harmonics would amount to ∼ 1% and would be insensitive to departures of the inclination from the originally proposed value of many degrees. No semisecular long-period perturbations would be introduced because the period of the node, which is also the period of the solar K 1 tidal perturbation, would amount to ∼ 10 2 days. Since the coefficient of the node of the new satellite would be smaller than 0.1 for such low altitudes, the impact of the non-gravitational perturbations of it on the proposed combination would be negligible. Then, a particular financial and technological effort for suitably building the satellite in order to minimize the non-conservative accelerations would be unnecessary.

The impact of the new Earth gravity model EIGEN-CG03C on the measurement of the Lense-Thirring effect with some existing Earth satellites

“…It has the great advantage of discarding the perigee of LAGEOS II. However, it is affected by J 4 , J 6 , J 8 ...,J 4 ,J 6 whose impact on the total available accuracy is still rather controversial [13,14]. It is so mainly because the error due to the static part of the geopotential even zonals J 4 , J 6 , J 8 , ... is still rather model-dependent ranging from ∼ 4% to ∼ 9% at 1-sigma level.…”

Gravitomagnetic field of rotating rings

“…For instance, the famous Lense-Thirring effect (Lense and Thirring 1918), that is the precessions of the node and the periapsis of a satellite orniting a central spinning mass, has been analyzed in different contexts: there are the LAGEOS tests around the Earth (Ciufolini and Pavlis 2004; Matteo Luca Ruggiero 1 DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy INFN, Sezione di Torino, Via Pietro Giuria 1, Torino, Italy 2010a), the MGS tests around Mars (Iorio 2006a(Iorio , 2010 and other tests around the Sun and the planets (Iorio 2012a); see Ciufolini (2007); Iorio et al (2011Iorio et al ( , 2013; Renzetti (2013b) for a discussion and a review of the recent results. In February 2012 the LARES mission (Ciufolini et al 2012) has been launched to measure the Lense-Thirring effect of the Earth, and is now gathering data; a comprehensive discussion on this mission can be found in Iorio (2005Iorio ( , 2009); Renzetti (2013aRenzetti ( , 2012; Ciufolini et al (2010bCiufolini et al ( , 2015. In the recent past, the Gravity Probe B (Everitt et al 2011) mission was launched to measure the precession of orbiting gyroscopes (Pugh 1959;Schiff 1960).…”

Towards a One Percent Measurement of Frame Dragging by Spin with Satellite Laser Ranging to LAGEOS, LAGEOS 2 and LARES and GRACE Gravity Models

“…The altitude achievable with this qualifying launch is of about 1450 km. Nevertheless, Ries (2005) informed us that CSR had done some simulations supporting the possibility of using a lower orbit laser-ranged satellite to measure the Lense-Thirring effect, this possibility was later on also discussed in Iorio (2005b). Precise calculations of the LARES gravitational errors were analyzed in Ciufolini (2006) 5.2 A New Laser-Ranged Satellite at a Lower Altitude than LAGEOS and LAGEOS 2…”