A Hybrid-Precision Numerical Orbit Integration Technique for Next Generation Gravity Missions

2020 ◽  
Author(s):  
Yufeng Nie ◽  
Yunzhong Shen ◽  
Qiujie Chen
Keyword(s):  
Double Precision ◽  
Next Generation ◽  
Integration Technique ◽  
Reference Orbit ◽  
Orbit Propagation ◽  
Quadruple Precision ◽  
Range Rate ◽  
Orbit Integration ◽  
Numerical Orbit ◽  
Best Fit

<p>In Next Generation Gravity Missions (NGGM) the Laser Ranging Interferometer (LRI) is applied to measure inter-satellite range rate with nanometer-level precision. Thereby the precision of numerical orbit integration must be higher or at least same as that of LRI and the currently widely-used double-precision orbit integration technique cannot meet the numerical requirements of LRI measurements. Considering quadruple-precision orbit integration arithmetic is time consuming, we propose a hybrid-precision numerical orbit integration technique, in which the double- and quadruple-precision arithmetic is employed in the increment calculation part and orbit propagation part, respectively. Since the round-off errors are not sensitive to the time-demanding increment calculation but to the least time-consuming orbit propagation, the proposed hybrid-precision numerical orbit integration technique is as efficient as the double-precision orbit integration technique, and as precise as the quadruple-precision orbit integration. By using hybrid-precision orbit integration technique, the range rate precision is easily achieved at 10-12m/s in either nominal or Encke form, and furthermore the sub-nanometer-level range precision is obtainable in the Encke form with reference orbit selected as the best-fit one. Therefore, the hybrid-precision orbit integration technique is suggested to be used in the gravity field solutions for NGGM.</p>

scholarly journals Research on IEEE 754 Standard Single Precision Floating Point Multipliers Designed using Urdhva Triyagbhyam Sutra of Vedic Mathematics

2019 ◽  
Vol 8 (2S11) ◽  
pp. 2990-2993
Keyword(s):  
Floating Point ◽  
Double Precision ◽  
Single Precision ◽  
Vedic Mathematics ◽  
Quadruple Precision

Duplication of the coasting element numbers is the big activity in automated signal handling. So the exhibition of drifting problem multipliers count on a primary undertaking in any computerized plan. Coasting factor numbers are spoken to utilizing IEEE 754 modern day in single precision(32-bits), Double precision(sixty four-bits) and Quadruple precision(128-bits) organizations. Augmentation of those coasting component numbers can be completed via using Vedic generation. Vedic arithmetic encompass sixteen wonderful calculations or Sutras. Urdhva Triyagbhyam Sutra is most usually applied for growth of twofold numbers. This paper indicates the compare of tough work finished via exceptional specialists in the direction of the plan of IEEE 754 ultra-modern-day unmarried accuracy skimming thing multiplier the usage of Vedic technological statistics.

Special-purpose computing for dense stellar systems

2006 ◽  
Vol 2 (14) ◽  
pp. 424-425 ◽  
Author(s):  
Junichiro Makino
Keyword(s):  
Current Status ◽  
Stellar Systems ◽  
Double Precision ◽  
Next Generation ◽  
Single Chip ◽  
Clock Speed ◽  
Peak Speed

AbstractI'll describe the current status of the GRAPE-DR project. The GRAPE-DR is the next-generation hardware for N-body simulation. Unlike the previous GRAPE hardwares, it is programmable SIMD machine with a large number of simple processors integrated into a single chip. The GRAPE-DR chip consists of 512 simple processors and operates at the clock speed of 500 MHz, delivering the theoretical peak speed of 512/226 Gflops (single/double precision). As of August 2006, the first prototype board with the sample chip successfully passed the test we prepared. The full GRAPE-DR system will consist of 4096 chips, reaching the theoretical peak speed of 2 Pflops.

Hybrid-precision arithmetic for numerical orbit integration towards future satellite gravimetry missions

2020 ◽  
Vol 66 (3) ◽  
pp. 671-688
Author(s):  
Yufeng Nie ◽  
Yunzhong Shen ◽  
Qiujie Chen ◽  
Yun Xiao
Keyword(s):  
Satellite Gravimetry ◽  
Orbit Integration ◽  
Numerical Orbit

scholarly journals Disentangling atmospheric compositions of K2-18 b with next generation facilities

2021 ◽  
Author(s):  
Quentin Changeat ◽  
Billy Edwards ◽  
Ahmed F. Al-Refaie ◽  
Angelos Tsiaras ◽  
Ingo P. Waldmann ◽  
...  
Keyword(s):  
Water Vapour ◽  
Hubble Space Telescope ◽  
Recent Analysis ◽  
Next Generation ◽  
Three Solutions ◽  
Space Telescope ◽  
James Webb Space Telescope ◽  
Cloudy Atmosphere ◽  
Low Mass ◽  
Best Fit

AbstractRecent analysis of the planet K2-18 b has shown the presence of water vapour in its atmosphere. While the H2O detection is significant, the Hubble Space Telescope (HST) WFC3 spectrum suggests three possible solutions of very different nature which can equally match the data. The three solutions are a primary cloudy atmosphere with traces of water vapour (cloudy sub-Neptune), a secondary atmosphere with a substantial amount (up to 50% Volume Mixing Ratio) of H2O (icy/water world) and/or an undetectable gas such as N2 (super-Earth). Additionally, the atmospheric pressure and the possible presence of a liquid/solid surface cannot be investigated with currently available observations. In this paper we used the best fit parameters from Tsiaras et al. (Nat. Astron. 3, 1086, 2019) to build James Webb Space Telescope (JWST) and Ariel simulations of the three scenarios. We have investigated 18 retrieval cases, which encompass the three scenarios and different observational strategies with the two observatories. Retrieval results show that twenty combined transits should be enough for the Ariel mission to disentangle the three scenarios, while JWST would require only two transits if combining NIRISS and NIRSpec data. This makes K2-18 b an ideal target for atmospheric follow-ups by both facilities and highlights the capabilities of the next generation of space-based infrared observatories to provide a complete picture of low mass planets.

scholarly journals Numerical validation in quadruple precision using stochastic arithmetic

10.29007/5c91 ◽  
2018 ◽  
Author(s):  
Stef Graillat ◽  
Fabienne Jézéquel ◽  
Romain Picot ◽  
François Févotte ◽  
Bruno Lathuilière
Keyword(s):  
Double Precision ◽  
Rounding Errors ◽  
Numerical Validation ◽  
Stochastic Arithmetic ◽  
Quadruple Precision ◽  
Cadna Library ◽  
Numerical Instabilities ◽  
Significant Performance ◽  
Arbitrary Precision

Discrete Stochastic Arithmetic (DSA) enables one to estimate rounding errors and to detect numerical instabilities in simulation programs. DSA is implemented in the CADNA library that can analyze the numerical quality of single and double precision programs. In this article, we show how the CADNA library has been improved to enable the estimation of rounding errors in programs using quadruple precision floating-point variables, i.e. having 113-bit mantissa length. Although an implementation of DSA called SAM exists for arbitrary precision programs, a significant performance improvement has been obtained with CADNA compared to SAM for the numerical validation of programs with 113-bit mantissa length variables. This new version of CADNA has been successfully used for the control of accuracy in quadruple precision applications, such as a chaotic sequence and the computation of multiple roots of polynomials. We also describe a new version of the PROMISE tool, based on CADNA, that aimed at reducing in numerical programs the number of double precision variable declarations in favor of single precision ones, taking into account a requested accuracy of the results. The new version of PROMISE can now provide type declarations mixing single, double and quadruple precision.

Celestial Mechanics

2018 ◽  
Author(s):  
Prasenjit Saha ◽  
Paul A. Taylor
Keyword(s):  
Celestial Mechanics ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Hamiltonian Form ◽  
Three Body Problem ◽  
Lagrange Points ◽  
Chaotic Orbits ◽  
Orbit Integration ◽  
Numerical Orbit ◽  
Three Body

Celestial mechanics abounds in interesting and counter-intuitive phenomena, such as descriptions of mass transfer between stars or optimal placements of satellites within the Solar System. Remarkably, many such features are already present in the restricted three-body problem, whose assumptions still allow for analytical understanding, and to which the second chapter is devoted. This ‘simplified’ system is discussed first in terms of forces (both gravitational and fictitious), and then using the Hamiltonian form. As well as traditional topics like stable and unstable Lagrange points and Roche lobes, a brief introduction to chaotic orbits is given. Additionally, readers are guided towards exploring on their own with numerical orbit integration.

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