Earth Explorer CFI Software CONVENTIONS DOCUMENT

Total Page:16

File Type:pdf, Size:1020Kb

Earth Explorer CFI Software CONVENTIONS DOCUMENT Earth Explorer CFI Software CONVENTIONS DOCUMENT Code: EE-MA-DMS-GS-0001 Issue: 1.5 Date: 13/03/09 Name Function Signature Prepared by: Mariano Sánchez-Nogales Project Engineer Fabrizio Pirondini Project Engineer José Antonio González Abeytua Project Manager Juan José Borrego Bote Project Engineer Checked by: Javier Babe Quality A. Manager Approved by: José Antonio González Abeytua Project Manager DEIMOS Space S.L. Ronda de Poniente, 19, Edificio Fiteni VI, Portal 2, 2ª Planta, Tres Cantos 28670 Madrid, SPAIN Tel.: +34 91 806 34 50 Fax: +34 91 806 34 51 E-mail: [email protected] © DEIMOS Space S.L., 2009 All Rights Reserved. No part of this document may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of DEIMOS Space S.L. or ESA. Code: EE-MA-DMS-GS-0001 Date: 13/03/09 Issue: 1.5 Page: 2 Document Information Contract Data Classification Contract Number: 15583/01/NL/GS Internal Public Contract Issuer: ESA / ESTEC Industry X Confidential External Distribution Name Organisation Copies Electronic handling Word Processor: Adobe Framemaker 6.0 Archive Code: P/MCD/DMS/01/026-003 Electronic file name: ee-ma-dms-gs-0001-12 Mission CFI Software Conventions Document 3 Code: EE-MA-DMS-GS-0001 Date: 13/03/09 Issue: 1.5 Page: 3 Document Status Log Issue Change Description Date Approval 1.0 New document based on Envisat Mission CFI Soft- 08/11/01 ware Mission Convention Document 1.1 Minor changes on ASCII time formats (Table 2) 04/02/02 1.2 Minor changes on ASCII time formats (Table 2) 15/04/02 Added CryoSat SIRAL extra counter description (sec- tion 4.4.3) Corrected an error in Mean Local Solar Time drift for- mula (pag.33) 1.3 Added GOCE values in ANNEX A. 15/07/03 See change bars for other minor changes 1.4 New Reference frame definitions 02/08/07 New Attitude reference frame definitions Updates for new missions. 1.5 New propagation models 13/03/09 Mission CFI Software Conventions Document 3 Code: EE-MA-DMS-GS-0001 Date: 13/03/09 Issue: 1.5 Page: 4 Table of Contents 1. SCOPE......................................................................................................... 9 2. ACRONYMS............................................................................................. 10 3. APPLICABLE AND REFERENCE DOCUMENTS............................ 12 3.1. Applicable Documents ........................................................................................12 3.2. Reference Documents .........................................................................................12 4. TIME REFERENCES AND MODELS.................................................. 13 4.1. Time References..................................................................................................13 4.2. Time formats .......................................................................................................14 4.2.1. Earth Explorer time formats ............................................................................................14 4.3. Time resolution ...................................................................................................17 4.4. Earth Explorer On-board times ...........................................................................17 4.4.1. Envisat On-board clock ticks...........................................................................................17 4.4.2. TAI time ..........................................................................................................................18 4.4.3. CryoSat SIRAL extra counter .........................................................................................18 4.4.4. SMOS On-board time......................................................................................................18 4.4.5. Aeolus On-board Time ....................................................................................................19 4.4.6. GOCE On-board Time ....................................................................................................19 5. REFERENCE FRAMES.......................................................................... 20 5.1. General Reference Frames ..................................................................................21 5.1.1. Galactic............................................................................................................................21 5.1.2. Barycentric Mean of 1950...............................................................................................21 5.1.3. Barycentric Mean of 2000...............................................................................................21 5.1.4. Heliocentric Mean of 2000..............................................................................................21 5.1.5. Geocentric Mean of 2000 ................................................................................................21 5.1.6. Mean of Date ...................................................................................................................22 5.1.7. True of Date.....................................................................................................................22 5.1.8. Earth Fixed ......................................................................................................................22 5.1.9. Topocentric......................................................................................................................22 5.2. Satellite Reference Frames..................................................................................22 5.2.1. Satellite Orbital................................................................................................................23 5.3. General Reference Frames Transformations.......................................................24 5.3.1. Galactic to Barycentric Mean of 1950.............................................................................25 5.3.2. Barycentric Mean of 1950.0 to Barycentric Mean of 2000.............................................26 5.3.3. Barycentric Mean of 2000 to Geocentric Mean of 2000.................................................26 5.3.4. Heliocentric Mean of 2000 to Geocentric Mean of 2000................................................27 5.3.5. Geocentric Mean of 2000 to Mean of Date .....................................................................27 5.3.6. Mean of Date to True of Date..........................................................................................28 Mission CFI Software Conventions Document 6 Code: EE-MA-DMS-GS-0001 Date: 13/03/09 Issue: 1.5 Page: 5 5.3.7. True of Date to Earth Fixed.............................................................................................30 5.4. Satellite Reference Frames Transformations ......................................................31 6. ORBIT CHARACTERISATION............................................................ 32 6.1. Orbit Definition...................................................................................................32 6.1.1. Sun-synchronous Orbit....................................................................................................32 6.1.2. Quasi Sun-synchronous Orbit..........................................................................................32 6.1.3. Geo-synchronous Orbit ...................................................................................................33 6.2. Orbit Types..........................................................................................................33 6.2.1. Reference Orbit ...............................................................................................................33 6.2.2. Predicted Orbit.................................................................................................................33 6.2.3. Restituted Orbit ...............................................................................................................33 6.2.4. TLE Orbit ........................................................................................................................33 6.3. Orbit Propagation Definition...............................................................................33 6.4. Orbit Propagation Models ...................................................................................33 6.4.1. Mean Keplerian Orbit Propagator ...................................................................................34 6.4.1.1. Simulation mode ..................................................................................................34 6.4.1.2. Operational mode ................................................................................................34 6.4.1.3. Non-Sun-synchronous Simulation mode..............................................................34 6.4.1.4. Non-Sun-synchronous Operational mode............................................................34 6.4.2. Precise Orbit Propagator..................................................................................................34 6.4.3. TLE Propagator ...............................................................................................................35 7. PARAMETERS ........................................................................................ 36 7.1. Orbit Parameters..................................................................................................36 7.1.1. Cartesian State Vector .....................................................................................................36
Recommended publications
  • A Study of Ancient Khmer Ephemerides
    A study of ancient Khmer ephemerides François Vernotte∗ and Satyanad Kichenassamy** November 5, 2018 Abstract – We study ancient Khmer ephemerides described in 1910 by the French engineer Faraut, in order to determine whether they rely on observations carried out in Cambodia. These ephemerides were found to be of Indian origin and have been adapted for another longitude, most likely in Burma. A method for estimating the date and place where the ephemerides were developed or adapted is described and applied. 1 Introduction Our colleague Prof. Olivier de Bernon, from the École Française d’Extrême Orient in Paris, pointed out to us the need to understand astronomical systems in Cambo- dia, as he surmised that astronomical and mathematical ideas from India may have developed there in unexpected ways.1 A proper discussion of this problem requires an interdisciplinary approach where history, philology and archeology must be sup- plemented, as we shall see, by an understanding of the evolution of Astronomy and Mathematics up to modern times. This line of thought meets other recent lines of research, on the conceptual evolution of Mathematics, and on the definition and measurement of time, the latter being the main motivation of Indian Astronomy. In 1910 [1], the French engineer Félix Gaspard Faraut (1846–1911) described with great care the method of computing ephemerides in Cambodia used by the horas, i.e., the Khmer astronomers/astrologers.2 The names for the astronomical luminaries as well as the astronomical quantities [1] clearly show the Indian origin ∗F. Vernotte is with UTINAM, Observatory THETA of Franche Comté-Bourgogne, University of Franche Comté/UBFC/CNRS, 41 bis avenue de l’observatoire - B.P.
    [Show full text]
  • Elliptical Orbits
    1 Ellipse-geometry 1.1 Parameterization • Functional characterization:(a: semi major axis, b ≤ a: semi minor axis) x2 y 2 b p + = 1 ⇐⇒ y(x) = · ± a2 − x2 (1) a b a • Parameterization in cartesian coordinates, which follows directly from Eq. (1): x a · cos t = with 0 ≤ t < 2π (2) y b · sin t – The origin (0, 0) is the center of the ellipse and the auxilliary circle with radius a. √ – The focal points are located at (±a · e, 0) with the eccentricity e = a2 − b2/a. • Parameterization in polar coordinates:(p: parameter, 0 ≤ < 1: eccentricity) p r(ϕ) = (3) 1 + e cos ϕ – The origin (0, 0) is the right focal point of the ellipse. – The major axis is given by 2a = r(0) − r(π), thus a = p/(1 − e2), the center is therefore at − pe/(1 − e2), 0. – ϕ = 0 corresponds to the periapsis (the point closest to the focal point; which is also called perigee/perihelion/periastron in case of an orbit around the Earth/sun/star). The relation between t and ϕ of the parameterizations in Eqs. (2) and (3) is the following: t r1 − e ϕ tan = · tan (4) 2 1 + e 2 1.2 Area of an elliptic sector As an ellipse is a circle with radius a scaled by a factor b/a in y-direction (Eq. 1), the area of an elliptic sector PFS (Fig. ??) is just this fraction of the area PFQ in the auxiliary circle. b t 2 1 APFS = · · πa − · ae · a sin t a 2π 2 (5) 1 = (t − e sin t) · a b 2 The area of the full ellipse (t = 2π) is then, of course, Aellipse = π a b (6) Figure 1: Ellipse and auxilliary circle.
    [Show full text]
  • World Geodetic System 1984
    World Geodetic System 1984 Responsible Organization: National Geospatial-Intelligence Agency Abbreviated Frame Name: WGS 84 Associated TRS: WGS 84 Coverage of Frame: Global Type of Frame: 3-Dimensional Last Version: WGS 84 (G1674) Reference Epoch: 2005.0 Brief Description: WGS 84 is an Earth-centered, Earth-fixed terrestrial reference system and geodetic datum. WGS 84 is based on a consistent set of constants and model parameters that describe the Earth's size, shape, and gravity and geomagnetic fields. WGS 84 is the standard U.S. Department of Defense definition of a global reference system for geospatial information and is the reference system for the Global Positioning System (GPS). It is compatible with the International Terrestrial Reference System (ITRS). Definition of Frame • Origin: Earth’s center of mass being defined for the whole Earth including oceans and atmosphere • Axes: o Z-Axis = The direction of the IERS Reference Pole (IRP). This direction corresponds to the direction of the BIH Conventional Terrestrial Pole (CTP) (epoch 1984.0) with an uncertainty of 0.005″ o X-Axis = Intersection of the IERS Reference Meridian (IRM) and the plane passing through the origin and normal to the Z-axis. The IRM is coincident with the BIH Zero Meridian (epoch 1984.0) with an uncertainty of 0.005″ o Y-Axis = Completes a right-handed, Earth-Centered Earth-Fixed (ECEF) orthogonal coordinate system • Scale: Its scale is that of the local Earth frame, in the meaning of a relativistic theory of gravitation. Aligns with ITRS • Orientation: Given by the Bureau International de l’Heure (BIH) orientation of 1984.0 • Time Evolution: Its time evolution in orientation will create no residual global rotation with regards to the crust Coordinate System: Cartesian Coordinates (X, Y, Z).
    [Show full text]
  • Interplanetary Trajectories in STK in a Few Hundred Easy Steps*
    Interplanetary Trajectories in STK in a Few Hundred Easy Steps* (*and to think that last year’s students thought some guidance would be helpful!) Satellite ToolKit Interplanetary Tutorial STK Version 9 INITIAL SETUP 1) Open STK. Choose the “Create a New Scenario” button. 2) Name your scenario and, if you would like, enter a description for it. The scenario time is not too critical – it will be updated automatically as we add segments to our mission. 3) STK will give you the opportunity to insert a satellite. (If it does not, or you would like to add another satellite later, you can click on the Insert menu at the top and choose New…) The Orbit Wizard is an easy way to add satellites, but we will choose Define Properties instead. We choose Define Properties directly because we want to use a maneuver-based tool called the Astrogator, which will undo any initial orbit set using the Orbit Wizard. Make sure Satellite is selected in the left pane of the Insert window, then choose Define Properties in the right-hand pane and click the Insert…button. 4) The Properties window for the Satellite appears. You can access this window later by right-clicking or double-clicking on the satellite’s name in the Object Browser (the left side of the STK window). When you open the Properties window, it will default to the Basic Orbit screen, which happens to be where we want to be. The Basic Orbit screen allows you to choose what kind of numerical propagator STK should use to move the satellite.
    [Show full text]
  • Mission Conventions Document
    Earth Observation Mission CFI Software CONVENTIONS DOCUMENT Code: EO-MA-DMS-GS-0001 Issue: 4.19 Date: 29/05/2020 Name Function Signature Prepared by: Fabrizio Pirondini Project Engineer José Antonio González Abeytua Project Manager Juan José Borrego Bote Project Engineer Carlos Villanueva Project Manager Checked by: Javier Babe Quality A. Manager Approved by: Carlos Villanueva Project Manager DEIMOS Space S.L.U. Ronda de Poniente, 19 Edificio Fiteni VI, Portal 2, 2ª Planta 28760 Tres Cantos (Madrid), SPAIN Tel.: +34 91 806 34 50 Fax: +34 91 806 34 51 E-mail: [email protected] © DEIMOS Space S.L.U. All Rights Reserved. No part of this document may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of DEIMOS Space S.L.U. or ESA. Code: EO-MA-DMS-GS-0001 Date: 29/05/2020 Issue: 4.19 Page: 2 DOCUMENT INFORMATION Contract Data Classification Internal Contract Number: 4000102614/1O/NL/FF/ef Public Industry X Contract Issuer: ESA / ESTEC Confidential External Distribution Name Organization Copies Electronic handling Word Processor: LibreOffice 5.2.3.3 Archive Code: P/MCD/DMS/01/026-003 Electronic file name: eo-ma-dms-gs-001-12 Earth Observation Mission CFI Software. CONVENTIONS DOCUMENT Code: EO-MA-DMS-GS-0001 Date: 29/05/2020 Issue: 4.19 Page: 3 DOCUMENT STATUS LOG Issue Change Description Date Approval 1.0 New Document 27/10/09 • Issue in-line wit EOCFI libraries version 4.1 • Section 8.2.4 Refractive
    [Show full text]
  • IERS Annual Report 2000
    International Earth Rotation Service (IERS) Service International de la Rotation Terrestre Member of the Federation of the Astronomical and Geophysical data analysis Service (FAGS) IERS Annual Report 2000 Verlag des Bundesamts für Kartographie und Geodäsie Frankfurt am Main 2001 IERS Annual Report 2000 Edited by Wolfgang R. Dick and Bernd Richter Technical support: Alexander Lothhammer International Earth Rotation Service Central Bureau Bundesamt für Kartographie und Geodäsie Richard-Strauss-Allee 11 60598 Frankfurt am Main Germany phone: ++49-69-6333-273/261/250 fax: ++49-69-6333-425 e-mail: [email protected] URL: www.iers.org ISSN: 1029-0060 (print version) ISBN: 3-89888-862-2 (print version) An online version of this document is available at: http://www.iers.org/iers/publications/reports/2000/ © Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, 2001 Table of Contents I Forewords............................................................................................. 4 II Organisation of the IERS in 2000............................................................. 7 III Reports of Coordination Centres III.1 VLBI Coordination Centre.............................................................. 10 III.2 GPS Coordination Centre.............................................................. 13 III.3 SLR and LLR Coordination Centre................................................. 16 III.4 DORIS Coordination Centre........................................................... 19 IV Reports of Bureaus, Centres and
    [Show full text]
  • 2 Coordinate Systems
    2 Coordinate systems In order to find something one needs a system of coordinates. For determining the positions of the stars and planets where the distance to the object often is unknown it usually suffices to use two coordinates. On the other hand, since the Earth rotates around it’s own axis as well as around the Sun the positions of stars and planets is continually changing, and the measurment of when an object is in a certain place is as important as deciding where it is. Our first task is to decide on a coordinate system and the position of 1. The origin. E.g. one’s own location, the center of the Earth, the, the center of the Solar System, the Galaxy, etc. 2. The fundamental plan (x−y plane). This is often a plane of some physical significance such as the horizon, the equator, or the ecliptic. 3. Decide on the direction of the positive x-axis, also known as the “reference direction”. 4. And, finally, on a convention of signs of the y− and z− axes, i.e whether to use a left-handed or right-handed coordinate system. For example Eratosthenes of Cyrene (c. 276 BC c. 195 BC) was a Greek mathematician, elegiac poet, athlete, geographer, astronomer, and music theo- rist who invented a system of latitude and longitude. (According to Wikipedia he was also the first person to use the word geography and invented the disci- pline of geography as we understand it.). The origin of this coordinate system was the center of the Earth and the fundamental plane was the equator, which location Eratosthenes calculated relative to the parts of the Earth known to him.
    [Show full text]
  • New Closed-Form Solutions for Optimal Impulsive Control of Spacecraft Relative Motion
    New Closed-Form Solutions for Optimal Impulsive Control of Spacecraft Relative Motion Michelle Chernick∗ and Simone D'Amicoy Aeronautics and Astronautics, Stanford University, Stanford, California, 94305, USA This paper addresses the fuel-optimal guidance and control of the relative motion for formation-flying and rendezvous using impulsive maneuvers. To meet the requirements of future multi-satellite missions, closed-form solutions of the inverse relative dynamics are sought in arbitrary orbits. Time constraints dictated by mission operations and relevant perturbations acting on the formation are taken into account by splitting the optimal recon- figuration in a guidance (long-term) and control (short-term) layer. Both problems are cast in relative orbit element space which allows the simple inclusion of secular and long-periodic perturbations through a state transition matrix and the translation of the fuel-optimal optimization into a minimum-length path-planning problem. Due to the proper choice of state variables, both guidance and control problems can be solved (semi-)analytically leading to optimal, predictable maneuvering schemes for simple on-board implementation. Besides generalizing previous work, this paper finds four new in-plane and out-of-plane (semi-)analytical solutions to the optimal control problem in the cases of unperturbed ec- centric and perturbed near-circular orbits. A general delta-v lower bound is formulated which provides insight into the optimality of the control solutions, and a strong analogy between elliptic Hohmann transfers and formation-flying control is established. Finally, the functionality, performance, and benefits of the new impulsive maneuvering schemes are rigorously assessed through numerical integration of the equations of motion and a systematic comparison with primer vector optimal control.
    [Show full text]
  • Impulsive Maneuvers for Formation Reconfiguration Using Relative Orbital Elements
    JOURNAL OF GUIDANCE,CONTROL, AND DYNAMICS Vol. 38, No. 6, June 2015 Impulsive Maneuvers for Formation Reconfiguration Using Relative Orbital Elements G. Gaias∗ and S. D’Amico† DLR, German Aerospace Center, 82234 Wessling, Germany DOI: 10.2514/1.G000189 Advanced multisatellite missions based on formation-flying and on-orbit servicing concepts require the capability to arbitrarily reconfigure the relative motion in an autonomous, fuel efficient, and flexible manner. Realistic flight scenarios impose maneuvering time constraints driven by the satellite bus, by the payload, or by collision avoidance needs. In addition, mission control center planning and operations tasks demand determinism and predictability of the propulsion system activities. Based on these considerations and on the experience gained from the most recent autonomous formation-flying demonstrations in near-circular orbit, this paper addresses and reviews multi- impulsive solution schemes for formation reconfiguration in the relative orbit elements space. In contrast to the available literature, which focuses on case-by-case or problem-specific solutions, this work seeks the systematic search and characterization of impulsive maneuvers of operational relevance. The inversion of the equations of relative motion parameterized using relative orbital elements enables the straightforward computation of analytical or numerical solutions and provides direct insight into the delta-v cost and the most convenient maneuver locations. The resulting general methodology is not only able to refind and requalify all particular solutions known in literature or flown in space, but enables the identification of novel fuel-efficient maneuvering schemes for future onboard implementation. Nomenclature missions. Realistic operational scenarios ask for accomplishing such a = semimajor axis actions in a safe way, within certain levels of accuracy, and in a fuel- B = control input matrix of the relative dynamics efficient manner.
    [Show full text]
  • NOAA Technical Memorandum ERL ARL-94
    NOAA Technical Memorandum ERL ARL-94 THE NOAA SOLAR EPHEMERIS PROGRAM Albion D. Taylor Air Resources Laboratories Silver Spring, Maryland January 1981 NOAA 'Technical Memorandum ERL ARL-94 THE NOAA SOLAR EPHEMERlS PROGRAM Albion D. Taylor Air Resources Laboratories Silver Spring, Maryland January 1981 NOTICE The Environmental Research Laboratories do not approve, recommend, or endorse any proprietary product or proprietary material mentioned in this publication. No reference shall be made to the Environmental Research Laboratories or to this publication furnished by the Environmental Research Laboratories in any advertising or sales promotion which would indicate or imply that the Environmental Research Laboratories approve, recommend, or endorse any proprietary product or proprietary material mentioned herein, or which has as its purpose an intent to cause directly or indirectly the advertised product to be used or purchased because of this Environmental Research Laboratories publication. Abstract A system of FORTRAN language computer programs is presented which have the ability to locate the sun at arbitrary times. On demand, the programs will return the distance and direction to the sun, either as seen by an observer at an arbitrary location on the Earth, or in a stan- dard astronomic coordinate system. For one century before or after the year 1960, the program is expected to have an accuracy of 30 seconds 5 of arc (2 seconds of time) in angular position, and 7 10 A.U. in distance. A non-standard algorithm is used which minimizes the number of trigonometric evaluations involved in the computations. 1 The NOAA Solar Ephemeris Program Albion D. Taylor National Oceanic and Atmospheric Administration Air Resources Laboratories Silver Spring, MD January 1981 Contents 1 Introduction 3 2 Use of the Solar Ephemeris Subroutines 3 3 Astronomical Terminology and Coordinate Systems 5 4 Computation Methods for the NOAA Solar Ephemeris 11 5 References 16 A Program Listings 17 A.1 SOLEFM .
    [Show full text]
  • Mission Concept for a Satellite Mission to Test Special Relativity
    Mission Concept for a Satellite Mission to Test Special Relativity VOLKAN ANADOL Space Engineering, masters level 2016 Luleå University of Technology Department of Computer Science, Electrical and Space Engineering LULEÅ UNIVERSITY of TECHNOLOGY Master Thesis SpaceMaster Mission Concept for a Satellite Mission to Test Special Relativity Supervisors: Author : Dr. Thilo Schuldt Volkan Anadol Dr. Norman Gürlebeck Examiner : Assoc. Prof. Thomas Kuhn September 29, 2016 Abstract In 1905 Albert Einstein developed the theory of Special Relativity. This theory describes the relation between space and time and revolutionized the understanding of the universe. While the concept is generally accepted new experimental setups are constantly being developed to challenge the theory, but so far no contradictions have been found. One of the postulates Einsteins theory of Relativity is based on states that the speed of light in vac- uum is the highest possible velocity. Furthermore, it is demanded that the speed of light is indepen- dent of any chosen frame of reference. If an experiment would find a contradiction of these demands, the theory as such would have to be revised. To challenge the constancy of the speed of light the so- called Kennedy Thorndike experiment has been developed. A possible setup to conduct a Kennedy Thorndike experiment consists of comparing two independent clocks. Likewise experiments have been executed in laboratory environments. Within the scope of this work, the orbital requirements for the first space-based Kennedy Thorndike experiment called BOOST will be investigated. BOOST consists of an iodine clock, which serves as a time reference, and an optical cavity, which serves as a length reference.
    [Show full text]
  • 1 CHAPTER 10 COMPUTATION of an EPHEMERIS 10.1 Introduction
    1 CHAPTER 10 COMPUTATION OF AN EPHEMERIS 10.1 Introduction The entire enterprise of determining the orbits of planets, asteroids and comets is quite a large one, involving several stages. New asteroids and comets have to be searched for and discovered. Known bodies have to be found, which may be relatively easy if they have been frequently observed, or rather more difficult if they have not been observed for several years. Once located, images have to be obtained, and these have to be measured and the measurements converted to usable data, namely right ascension and declination. From the available observations, the orbit of the body has to be determined; in particular we have to determine the orbital elements , a set of parameters that describe the orbit. For a new body, one determines preliminary elements from the initial few observations that have been obtained. As more observations are accumulated, so will the calculated preliminary elements. After all observations (at least for a single opposition) have been obtained and no further observations are expected at that opposition, a definitive orbit can be computed. Whether one uses the preliminary orbit or the definitive orbit, one then has to compute an ephemeris (plural: ephemerides ); that is to say a day-to-day prediction of its position (right ascension and declination) in the sky. Calculating an ephemeris from the orbital elements is the subject of this chapter. Determining the orbital elements from the observations is a rather more difficult calculation, and will be the subject of a later chapter. 10.2 Elements of an Elliptic Orbit Six numbers are necessary and sufficient to describe an elliptic orbit in three dimensions.
    [Show full text]