Southwest Jiaotong University Principles of the Global Positioning System Lecture 03 YUAN LInguo EmailIgyuan@163.com Dept of Surveying Engineering, Southwest Jiaotong University Fundamental knowledg Quick Overview Kelperian 3 Laws First Law: ellipse, Sun is a focus Second law: the same area in same time Earth Third law: 1_ai Principles of the Global Positioning System 2005-3-11(2
1 Principles of the Global Positioning System Lecture 03 YUAN Linguo Email: lgyuan@163.com Dept. of Surveying Engineering, Southwest Jiaotong University Principles of the Global Positioning System 2005-3-11 2
Perigee and Apogee: The point of closest approach of the satellite with to the earth' s center of mass is called perigee and the most distant position is the apogee. Nodes: The intersection between the equatorial and the orbital plane with the unit sphere is termed the nodes, where the ascending node defines the northward crossing of the equator. ae E apogee geocenter perigee 電 Principles of the Global Positioning System 2005-3-11(3 Introduction Principles of the Global Positioning System 2005-3-11(4
2 Principles of the Global Positioning System 2005-3-11 3 Principles of the Global Positioning System 2005-3-11 4 Introduction
Why do We study orbit? The applications of gPs depend substantially on knowing the satellite orbits 1. For single receiver positioning, an orbital error is highly correlated with the positional error In relative positioning, relative orbital errors are considered to be approximately equal to relative baseline errors 電 Principles of the Global Positioning System 2005-3-11(5 Orbit Information and SA Technology How to obtain orbital information: o either transmitted by the satellite as part of the broadcast message or o can be obtained(typically some days after the observation) from several sources Principles of the Global Positioning System 20053-11(6
3 Principles of the Global Positioning System 2005-3-11 5 Why do We Study Orbit? The applications of GPS depend substantially on knowing the satellite orbits. 1. For single receiver positioning, an orbital error is highly correlated with the positional error. 2. In relative positioning, relative orbital errors are considered to be approximately equal to relative baseline errors. Principles of the Global Positioning System 2005-3-11 6 Orbit Information and SA Technology How to obtain Orbital Information: either transmitted by the satellite as part of the broadcast message, or can be obtained (typically some days after the observation) from several sources
Orbit Information and SA Technology Orbit Inf and sa: o The activation of sa in the block ii satellites may lead to a degradation of the broadcast orbit up to 50-100m Civil Community Since some users need more precise ephemerides, the civil community must generate its own precise satellite ephemerides 電 Principles of the Global Positioning System 2005-3-11(7 Orbit Description Principles of the Global Positioning System 2005-3-11(8
4 Principles of the Global Positioning System 2005-3-11 7 Orbit Inf. and SA: The activation of SA in the Block II satellites may lead to a degradation of the broadcast orbit up to 50-100 m. Civil Community: Since some users need more precise ephemerides, the civil community must generate its own precise satellite ephemerides. Orbit Information and SA Technology Principles of the Global Positioning System 2005-3-11 8 Orbit Description
Keplerian Motion Orbital parameters The movement of mass m2 relative to m, is defined by the homogeneous 2nd order differential equation G(m1+m2) y=0 Principles of the Global Positioning System Artificial Earth Satellite. Points Mass: negligible W=GMa=3980005103m3s2 The analytical solution of differential equation leads to the well-known Keplerian motion defined by six orbital parameters The orbital parameters correspond to the six integration constants of the second-order vector equation Principles of the Global Positioning System 2005-3-11(10 5
5 Principles of the Global Positioning System 2005-3-11 9 Keplerian Motion Principles of the Global Positioning System 2005-3-11 10 Artificial Earth Satellite: