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**Name of the Course****：****Foundmental Astrometry And Astrodynamics**

**Hours/score****：** 48/3

**Background required**: College physics, college mathematics, Fortran, C computer language.

**Objectives: **To learn and grasp the basic definition of spherical coordinates, fundamental principle and method for astrometry, basic theory of astrodynamics; to learn and grasp the acknowledge of space position and movement of astronomical bodies, and the transferring relations between spherical coordinate and Eular coordinate, as well as to learn the basic methods to measure the positions and movements for celestial bodies, to grasp the algorithm and code recommended by the international earth rotation service, and to grasp the method to construct the giant planets and the moon ephemeris and the relevant applications.

**Brief content**

**Main contents: **spherical astronomy,

Principle and method of space-time transferring recommended in standard of international earth rotation service. Principle and method for two-body problem and three-body problem. Celestial mechanism for manned satellite and geodynamics. NOVAS astrometric package, JPL/NASA giant planets and the moon ephemeris and the relevant applications.

**Fundamental spherical astronomy:**

18hr

- Astrometric reference frame 3hr

Basic concepts in astrometry and for astrometric reference frame, types and realizations of basic celestial reference frame, types and realizations of basic earth reference frame, links and transferring between systems, vector algorithm for positions. - Attitude and movement of the Earth in space 3hr

Earth spin, earth orbit surround the Sun, description for earth attitude in space, movement of earth dynamical spin axis in space, wobble of earth dynamical spin axis in space. - Spherical algebra and spherical coordinate system 3hr

Point, line and circle on a sphere, spherical coordinate, spherical triangle functions, spherical coordinate system, transferring between spherical coordinate systems.

- Description of space position and direction for celestial bodies 3hr

space position and direction for celestial bodies, algebra position and direction, light time distance and direction, photon start and end directions, observation directions, calculating the position and direction for celestial body.

- Algorithm for ground astrometry 3hr

Date types of astrometric observation，equations for the ground astrometry, error functions and the solving method, mathematical descriptions for the astrometry

- Fundamental space geodetic technology and method 3hr

Introduction of space geodetic technology and method for the GNSS, VLBI, SLR/LLR, DORIS, introduction of astro-geodynamics, as well as the applications of space geodetic technology and method for the astro-geodynamics.

- Standard of astrometry recommended by IERS (1) 3hr

Introduction of IERS, its application range, state of art astrometric standard(1).

- Standard of astrometry recommended by IERS (2) 3hr

Introduction of IERS in China，foreseeing its development in 5~10 years, state of art astrometric standard(2).

- NOVAS astrometric software package and applications(1) 3hr

NOVAS astrometric software package structure, 3 types of routines; I/O; common used star catalogue; calculation processing for observation position of a star seen from campus

- NOVAS astrometric software package and applications(1) 3hr

Earth reference frame, atmospheric delay models; calculation processing for catalogue position of a given star from its observation position seen from campus

- Fundamental astrodynamics 3hr

Astrodynamical concept, history, study objectives/bodies, problems to be solved.

- Two body problems 3hr

Gravity law, potential function, movement equations, orbit roots, orbit types, orbit descriptions in various coordinate system, orbit root function

- Limited three-body problem限制性三体问题 3学时

three-body problem, N-body problem, limited N-body problem, limited three-body problem, Lagrange points and the stabilities.

- Giant planets and the moon ephemeris and the relevant applications. 3hr

Definition, structure and format of JPL/NASA giant planets and the moon ephemeris and the relevant applications. Chebyshev function. Install JPL ephemeris in computer. Application of JPL ephemeris: retrieving the information of lunar position, lunar physical liberation, planetary position, solar position, and the relevant calculation, light-time distance between bodies and calculation; calculation with NOVAS package.

- Perturbation two-body problem 3hr

Research body/objective in perturbation two-body problem, perturbation by the third body, orbit root Expansion equation; perturbation function, long term perturbation, center body figure perturbation, solar pressure, atmospheric damping, digital integration and digital integrators

- Satellite initial orbit determination 3hr

Principle and algorithm for orbit determination using optical photo data; Principle and algorithm for orbit determination using satellite laser ranging data; Principle and algorithm for orbit determination using radio range and range rate data, Principle and algorithm for orbit determination using satellite-satellite link data.

**Test**

Join lesion and homework: 20%

NOVAS package exercise and report 20%

JPL ephemeris exercise and report 20%

Last test 40%

**Text books****：**

Spherical astronomy, any English version text book

Fundamental astrometry and astro-dynamics, any English version text book

Fundamental astrometry and celestial mechanisms, any English version text book

**Reference books:**

Astrometric method, any English version text book

Fundamental astrodynamics, any English version text book

NOVAS introduction, U.S. Navy observatory home page

JPL/NASA ephemeris home page

**Exercise lesson****：**

Together with the astrometric software, lunar and planetary ephemeris application

**Teacher****：**PING Jinsong Ph.D, Professor

B.C. Degree at Beijing Normal University; M.A. and Ph.D at Shanghai astronomical Observatory. VLBI astrometry, radio astronomy, lunar and planetary exploration. Planetary radio science experiments, lunar radio range, lunar laser range.