大地測量學基礎(chǔ)期末考試A(雙語).doc

Final Examination-Foundation of Geodesy_2007(A)武漢大學 測繪學院2007-2008學年第 1 學期期末考試大地測量學基礎(chǔ)（雙語教學）課程試卷(A)出題者Spiros Pagiatakis審核人 班級測繪工程2005級School of Geodesy and Geomatics, Wuhan University. Final Term Examination of 1st Term, 2007-2008. Course Title: FOUNDATION OF GEODESY. Question paper (A)Notes: The questions should be answered by English.Section I: Definitions (total 24 points, 3 points each).Describe the following terms in one or two sentences. You can use sketches where appropriate, if you wish. 1. CIO2. Earths precession 3. Gravitational field of the Earth 4. Horizontal Datum5. GAST 6. TAI 7. Conformal map 8. Deflection of the verticalSection II: Multiple choice questions (total 25 points, 5 points each)Please choose the most correct answer.1. The Earths free nutation (polar motion, or polar wobble) is caused bya) external torques applied to the equatorial bulge of the Earthb) the fact that the spin axis of the Earth does not coincide with the axis of the maximum moment of inertiac) the fact that the orbital plane of moon in not coincident with the equatorial planed) all the above2. Coordinated Universal Time (UTC) a) has the same rate as TAIb) UTC is different from UT1 by 3.175sc) is a solar time scaled) is equivalent to GPS time3. Apparent coordinate systems a) have their origin at the centre of mass of the Earthb) are always defined with respect to the starsc) their x-axis is always pointing towards the Greenwich meridiand) all the above4. The reference ellipsoid is also called level ellipsoid becausea) it describes, as close as possible, the Earths gravity field.b) its surface is by definition an equipotential surface.c) its mass is equal to that of the real Earthd) it spins with an angular velocity equal to that of the Earth5. In map projections, meridian convergencea) is the angle between two meridians on the mapping planeb) describes the fact that the meridians meet at the same point (north or south pole) c) is the angle between the x-axis(Grid North) of the map and the tangent to the projected meridian at any point on the mapping plane.d) all the aboveSection III: Essay type questions(total 51 points, 17 points each)Please answer all questions below.1. Define the Instantaneous terrestrial (IT) and Local Astronomic (LA) coordinate systems. Which angles are required to achieve the transformation between them Write the transformation between the two systems using rotation matrices. Please explain the variables involved.2. List and discuss briefly the similarities and differences between Gauss-Krger and Universal Transverse Mercator projections.3. One of the three main tasks of Geodesy is positioning. Please describe briefly what geodetic positioning means and how you can achieve it by explaining: a) what you need to know in advance (“given”), b) what you have to observe (“observables”) and c) how you calculate the positions. For the calculation of positions please discuss briefly the different coordinate systems involved and the sequence of transformations needed (do not write the transformation equations). Please discuss any reductions (corrections) to the observations that might be necessary.Geodesy2007(A)_Answer武漢大學 測繪學院2007-2008學年第 1 學期期末考試大地測量學基礎(chǔ)（雙語教學）課程試卷(A)參考答案出題者Spiros Pagiatakis審核人 班級測繪工程2005級School of Geodesy and Geomatics, Wuhan University. Final Term Examination of 1st Term, 2007-2008. Course Title: FOUNDATION OF GEODESY. Question paper (A) Sample answersNotes: The questions should be answered by English.Section I: Definitions (total 24 points, 3 points each).Describe the following terms in one or two sentences. You can use sketches where appropriate, if you wish. 1. CIO: Conventional International Origin. It is the reference pole that defines the direction of the z-axis of the conventional terrestrial coordinate system2. Earths precession: The axis of the Earth moves on a conical surface with respect to the stars due to external torques applied from the sun and planets on the Earths equatorial bulge.3. Gravitational field of the Earth：It is the vector field (force field) due to the pure Newtonian attraction of masses from the Earth mass.4. Horizontal Datum：appropriately positioned reference ellipsoid with 8 datum parameters: size of ellipsoid (2), origin (3), orientation (3)5. GAST：is the time elapsed since a transit of the Greenwich Meridian across the true vernal equinox.6. TAI：International Atomic Time defined by atomic clocks that are under the influence of the gravitational field of the Earth7. Conformal map：A map that preserves angles and therefore shapes.8. Deflection of the vertical：The angle between the normal to the ellipsoid and the vertical (gravity vector) at any point on the surface of the Earth.Section II: Multiple choice questions (total 25 points, 5 points each)Please choose the most correct answer.1. The Earths free nutation (polar motion, or polar wobble) is caused bya) external torques applied to the equatorial bulge of the Earthb) the fact that the spin axis of the Earth does not coincide with the axis of the maximum moment of inertiac) the fact that the orbital plane of moon in not coincident with the equatorial planed) all the above2. Coordinated Universal Time (UTC) a) has the same rate as TAIb) UTC is different from UT1 by 3.175sc) is a solar time scaled) is equivalent to GPS time3. Apparent coordinate systems a) have their origin at the centre of mass of the Earthb) are always defined with respect to the starsc) their x-axis is always pointing towards the Greenwich meridiand) all the above4. The reference ellipsoid is also called level ellipsoid becausea) it describes, as close as possible, the Earths gravity field.b) its surface is by definition an equipotential surface.c) its mass is equal to that of the real Earthd) it spins with an angular velocity equal to that of the Earth5. In map projections, meridian convergencea) is the angle between two meridians on the mapping planeb) describes the fact that the meridians meet at the same point (north or south pole) c) is the angle between the x-axis(Grid North) of the map and the tangent to the projected meridian at any point on the mapping plane.d) all the aboveAnswer: 1 b) 2 a) 3 a) 4 b) 5 c)Section III: Essay type questions(total 51 points, 17 points each)Please answer all questions below.1. Define the Instantaneous terrestrial (IT) and Local Astronomic (LA) coordinate systems. Which angles are required to achieve the transformation between them Write the transformation between the two systems using rotation matrices. Please explain the variables involved.IT coordinate system: a) Origin at the centre of mass of the Earth,b) Z-axis towards the true or instantaneous spin axis of the Earthc) X-Z plane is the instantaneous Greenwich meridian plane. X-axis is normal to the the Z-axis.d) Y-axis completes the right-handed coordinate system LA coordinate system: a) Origin at a local point on the surface of the Earth (topocentric)b) Z-axis towards the opposite direction of the local gravity vector. c) X-axis is pointing towards the true or instantaneous spin axis (true north).d) Y-axis completes the left-handed coordinate system Transformation: where F and L are the astronomic latitude and longitude respectively2. List and discuss briefly the similarities and differences between Gauss-Krger and Universal Transverse Mercator projections. Similarities:a) cylindrical transverse projectionsb) they project the ellipsoid onto the mapping planec) they project zones of 6 or 3 degree width onto the mapping plane Differences a) UTM scale is k=0.9996 at the central meridian whereas Gauss-Krger projection scale is unityb) UTM uses GRS80 reference ellipsoid whereas Gauss-Krger uses any ellipsoid (geocentric or not).c) UTM covers systematically the whole globe with 6 zones, whereas Gauss-Krger zones are defined for European and Asian coverage (local/regional coverage). 3. One of the three main tasks of Geodesy is positioning. Please describe briefly what geodetic positioning means and how you can achieve it by explaining: a) what you need to know in advance (“given”), b) what you have to observe (“observables”) and c) how you calculate the positions. For the calculation of positions please discuss briefly the different coordinate systems involved and the sequence of transformations needed (do not write the transformation equations). Please discuss any reductions (corrections) to the observations that might be necessary. Geodetic positioning deals with the determination the location of a point on land, at sea or in space w.r.t. a selected (or implied) reference coordinate system. Given: Coordinates of extraterrestrial objects such as stars or artificial satellites. They are used as reference points in the determination of positions of unknown points. For vertical positioning (heights), elevations of benchmarks w.r.t. a reference level surface (usually the geoid) are required. Observed: Quantities such as distances and angles or directions that link the unknown point to the extraterrestrial objects. Fo