# Summary of review points of Geodesy

2022-05-15 07:27:54

Key points of Geodesy review
Chapter one The introduction
1、 The branch of surveying ： It is divided into general surveying （ Surveying for short ） And geodesy .
2、 The definition and function of Geodesy
Definition ： It means in a certain time and space reference system , Measure and describe the shape of the earth and its gravity field and monitor its changes , A discipline that provides human activities with spatial information about the earth .
effect ：① Geodesy is the foundation of all surveying and Mapping Science and technology . It plays a decisive basic guarantee role in national economic construction and social development .
② Geodesy in disaster prevention , disaster reduction , Disaster relief and environmental monitoring 、 It plays a special role in evaluation and protection .
③ Geodesy is an important guarantee for the development of space technology and national defense construction .
3、 The basic system of geodesy
From geometric geodesy （ Astrogeodesy ）、 Physical geodesy （ Geodetic theory ）、 Composition of space geodesy .
4、 Geometric geodesy 、 The basic tasks and contents of physical geodesy and space geodesy
① Basic tasks ： It is to determine the shape and size of the earth and the geometric position of ground points .
primary coverage ： National geodetic control network ( Including horizontal control network and vertical control network ) The basic principle and method of establishing , Precision angle measurement , Distance measurement , Leveling ; Mathematical properties of the earth ellipsoid , Measurement and calculation on ellipsoid , Mathematical projection transformation of ellipsoid and mathematical model of geometric parameters of earth ellipsoid .
② Basic tasks ： It's physical ( Gravimetry ) Determine the shape of the earth and its external gravity field .
primary coverage ： Including bit theory , The earth's gravity field , Gravimetry and its reduction , The theory and method of deducing the shape of the earth and the external gravity field .
③ Basic tasks ： This paper mainly studies the theory of space geodesy represented by artificial earth satellites and other space detectors 、 Technology and methods .
5、 Characteristics of modern geodesy
answer ：① The research scope is large （ The global ： Such as the two poles of the earth 、 ocean ）;② From static to dynamic , From the internal structure of the earth to the dynamic process ;③ The higher the observation accuracy , The relative accuracy is up to 10-8~10-9, The absolute accuracy can reach mm ;④ The measurement and data processing cycle is short , But data processing is becoming more and more complex .

Chapter two Time and coordinate system
1、 The concept of the celestial sphere
Concept ： The so-called celestial sphere , It refers to the center of mass of the earth O（ Or station ） Centered , radius r An imaginary sphere of arbitrary length . In Astronomy , Celestial bodies are usually projected onto the sphere of the celestial sphere , And use spherical coordinates to express or study the position of celestial bodies and the relationship between celestial bodies .
2、 Geodetic datum and establishment of geodetic datum
Geodetic datum ： Refers to the parameters of the reference ellipsoid used to describe the shape of the earth , And the positioning and orientation of the reference ellipsoid in space , And the definition of unit length used in describing these positions .
The establishment of geodetic datum is to determine the parameters of rotating ellipsoid and its orientation and positioning .
3、 Basic concepts related to the celestial sphere
The celestial axis ： The straight line extending from the earth's rotation axis is the celestial axis .
Celestial pole ： The intersection of the celestial axis and the celestial sphere becomes the celestial pole （Pn North celestial pole ,Ps For the southern celestial pole ）.
The equatorial plane of the celestial sphere ： Through the center of mass of the earth O The plane perpendicular to the celestial axis is called the equatorial plane of the celestial sphere .
celestial equator ： The great circle where the equatorial plane of the celestial sphere intersects the celestial sphere is called the celestial equator .
The meridian of the celestial sphere ： A plane with a celestial axis and passing through any point , Called the meridian of the celestial sphere .
Meridian circle ： The great circle where the meridian plane of the celestial sphere intersects the celestial sphere is called the celestial meridian circle .
Time circle ： The great circle that passes through the plane of the celestial axis and intersects the celestial sphere is called the time circle .
Ecliptic ： Orbital plane of the earth's revolution ( The ecliptic ) The great garden intersecting the celestial sphere is called the ecliptic . The angle between the ecliptic plane and the equatorial plane is called the Yellow equatorial intersection angle , about 23.5 degree .
Huangji ： Through the center of the celestial sphere , And the intersection of the straight line perpendicular to the ecliptic and the celestial sphere , It's called the Yellow pole . The intersection near the north celestial pole is called the North Yellow pole , The intersection near the south celestial pole is called the South Yellow pole .
Vernal equinox and autumnal equinox ： The two intersections of the ecliptic and the equator are called the spring equinox and the autumn equinox . When the apparent sun moves from the southern hemisphere to the northern hemisphere on the ecliptic , The intersection of the ecliptic and the celestial equator is called the vernal equinox , On the contrary, it is the autumnal equinox .
Right ascension and declination ： The angle between the line from the center of the celestial sphere to the celestial body and the equatorial plane of the celestial sphere is called declination , The angle between the meridian of the celestial sphere passing through the spring equinox and the meridian of the celestial sphere passing through the celestial body is the right ascension .
precession of the equinoxes ： The earth rotates on its axis , Due to day 、 The influence of celestial bodies such as the moon , The earth's axis of rotation occurs slowly around the Yellow level in space .
nutation ： The earth's rotation axis is superimposed on the precession 18.6 The short-term circular motion in , The amplitude is 9.21 second , This phenomenon is called nutation .
Pole shift ： The earth's rotation changes the relative position of the earth's internal structure , As a result, the position of the poles on the earth's surface changes with time , This phenomenon is called pole shift .
4、 The characteristics of the earth's rotation
answer ：① The change in the direction of the earth's axis relative to space ： Precession and nutation
② The relative position of the earth's axis relative to the earth itself changes ： Pole shift
③ The earth's rotation speed changes ： Day length changes
5、 Describe the elements of time
answer ： origin 、 Company （ scale ） Two elements .
6、 Periodic motion meets the following three requirements , It can be used as a method of measuring time .
answer ：① Motion is continuous ;
② The period of motion has sufficient stability ;
③ Motion is observable .
7、 Time system
When stars (ST)： Take the vernal equinox as the basic reference point , The time determined by the Sunday apparent movement at the vernal equinox , When it's called a star .
In the real sun MT： Take the true sun as the basic reference point , The time determined by its Sunday apparent movement , When it is called the true sun . A true sun day is when the true sun passes through the upper midheaven of a place twice in a row （ Upper meridian circle ） The time it took .
World time UT： The average solar time, which starts from zero o'clock at midnight, is called universal time .UT = GAMT + 12;GAMT Represents Greenwich mean solar hour angle . The uncorrected universal time is expressed as UT0, The universal time corrected by the pole shift is expressed as UT1, Further, the world time after seasonal correction of the earth's rotation speed is expressed as UT2.UT1=UT0+Δλ, UT2=UT1+ΔT
Atomic time (AT)： Atomic time is based on the period of atomic resonance signal . The basic unit of atomic time is atomic time seconds , Defined as ： Under zero magnetic field , The transition radiation between two hyperfine energy levels in the ground state of cesium atom at sea level 192631770 The duration of the cycle is atomic hours and seconds , Specified as the time unit in the international system of units .
The origin definition of atomic time ：1958 year 1 month 1 Japan UT2 Of 0 when . AT=UT2－0.0039(s)
World coordinated time (UTC)： Atomic time is not directly related to the rotation of the earth , Due to the long-term trend of slowing down the rotation speed of the earth , The difference between atomic time and universal time will gradually become larger , Second length , About every year 1 second , Easy for daily use , Coordinate the relationship between the two , It is established that the unit of measurement is atomic time and second 、 The difference in time from the flat sun time is less than 0.9 Second time system , Call it universal coordinated time (UTC).

8、 Geodetic coordinate system

Celestial coordinate system

Geodetic coordinate system Geodetic coordinate system

The earth coordinate system Space rectangular coordinate system
① Astronomical coordinate system
origin ： The center of mass of the earth ; Z Axis ： The axis of rotation of the earth ;
Starting meridian ： Passing through the astronomical meridian plane of Greenwich Observatory ;
Latitude datum ： The equator of the earth .
Representation of points ：
Astronomical longitude （λ）： too P The angle between the meridian plane of the point and the starting meridian plane ;
Astronomical latitude （φ）： too P The angle between the plumb line direction of the point and the equatorial plane ;
It's high （H just ）： Distance from plumb line to geoid .
Astronomical azimuth （α）： too P The astronomical meridional plane of point and passing P The plumb line of a point and another point Q The angle formed by the plane of the point .
② Geodetic coordinate system
origin ： The center of the rotating ellipsoid ; Z Axis ： The axis of rotation of the ellipsoid ;
Starting meridian ： Across the great meridian of Greenwich Observatory in the UK ;
Latitude datum ： Ellipsoid equator .
Representation of points ：
The longitude of the earth （L）： too P The angle between the meridian plane of the point and the starting meridian plane ;
Latitude of the earth （B）： too P The angle between the normal of the point and the equatorial plane ;
The earth is high （H）： from P The distance from the point along the normal direction to the ellipsoid .
Large local potential angle （A）： too P The meridional plane of the point and the cross P The normal of the point and Q The angle formed by the plane of the point .
③ Geocentric space rectangular coordinate system
origin ： The center of mass of the earth ; Z Axis ： The earth's axis of rotation ;
X Axis ： Cross the line between the starting meridian of the Greenwich Observatory and the equator ;
Y Axis ： And X The axis is vertical , Right hand coordinate system .
Representation of points ：
spot k The geocentric space rectangular coordinates of （x,y,z） Express . The geocentric coordinate system is unique , It is widely used in satellite geodesy .
④ Space （ Take heart ） Geodetic rectangular coordinate system
origin ： Ellipsoid center ; Z Axis ： The axis of rotation of the ellipsoid ;
X Axis ： Cross the line between the starting meridian of the Greenwich Observatory and the equator of the ellipsoid ;
Y Axis ： And X The axis is vertical , Right hand coordinate system .
Representation of points ：
spot k The space geodetic rectangular coordinates of （X,Y,Z) Express . The center of the ellipsoid usually does not coincide with the center of mass of the earth , This coordinate system whose origin is located near the center of mass of the earth is usually called the reference center coordinate system .
⑤WGS-84 World geodetic coordinate system
origin ： The center of mass of the earth ; Z Axis ： The earth's axis of rotation ; International Time Bureau BIH1984.0 The agreement of definition earth pole （CIO)
X Axis ： Point to BIH1984.0 The zero meridional plane of CTP The intersection of the equator ;
Y Axis ： And X The axis is vertical , Right hand coordinate system .
⑥ Gauss plane rectangular coordinate system
In order to establish the mapping control and engineering survey control of topographic maps of various scales , The geodetic coordinates of each point on the ellipsoid need to be , Project onto a plane according to a certain mathematical model , Use the corresponding plane rectangular coordinates to represent . Let the geodetic coordinates of a point on the ellipsoid be （B.L), The coordinates projected onto the plane are （x,y), The relationship is ：X= F1(B,L); y=F2(B,L)
⑦ Meridian rectangular coordinate system
origin ： The center of the meridional circle ellipse passing through this point ;
x Axis ： The intersection of the equatorial plane and the meridional plane passing through this point ;
Y Axis : The axis of rotation of a rotating ellipsoid .
Representation of points ： The longitude of the earth （L,x,y）, among ：L Is the longitude of the earth ;x,y by P The coordinates of the point in the above coordinate system .
⑧ Geodetic polar coordinate system
origin ： Any point on the surface of an ellipsoid ; Reference direction ： The direction of the meridian passing through the origin .
Representation of points ：
P（S,A), among （ Set the origin to M）：
S：MP The length of the earth line , It is called polar diameter ;
A： Polar angle , It is a ground wire MP stay M The large local potential angle of the point .

The third chapter Elevation system
1、 Related concepts of elevation datum
Geoid ： Suppose the ocean is in a completely static equilibrium state, the sea surface extends below the continental surface to form a closed surface , It's called geoid .
Characteristics of water level ：① The level is the gravitational equipotential surface , That is, the gravitational potential energy of each point on the same level is equal ;
② Non parallelism of the level .
Normal ellipsoid ： An ellipsoid with the same mass as the earth and uniform mass distribution .
Normal gravitational acceleration ： The gravitational acceleration of a normal ellipsoid to its surface and external points .
Normal level ： The gravitational equipotential surface corresponding to the normal gravitational acceleration .
Theoretical closure error ： The closure error of the leveling loop caused by the non parallelism of the leveling surface , It is called theoretical closure error .
Normal ellipsoid ： Is the regular shape of geoid （ Generally refers to the rotating ellipsoid ）. Therefore, after introducing the normal ellipsoid , The earth's gravity potential is divided into two parts: normal gravity potential and disturbance potential , Actual gravity is also divided into normal gravity and gravity anomaly .
The total earth ellipsoid ： One that fits most closely with the whole earth . The center of the total earth ellipsoid coincides with the center of mass of the earth , The minor axis of the total earth ellipsoid coincides with the earth's earth axis , The initial geodesic meridional plane coincides with the initial astronomical meridional plane , The total earth ellipsoid is most closely connected with the earth body .
Geoid height is also called geoid gap N, Quasi geoid height is also called elevation anomaly ζ
2、 Elevation system
The elevation system with geoid as the reference plane is called positive height ;
The elevation system with quasi geoid as the reference surface is called normal height ;
The distance from the ground point along the normal to the ellipsoid , Call the earth high .
3、 What causes the level not to be parallel ？
answer ： Because the difference between the two levels is dh=-dw/g, Because the value of gravity at different points on the level is different , The difference between two infinitely close levels is not a constant , Therefore, the two levels are not parallel to each other .

Chapter four Establishment of geodetic datum
1、 Related concepts of ellipsoid positioning and orientation
Reference ellipsoid ： With definite parameters ( Long radius a Flattening rate α), After local positioning and orientation , The earth ellipsoid that best fits the geoid of a certain area .

Total earth ellipsoid ： In addition to satisfying the geocentric positioning and double parallel conditions , When determining the parameters of the ellipsoid, it can make it the earth's ellipsoid which is the closest to the earth in the world .

Local positioning ： It is required that the ellipsoid and geoid have the best coincidence in a certain range , And yes
There are no special requirements for the center position of the ellipsoid .

Ellipsoid positioning Geocentric positioning ： It is required that the ellipsoid and geoid should conform to each other best in the world , Simultaneous requirements
The center of the ellipsoid coincides with the center of mass of the earth .
Ellipsoidal orientation ： To determine the direction of the axis of rotation of an ellipsoid .
2、 What conditions should ellipsoid orientation meet ？
answer ：① The minor axis of the ellipsoid is parallel to the earth's axis of rotation ② The earth starting meridian plane is parallel to the astronomical starting meridian plane
3、 Inertial coordinate system (CIS) And protocol coordinate system
Inertial coordinate system ： It refers to the coordinate system that is fixed in space or moves in a straight line at a uniform speed .
Agreement on the establishment of inertial coordinate system ： Because the earth's axis of rotation is constantly changing , Usually at a certain moment t0 As a reference epoch , The direction of the instantaneous rotation axis corresponding to this time after precession and nutation correction is taken as Z Axis , Take the corresponding equinox as X The pointing point of the axis , With XOZ The vertical direction of the is Y The axis establishes the celestial coordinate system , It is called the agreement celestial coordinate system or the agreement inertial coordinate system .
4、 Geostationary coordinate system （ The earth coordinate system ）
Centroid geostationary coordinate system ： A coordinate system based on a reference ellipsoid , It is firmly connected with the earth and moves synchronously with the earth , A coordinate system in which the center of the reference ellipsoid is the origin .
Geocentric geostationary coordinate system ： A coordinate system based on the total earth ellipsoid . It is firmly connected with the earth and moves synchronously with the earth , A coordinate system with the center of the earth as the origin .
characteristic ： The coordinates of points on the ground remain unchanged in the ground fixed coordinate system （ Regardless of tides 、 Plate movement ）, It changes in the celestial coordinate system ( The earth rotates ).
5、54 Beijing coordinate system 、 Xi'an 80 Coordinate system
（1）54 Beijing coordinate system
origin ： Located in Pulkovo, the former Soviet Union ellipsoid ： Krasovsky ellipsoid
1954 The lack of Beijing coordinate system in ：
① There is a large error in ellipsoid parameters .
② There is an obvious systematic inclination from west to east between the reference ellipsoid and China's geoid , In the eastern region, the geoid gap is the largest, up to +68m.
③ The reference plane of geometric geodesy and physical geodesy is not unified . Helmert is adopted in processing gravity data in China 1900～1909 Annual normal gravity formula , The Helmert flat sphere corresponding to this formula is not a rotating ellipsoid , It is inconsistent with krasovsky's ellipsoid , This brings trouble to the actual work .
④ Unclear orientation .
（2） Xi'an 80 Coordinate system
origin ： Located in Yongle Town, Jingyang County, Xi'an ellipsoid ：1975 International ellipsoid
1980 Characteristics of national geodetic coordinate system ：
① use 1975 International Union of Geodesy and Geophysics IUGG The first 16 Recommended at the conference 5 Basic parameters of an ellipsoid .
② stay 1954 Established on the basis of Beijing coordinate system in .
③ Ellipsoid and quasi geoid are most closely related in China , It's multipoint positioning .
④ Clear orientation . The minor axis of the ellipsoid is parallel to the direction of the earth's center of mass pointing to the origin of the earth's pole .
⑤ The geodetic origin is located in the middle of China , Located in the north of Xi'an 60 km Yongle Town, Jingyang County , Xi'an origin for short .
⑥ The geodetic elevation datum adopts 1956 The Yellow Sea elevation system .

The fifth chapter The earth's gravity field
1、 Concepts related to vertical deviation
Vertical deviation ： The vector of gravity at a point on the ground g And the normal vector on the corresponding ellipsoid n The Angle between .
Absolute vertical deviation ： The angle formed by the vertical line and the normal of the total earth ellipsoid .
Relative vertical deviation ： The angle formed by the vertical line and the normal of the reference ellipsoid .
Method of measuring vertical deviation ： Astrogeodesy 、 Gravimetry 、 Astronomical gravimetry 、GPS Measurement method
2、 Vertical deviation formula （u Is the vertical deviation ,ξ、η Namely u The component on the meridional circle and the Mao unitary circle ）
① The astronomical longitude of a known point λ、 latitude φ And earth longitude L、 latitude B The vertical deviation can be obtained .
ξ=φ-B　η=(λ-L)cosφ
B= φ-ξ L= λ-ηsecφ
According to the above formula , The astronomical latitude and longitude can be converted into earth latitude and longitude .
② Laplace's equation can transform astronomical azimuth α Return to the large local potential angle A.
A=α-(λ-L)sinφ-(ξsinA-ηcosA)cotZ( God )
simplify A=α-(λ-L)sinφ or A=α-ηtanφ
3、 Geoid difference measurement method ？
answer ：① The geoid gap is calculated by the earth gravity field model method
② Use Stokes integral formula to calculate
③ Research on geoid by satellite radio altimetry
④ utilize GPS Study on Quasi Geoid by height fitting method
⑤ The least square collocation method is used to study geoid

Chapter six Ellipsoidal projection of the earth
1、 Normal section ： Through any point on the ellipsoid, a normal perpendicular to the ellipsoid can be made , The plane containing this normal is called the cross section . There are countless normal sections .
French intercept ( Or arc cutting ）： The intersection of normal section and ellipsoid is called normal section ( Or arc cutting ）.
Relative normal intercept ： use A Point by point B spot , Then aim at the plane AnaB The section of the same ellipsoid is AaB, be called A The normal section of a point , or B The inverse intercept of the point ; Empathy , from B mirror A spot , Then aim at the plane BnbA The section of the same ellipsoid is BbA , be called B The normal section of a point , or A The inverse intercept of the point . because A,B The normals of do not intersect each other , Therefore, the two normal sections do not coincide . We put AaB and BbA be called A、B The relative normal section of two points .
Mao Youquan ： Normal passing through a point on the ellipsoid , It can be used as an infinite number of normal sections , The closed circle formed by a normal section perpendicular to the meridional plane of the point intersecting with the ellipsoid is called Mao unitary circle .
McNeil's theorem ： Suppose two truncated arcs are drawn through a point on the surface , One is arc cutting , One is oblique arc cutting , And at this point, the two cut-off arcs have a common tangent , At this time, the radius of curvature of the oblique arc at this point is equal to the radius of curvature of the normal arc multiplied by the cosine of the angle between the two arc planes .
2、 Several common radii of curvature
Radius of curvature of meridional circle （M）： The limit of the ratio of a small arc segment on the meridional circle to the radian corresponding to this arc segment .
Radius of curvature of the unitary circle （N）： The limit of the ratio of a small arc segment on the Mao unitary circle to the radian corresponding to this arc segment .
Radius of curvature of arbitrary normal section arc ： The limit of the ratio of a small arc segment on any normal cut-off arc to the radian corresponding to this arc segment .
Mean radius of curvature ： The average radius of curvature of any point on the ellipsoid R Equal to the radius of curvature of the meridional circle of this sub point M And the radius of curvature of the unitary circle N The geometric mean of .
3、 Related concepts of ground wire
Definition ： The shortest distance curve between two points on the ellipsoid is called geodesic line .
nature ：① The geodesic line is the only shortest line between two points , And between the relative normal sections , And close to the normal section .
② The length difference between the geodesic line and the normal section line is only one millionth of a millimeter . The length difference is negligible , The direction difference needs to be changed （ Grade ）.
4、 The basic requirements of reducing the direction value of ground observation to ellipsoid
answer ：① Based on the normal of the ellipsoid ② The ground observation elements are transformed into the corresponding elements of the geodesic on the ellipsoid
5、 Three difference correction ：① Correction of vertical deviation ② Elevation difference correction ③ Section error correction
Correction of vertical deviation ： The correction number that should be added when the horizontal direction value of ground observation based on vertical line is reduced to the direction value based on normal line is called vertical deviation correction .
Elevation difference correction ： When making horizontal observation , If the aiming point is higher than a certain height of the ellipsoid , Then the collimation plane cannot pass through the intersection of the normal of the collimation point and the ellipsoid , The correction of the resulting direction deviation is called elevation difference correction .
Section error correction ： The correction that should be added to change the normal arc cutting direction into the direction of the earth wire is called the section difference correction .
6、 What is the earth theme solution ？ This paper briefly describes the basic idea of forward and inverse calculation of Gaussian average arguments .
Earth theme solution ： It is known that the calculation of some geodetic elements to deduce other geodetic elements is called geodetic subject solution .
Positive solution of Earth Theme ： The longitude of the earth at a given point 、 Geodetic latitude, geodesic length and large local potential angle from this point to the point to be solved , Calculate the geodetic longitude of the point to be solved 、 Solution of geodetic latitude and large local potential angle from the point to be solved to the known point .
Earth Theme inverse solution ： The geodetic longitude and latitude of two points are known , Calculate the length of the earth wire between these two points and the solution of the positive and negative large local potential angle .
Basic idea of forward and inverse calculation of Gaussian average arguments ：
① Put Legendre's series in P１ The point expansion is changed to the midpoint of the length of the geodesic Ms/2 It unfolds at , To reduce the number of terms in the formula of the series , Fast convergence , High precision ;
② Consider finding the midpoint M Of Bs/2 and As/2 complexity , take M The point shall correspond to the average latitude and average azimuth of the points at both ends of the geodesic m Point to replace the midpoint of the ground wire Ms/2 ;
③ Iterative calculation .

Chapter vii. Map mathematical projection transformation
1、 Map projection related concepts
Length ratio ： The ratio of the tiny line segment on the plane to the corresponding tiny line segment on the sphere , It's called the length ratio .
Main direction ： In the process of change , There must be a special position , Keep orthogonal after right angle projection , The direction of the two straight lines , Call it the main direction .
Deformed ellipse ： An infinitesimal circle on the earth ------- Differential circle （ Also called unit circle ）, After projection, it generally becomes a differential ellipse , This differential ellipse is called a deformed ellipse .
Projection distortion ： Because the sphere is a surface that cannot be directly developed into a plane , So whatever projection method is used , The shape of the longitude and latitude network is different , They are not completely similar to the shape of the longitude and latitude network on the sphere . This indicates that the longitude and latitude network on the map has undergone projection deformation . Include ： Length deformation 、 Directional deformation 、 Angular deformation and area deformation .
2、 Classification of map projection
answer ：① Classified by nature ： Isometric projection （ Conformal projection ）、 Isometric projection 、 Arbitrary projection
② Classified according to the projection shape of longitude and latitude network ： Azimuth projection 、 Conic projection 、 Cylindrical projection
③ Classified according to the relative position relationship between the projection plane and the original plane ： Orthaxial projection 、 Transverse projection 、 Oblique projection
3、 What are the conditions that Gaussian projection must meet ？
answer ：① Gaussian projection is conformal projection , Equiangular projection ;
② The central meridian is projected as a straight line , And is the axis of symmetry of the projection ;
③ The length of the central meridian remains unchanged after projection .
4、 Characteristics of Gaussian projection
answer ：① The central meridian is projected as a straight line , And the length remains the same .
② Except for the central meridian , The projection of other meridians is a curve concave to the central meridian , And take the central meridian as the axis of symmetry , There is length deformation after projection .
③ The equatorial line is projected as a straight line , But there is length deformation .
④ The rest of the latitude except the equator , After projection, it is a curve convex to the equator , And take the equator as the axis of symmetry .
⑤ The longitude and latitude remain orthogonal after projection .
⑥ All length deformed segments , The length deformation ratio is greater than l.
⑦ The farther away from the central meridian , The greater the length deformation .
5、 Zoning and map projection
Zonation ： To control the deformation , Using zonal projection , Regulations 1：2.5 ten thousand ——1：50 The ten thousand topographic map adopts longitude difference 6° Zonation ;1:1 10000 and larger scale topographic maps adopt 3° Zonation .
6° Zonation ： From Greenwich 0° Meridians （ Prime meridian ）, From west to East, according to the difference of longitude, every 6° For a video , The world is divided into 60 Two projection bands , The serial number is 1——60. China is located in the east longitude 72°——136° Between , Including 11 Two projection bands , namely 13——23 belt .
3° Zonation ： From east longitude 1 ° 30´ Count up , From west to East, according to the meridians 3° For a projection band , The world is divided into 120 Strip , Our country is located in 24——45 belt .
Projection ： China's big 、 The topographic map of medium scale adopts equiangular cross cutting elliptic cylinder projection , Gauss —— Kruger projection . Small scale topographic map （1：100 ten thousand ） Equiangular conic projection is adopted .
6、 The relationship between the band number and the central longitude
6° belt Central longitude λ in =6°x n -3°
3° belt Central longitude λ in =3°x n
7、 National unified coordinates
In our country x The coordinates are positive ,y Maximum of coordinates ( On the equator ) about 330km. To avoid negative abscissa , Specify adding... To the abscissa 500000m. In addition, the coordinates shall be preceded by a band number . Such coordinates are called national unified coordinates .
for example ： Y=19 123 456.789m
The point is at 19 Intraband , The true value of abscissa ： First, remove the number , subtracting 500 000m, In the end y = -376 543.211(m).
8、 Meridian convergence angle
Definition ： The angle between the tangent direction of the projection line of any sub Meridian on the Gaussian projection plane and the due north direction of the point coordinate .

Chapter viii. Basic techniques and methods of geodesy
1、 Method of establishing national geodetic control network .
① Triangulation advantage ： The graphics are simple , Strong structure , There are many geometric conditions , Easy to check , The accuracy of the net is high .
shortcoming ： Vulnerable to obstacles , Difficult to deploy , Increased the cost of standard construction ; The accuracy of calculating the side length is uneven , The farther away from the starting edge, the lower the accuracy of edge length .
② Traverse method advantage ： Flexible layout , Easy to overcome terrain obstacles ; Traverse survey only requires intervisibility between two adjacent points , Therefore, the target height can be reduced , The cost of bid making is less , And easy to organize observation ; The inner side length of the network is measured directly , The side length accuracy is uniform .
shortcoming ： The conductor structure is simple , There are not as many inspection conditions as triangulation , Gross error is not easy to find , Low reliability .
③ Trilateral measurement and simultaneous measurement of edges and corners
（2） Astrometry
advantage ： The points are observed independently of each other , There is no need for intervisibility , Measurement errors do not accumulate .
shortcoming ： Accuracy is not high , Affected by the weather .
（3） Modern positioning new technology
①GPS Measurement method
② Very long baseline interferometry system (VLBI)
③ Inertial measurement system (INS)
advantage ： Fully autonomous , Intervisibility is not required between points ; all-weather , It only depends on whether the car can start 、 Whether the plane can fly .
shortcoming ： Relative measurement , Accuracy is not high .
2、 Basic principles of establishing national plane Geodetic Control Network
answer ：① The geodetic control network shall be arranged in grades 、 Step by step control
② The geodetic control network shall have sufficient accuracy
③ The geodetic control network should have a certain density
④ The geodetic control network shall have unified technical specifications and requirements
3、 Layout principle of Engineering horizontal control network
answer ：① Grading network , Step by step control ② Have enough accuracy ③ Have enough density ④ There should be a unified specification
4、 Layout of plane geodetic control network ： technical design （ Data collection 、 Field survey 、 The design on the drawing ）, Field selection , Build a target , Mark stone embedding , Field survey , Adjustment calculation .
5、 The error source of precision leveling
answer ：① Instrument error ②i The error of angle affects ③φ Influence of angular error ④ Influence of the length error per meter of the leveling rod ④ Influence of zero point difference between two leveling rods ⑤ Error caused by external factors ⑥ Observation error
6、 Directional observation method ： Observe all directions in turn from the starting direction , So as to determine the observation method of the horizontal angle of each direction relative to the starting direction .
Instrument plus constant correction ： Because the rangefinder 、 Distance correction caused by the inconsistency between the placement center of the reflector and the ranging Center , Weigh the instrument plus constant to correct , Including rangefinder plus constant and reflector plus constant .
Instrument multiplication constant correction ： The scale parameters generated by the reference frequency of the rangefinder and other factors become multiplication constants .
Weather correction ΔDn： The essence of this correction is the correction of atmospheric refractive index to distance . Due to refractive index and air pressure 、 The temperature 、 Humidity related , So we call it meteorological correction .
GPS Network layout mode ： Tracking station 、 Battle style 、 Multi reference station 、 Synchronous Graphic expansion （ Point connection 、 Side connected 、 Net connected 、 Hybrid ）、 Star network layout .
GPS Net benchmark ： Scale datum 、 Azimuth datum 、 Position datum
7、 What calculation work is included in the budget estimate of precision leveling ？
answer ： The estimate of leveling is mainly calculated ：
① Calculation of correction number of length error per meter of leveling rod ② Calculation of correction number of non parallel normal level
③ Calculation of closure error of leveling line ④ Calculation of height difference correction number
8、 Why do I have to calculate the tape splitting and changing ？
answer ： Limit deformation , Take it separately , There is an adjacent band coordinate conversion .
① When a net spans two projection zones , In order to make adjustment in a certain area , It is necessary to convert the coordinates of another belt into the coordinates of this belt .
② The coordinate values of the adjacent two belt coordinate systems need to be calculated for the large location of the overlapping part near the dividing meridian .
③6° Dai Tong 3°、1.5 ° Coordinate conversion between belts .
④ Due to special needs , Convert the coordinates of the national zone into arbitrary zone coordinates .
9、 The method and essence of tape change
answer ： Tape changing method ：
① indirect method ： The forward and inverse calculation formula of Gaussian projection is used to calculate the band change
② direct method
The essence of coordinate transformation ： Use the coordinate transition on the ellipsoid , It's just that the longitude of the central meridian is different .