1Which geometric figure is used as the Earth model, an oblate spheroid of rotation?
Rotational ellipsoid
2Within about how many meters does the ellipsoid approximate the geoid?
About 100 meters
3What are the four parameters of the ellipsoid?
Semimajor axis, flattening, total mass and angular velocity
4Which two ellipsoid parameters are geometric and which two are physical?
Semimajor axis and flattening are geometric. Total mass and angular velocity are physical
5Which mathematically defined surface approximates the Earth and is used for horizontal coordinates, geodetic height and map projections?
Reference ellipsoid
6How is the reference ellipsoid generated?
By rotating the meridian ellipse about its minor axis
7What are the uses of the reference ellipsoid?
Reference for horizontal coordinates and geodetic height, reference to describe the shape of the geoid, and reference for map projections
8What is the difference between the semimajor and semiminor axes divided by the semimajor axis?
Flattening
9How can the semiminor axis be computed from the semimajor axis and flattening?
Semimajor axis multiplied by one minus the flattening
10What is the square root of the difference of the squared semimajor and semiminor axes?
Linear eccentricity
11What is the linear eccentricity divided by the semimajor axis?
First eccentricity
12What is the linear eccentricity divided by the semiminor axis?
Second eccentricity
13How is the first eccentricity squared related to flattening?
It equals twice the flattening minus the flattening squared
14What does one minus the first eccentricity squared equal in terms of the axes?
The semiminor axis squared divided by the semimajor axis squared
15What is the semimajor axis squared divided by the semiminor axis?
Polar radius of curvature
16What is the radius of curvature of the section perpendicular to the meridian (east-west direction)?
Normal radius (N), the radius of the prime vertical
17What is the radius of curvature of the ellipsoid along the meridian (north-south direction)?
Meridional radius (M)
18What is the value of N at the equator?
The semimajor axis
19What is the value of M at the equator?
The semimajor axis multiplied by one minus the first eccentricity squared
20What is the value of M and N at the poles?
The polar radius of curvature
21At what latitude is the normal radius N at its maximum?
At the poles (90 degrees)
22Why does the meridional radius of curvature increase toward the pole?
Because the Earth is flattened at the poles
23Which equation gives the radius of curvature at any azimuth?
Euler's equation
24What does Euler's equation state about the radius of curvature at an azimuth?
The reciprocal of the radius equals cosine squared of the azimuth divided by M plus sine squared of the azimuth divided by N
25What is the geometric mean of M and N called?
Gaussian mean radius
26What do you call the distance between two longitudes along the same latitude?
Length of a parallel
27What is the formula for the length of a parallel?
Difference in longitude multiplied by N times the cosine of latitude
28What do you call the distance along the meridian between two latitudes?
Meridian arc length
29What does the radius of the parallel circle represent?
The perpendicular distance from the Earth's rotation axis to a point on the ellipsoid at a given latitude
30What is the formula for X when converting geodetic to geocentric coordinates?
X equals (N plus h) times cosine of latitude times cosine of longitude
31What is the formula for Y when converting geodetic to geocentric coordinates?
Y equals (N plus h) times cosine of latitude times sine of longitude
32What is the formula for Z when converting geodetic to geocentric coordinates?
Z equals N times (1 minus e squared) plus h, all multiplied by sine of latitude
33Which two algorithms convert geocentric XYZ coordinates to geodetic coordinates?
Moritz's (Hirvonen) algorithm and Leick's algorithm
34How is longitude computed from geocentric XYZ coordinates?
Longitude equals the arctangent of Y divided by X
35What is P in the XYZ to geodetic conversion?
The square root of X squared plus Y squared
36What height is assumed to get the first latitude in the Moritz textbook version and in Leick's starting value?
Zero ellipsoidal height
37How is the ellipsoidal height computed in Leick's algorithm after the latitude converges?
P divided by cosine of latitude, minus N
38When do the iterations in the XYZ to geodetic algorithms stop?
When the latitude (and N) no longer changes between iterations, meaning the solution has converged
39Which latitude is the angle at the Earth's center between the equatorial plane and the point?
Geocentric latitude
40Which latitude corresponds to the point on the auxiliary sphere?
Reduced (parametric) latitude
41Which latitude is the angle between the ellipsoid normal and the equatorial plane?
Geodetic latitude