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the mean sea level of the Earth The actual Earth surface uctuates relative to the geoid For analytical convenience the geoid is approximated by an ellipsoid created by rotation of an ellipse around its minor axis as shown in Figure 28 The center of the ellipsoid is coincident with the center of mass of the Earth The minor axis of the ellipse is coincident with the mean rotational axis of the Earth Most charts and navigation tools are expressed in the ( , , h) geodetic coordinates, as depicted in Figure 28, where denotes latitude, denotes longitude, and h denotes altitude above the reference ellipsoid Latitude is the angle in the meridian plane from the equatorial plane to the ellipsoidal normal N Note that the extension of the normal towards the interior of the ellipsoid will not intersect the center of the Earth except in special cases such as = 0 or 90 See Exercise 21 Longitude is the angle in the equatorial plane from the prime meridian to the projection of the point of interest onto the equatorial plane Altitude is the distance along the ellipsoidal normal, away from the interior of the ellipsoid, between the surface of the ellipsoid and the point of interest A geodetic model is de ned by speci cation of four constants The eccentricity of the ellipsoid that approximates the geoid is determined by the gravitational attraction and angular rotation rate of the Earth Therefore, the de ning parameters for a geodetic system must be de ned consistently to determine the ellipsoid and the gravity model The parameters of a geodetic model are determined by least squares tting to experimental data Various geodetic parameter sets have been de ned by di erent users at di erent times The model accuracy has increased along with the associated instrumentation accuracy In particular,improved accuracy was made possible by the analysis of the trajectories of arti cial satellites This book will use the WGS84 geodetic system The WGS84 de ning constants are.

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Source: Thomas DeMark CQG Inc, copyright 2010, all rights reserved worldwide (wwwcqgcom)

wie N(f)

Figure 28: Geodetic reference coordinate system Left - Cross section of the ellipsoid containing the rotational axis and the projection of the point P onto the equatorial plane Right - Cross section of the ellipsoid containing the equatorial plane Name Equatorial radius Reciprocal attening Angular rate Gravitational constant Sysmbol a

Comment: This chart of Disney illustrates that when the trend is up and a short-term Force Index dips below its centerline, it gives a buy signal Its bearish divergences, marked by diagonal arrows, provide sell signals

Table 21: WGS84 de ning parameters contained in Table 21 [12] Two constants de ne the reference ellipse The ellipse de ning parameters are typically the length of the semimajor axis a and one of the following: semiminor axis: eccentricity: atness: b e= f=

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Small Players Large Players NXY EVF (in thousand shares) by size for 40 days Last LEV: 195 Last SEV: 288

The rst term in eqn (858) is the ionospheric delay The second term in eqn (858) is the tropospheric delay The increased path length is s = c ts = a a

(859)

The Cannon Mountain Ski Area in New Hampshire placed the following advertisement in local newspapers: Day-Care Workers/ Day-Care Supervisor Needed for the 2002 2003 ski season Applicants must demonstrate ability to care for children and be creative with child-centered activities Supervisor needs at least one year prior experience in a day-care facility and a high school education The need for day-care workers exists not only in ski areas but also in hotels and other facilities located in many popular resorts Cruise ships that provide child care for their passengers offer opportunity for paid travel to interesting and faraway places If a nearby country club does not offer child care to its membership, you might consider proposing that you operate such a service for the membership

800 600 400 200 0 200 400 600 800 1000

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The ionosphere is the layer of the atmosphere with altitude between 50 and 1000 km that contains free electrons and positively charged molecules The level of ionization is a ected by solar activity, season, and time-of-day Changes in the level of ionization a ect the refractive index along the path through the ionosphere and therefore a ect the travel time measured by the receiver For L-Band (eg, GPS) signals, the ionosphere is a dispersive medium For a modulated signal traveling through dispersive medium, the medium will a ect the carrier and modulating signals di erently Let y(t) = m(t) sin( c t) where m(t) represents a modulating signal with bandwidth signi cantly smaller than the carrier frequency c = 2 fc The modulating signal m(t) propagates at the group velocity as determined by the group refractive index g (l) while the carrier signal sin( c t) propagates at the phase velocity determined by the phase refractive index (l) Detailed analyses are presented on p 136 in [99] and p 309 in [76] To rst order, the phase and group refractive indices can be modeled, respectively, as (l) = 1 g (l) = = N (l) 2 e fc d (l) + fc dfc 1 + 2 Ne (l) fc (860)

(861)

03/25/10

where = 4028 and Ne (l) is the density of free electrons at location (l) Therefore, using the rst term in eqn (858), the delay experienced by the code is 1 Ne (l)dl (862) tg = 2 c fc I and the delay experience by the carrier phase is t = 1 2 c fc Ne (l)dl

03/29/10

(863)

To rst order, the group and phase experience the same delay with the same magnitude, but opposite in sign The code is delayed while the phase is advanced This phenomenon is referred to as code carrier divergence De ning the total electron count (TEC) along the path as T EC =

03/31/10

I i and de ning Ir = 4028 T EC, then at the L1 frequency the code and phase f1 f2 delays can be expressed simply as

04/06/10

t =

(864)

04/08/10

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