gps orbits

CSED, BAHIR DAR UNIVERSITY

GPS ORBITS


•What is the requirement of orbital information in GPS positioning.

•The nature of satellite orbits, design And forces acting on them.

•Orbit broad cast ephemeris..

•Tracking methodology


Orbital information is required for four major tasks involved in the GPS positioning process:

1. receiver position determination,

2. planning,

3. receiver aiding, and

4. satellite selection.


Orbital information can be accurate and approximate

• For receiver positioning accurate data is required

positioning can be of two types :-

1. Point positioning

2. Relative positioning


Point positioning

The positioning With respect to defined coordinate system usually by three coordinate values.


In the case of point position computations,

there strict requirement for precise orbital information


Relative Positioning

The positioning with respect to another point, taking

one point as the origin of a local coordinate system.


Shown above is Relative positioning Using local

astronomical system.

If R1 of point Pj is known in one coordinate system

& interstation vector ΔR12 (ΔX, ΔY, ΔZ) is determined in

the same coordinate system. Then the vector equation

gives us the position of P2 in the same coordinate

system


For relative positioning, the effects of any uncertainties

in the ephemeris data on the final position are less


The vector error db in the baseline vector b, is given by

Here db is determined as a function of dri ,in

position of i satellite used to determine b

ρi = range to ith satellite

ei = unit vector to ith satellite

db depends not only on the magnitudes of p, b,

and dr but also on their directions


Approximate information of orbits are required

in some other tasks:-

Planning the use of GPS. Knowing when to use GPS

Signal acquisition. first GPS receiver must acquire the

satellite signals to be used.

If nothing is known cold search is done

This involves selecting each of the 32 possible C/A-codes

(requires lot of time)


Almanac' data:- information provided by the visible

satellite regarding the tentative location of other sats.

Satellite alerts :- computing approximate satellite

positions for planning or receiver aiding.

*For planning , various graphical representation are there•linear plot -elevations and azimuths are plotted

against time for each satellite, with respect to a

specified location


• polar plot- elevations and azimuths , are predicted

and plotted, as a function of time for each

satellite, with respect to a specified location

•Track plot, satellite subpoint is plotted on a map.

•Visibility plot, plot against time of day,of the period

during which each satellite is visible from a specified

location


COORDINATE SYSTEMS


Dynamics of satellites is governed by

Newton's law of motion stating

Acceleration α C.O.M of free body

The position, velocity, acceleration, and force

components refer to a special coordinate system called

Inertial

#Inertial coordinate system, which is either stationary

or in uniform motion in space


For this purpose we adopt Right ascension (RA) system,

(which is an appropriate inertial coordinate system).

The orientation of the RA-system relative to the fixed

stars changes by about 1" per year, due to the forced

periodic motion of the earth's rotation axis.

this motion is called precession and nutation,


But for terrestrial positioning purposes, RA-system is not

a convenient reference frame.

#Here we define the coordinate system which is 'fixed to

the solid earth' i.e (stationary point on earth will have

Fixed coordinates ever).

Conventional terrestrial system (CT- also known as the

average terrestrial system)


•The 1st axis of the CT-system passes through the

intersection of the Greenwich meridian and the equatorial

Plane.

•The 3rd axis of the CT-system is defined by the

Conventional International Origin (CIO).

•The 2nd axis is orthogonal to the first and third axes .

[Until July 1985, the realization of the CT-system used to describe the GPS

broadcast ephemeris was the World Geodetic System 1972 (WGS-72)]

**(Since January 1987 the WGS-84 is adopted ww)


Forces acting on satellites


#Forces that contributes to satellite motion comprise:

•Gravitational attraction of the earth,

•Gravitational attractions of the sun, moon, and planets (called the third body effects),

• Atmospheric drag force,

•Solar radiation pressure, both direct and albedo effects,

•Magnetic forces, and

• The variable part of the earth's gravitational field


Above all forces the most prominent is gravitational

attraction of the earth.

Earth’s gravitational attraction can be further divided into:-

•Central part, the radial gravitational attraction.

•The non-central part.

#Perturbations The non-central part and remaining forces

introduce some small variations into the motion of satellite

these variations are called as perturbations.


KEPLER'S FIRST LAW

It states that “THE ORBIT IS AN ELLIPSE WITH ONE

OF THE FOCI LOCATED AT THE EARTH‘S CENTRE OF

MASS”

Which depicts that “It is not possible to launch

satellite directly into an orbit with an angle of

inclination less than the latitude of the launch site”


Kepler's first law is very usefull today in determining

the orbits which are achievable by satellites launched

from various launch sites.

*To obtain inclinations lower than the launch site latitude,

the satellite must first be launched into a 'parking orbit,'


Basically Keplerian motion is the idealized satellite motion

caused only by the earth's central gravitational field.

The main aspects of Keplerian motion are:

1. The motion relative to the RA-system occurs in a

stationary plane which contains the centre of mass of the

Earth.


2. The closest and farthest points of the orbit to the

earth's centre of mass, called perigee and apogee.

3. The size and shape of the elliptical orbit are constant.


KEPLER'S SECOND LAW

It states that “GEOCENTRIC POSITION VECTOR OF A

SATELLITE SWEEPS EQUAL AREA IN EQUAL TIME”

Basically it(2nd law) follows energy conservation law


As satellite is in motion possesses two kinds of energy —1. potential 2. kinetic.

Potential energy is governed only by the gravitational field

and is lowest when the satellite is closest to the attracting

body (i.e., at the perigee), and highest at apogee.

Total energy must remain constant

Therefore the kinetic energy must be the largest at perigee

and lowest at apogee.


Practical implications

1. spy satellites

2. communication satellites

3. lifetime of a satellite


KEPLER'S THIRD LAW

It states that the ratio between the square of the orbital

period and the cube of the semi-major axis, a,

is the same for all satellites

i.e,

Where , μ=GM


Generally if, Often the period is expressed in terms of itsreciprocal, the mean motion

n = 2π/T.

Then we have,

n2/a3=μ

Generally a & μ are known to us so,

n=(μ/a3)1/2


Practically it means that “Two satellites with the

same semi-major axis length have equal orbital

periods regardless of eccentricity”


KEPLERIAN ORBITAL ELEMENTS


A particular set of parameters called the

Keplerian elements is commonly used in

satellite positioning, Out of them only one is a

function of time. They are:-

•(Ω). Right ascension of the ascending node.

•(i) Inclination

Ω and i, define the orientation of the orbital plane inspace

•


•(ω) Argument of perigee. It defines the location of

the perigee

•(a) Semi-major axis of the elliptical orbit

•(e) Eccentricity of the orbit

a and e define the size and shape of the orbit.


THIRD-BODY EFFECTS AND TIDES

Direct effectT.B.E


It is nothing but the gravitational force per unit mass

of a satellite due to the attraction of a third body i.e

moon, sun and stars etc..

*(IMP# T.B.E of the moon and the sun need be

modelled for short to medium orbital arcs)


T.B.E (Ftb)is given by:-

Where, M* =Mass of TB r* = geocentric position vector of TB G = ?

∵ M* / |r*|3 for the sun is 0.46 times of moon, the solar TBE of sun=1/2 moon


For the planets, the masses M* are far smaller

a.c.t sun, and distances |r*| much greater than for

the moon; the Planetary T.B.E on GPS satellites are

negligible.

Point to be noted is:

* TBE is greatest due to moon.


Tides :The earth and the oceans undergo tidal

deformations at primarily the semi-diurnal and

diurnal frequencies.The tidal deformations cause a

periodic re-arrangement of the earth's mass which in

turn alters the earth's gravitational attraction.

These effects are insignificant for GPS satellites over

orbital periods.


SOLAR RADIATION PRESSURE AND

ATMOSPHERIC DRAG

D.EI.D.E


Direct Effect:-The photons emitted by the sun create a

repulsive pressure upon their impact on the satellite.

Indirect Effect:- The photons striking satellite after being

reflected from the earth. This I.E isalso called as

Albedo effect.

The direct radiation pressure is zero when the

satellite is in the earth's shadow.


Force of solar radiation/unit mass on a satellite varies

In accordance with

Fsr = v p A r / m

Where,

v = eclipse factor (1 in sunlight, 0 in shadow) p = solar radiation pressure A = C.S.A of the sat on which the radiation falls r = reflectivity of the satellite, and m = satellite mass.


Atmospheric drag:- It is a non-conservative force

arising due to friction betn the satellite & surrounding

atmosphere. This results in loss of satellite

energy which in turn results in secular changes which

are non-recoverable in a and M.

Where,

m = satellite mass.

A = C.S.A of the sat on which the radiation falls


The Fad per unit mass on a satellite varies in

Accordance with

Fad =ρ v2 A / mWhere,

ρ = the atmospheric density at satellite v = the sat's velocity relative the atmosphere A & m we know

The ρ at GPS satellite altitudes, ~20 000 km, is so

small that the Fad are negligible


EPHEMERIS PREDICTION


GPS MCS computes and controlles the broadcast

ephemeris information transmitted by the satellites & is

Pridicted in two ways:-

1. off-line least-squares to produce a reference

ephemeris.

2. on-line 1st-order correction by a Kalman filter &

additional measurements to predict current states of

satellite which, in turn, predicts future states


The reference ephemeris is an initial estimate of the

satellite trajectory,

The on-line ephemeris prediction is driven by pseudo-

range and integrated Doppler measurements from

each satellite in view at each monitor station

##Post computed ephemeris


BROADCAST EPHEMERIS MESSAGE PARAMETERS


Broadcast ephemerides for the GPS satellites are readily

available in the navigation message modulated on the

GPS carrier signals.

The 6 parameters (√a, e, iQ, ω, Ω0, Mo) describe a

smooth, elliptical orbit with the satellite position being

a function of time since t.


The parameters (Δn, Ω-dot, i-dot, and the six

sine and cosine coefficients) describe the deviations of

the actual satellite motion from this smooth ellipse.


GPS ORBIT DESCRIPTION


There are 4 points of importance along the orbital

ellipse. These are:

• The ascending node. This is the intersection of

the orbital plane, and the

equatorial plane,.

• Perigee. This is point at which the satellite most

closely approaches the earth..


The reference position. This is position of the

satellite at the reference time toe .

• The satellite position. This is what we want to

determine. It is separated from perigee by the true

anomaly f, and from the ascending node by the

Argument of latitude u = ω + f.

##Satellite coordinate computation

gps orbits

Engineering

bahir dar university

bahir dar university

local coordinate system

defined coordinate system

gps orbits csed

special coordinate system

satellite motion

rasystem relative