By examining the phases of satellites in the other planes 2 and 3, it becomes apparent

that these satellites will also appear at the same position as the reference satellite in

plane 1 within the same 8 day period.  This arises because the time taken by the  earth

to rotate through the angle 120 degrees separating planes 1 and 2 is the same time

taken by a satellite in that plane with phase +255 degrees to travel round to the same

position as the reference satellite.  The earth rotates through 120 degrees in 478.69

minutes, very nearly 8 hours, which corresponds almost exactly to 17/24 of a

GLONASS orbit or +255 degrees.  The same argument holds for plane 3 at 240 degree

separation for a satellite at phase +150 degrees (or twice +255 less 360 degrees).  The

 angular separation of 45 degrees within the plane together with the angular phase

differences of +/  30 degrees between planes assures that in an 8 day period, all 24

satellites will pass through the position with the reference sub satellite location.

The above argument holds for any valid pointing angle.  Once an antenna is pointed at

any satellite in the system, all others will in time pass through the main beam.  For any

location, the azimuth and elevation for a particular track have to be computed  over an

8 day period, following which suitable pointing angles and time may be chosen by the

observer for the reference orbit and satellite.  The entire subsequent orbital behavior is

synchronous as explained.  This argument has assumed a near perfect circular orbit

and precise orbital spacing and timing.

A.6   MANOEUVERING IN ORBIT

During recent years the Russians have moved several satellites within the orbital plane

to a new position.  This operation has occurred following a satellite failure or to position

a particular satellites in antipodal positions to allow broadcast using common

frequency.  Manoeuvres to change the phase of a satellite in orbit begin by firing of the

on board thrusters at apogee where the velocity vector is at right angles to the radius

vector.  This action takes the spacecraft into an orbit with altered period (slightly

eccentric) in such a way that the space craft gradually falls behind or moves forward

(depending on the direction of thruster firing) from its initial position.  After an integer

number of orbits, the required position in phase is reached and a reverse firing of

thrusters of exactly the same magnitude as the first ensures a new stable and circular

orbit.  Taking the semi major axis of the near circular orbit as  a  and the elliptical orbit

as  a Da , then the eccentricity of the new orbit is  e = Da/(a Da) .  The change in orbital

period DT, referred to the period of the circular orbit, is found from Kepler s third law :

T

3

a

m

= *

=

T

2

a

360n

A 5