Re: moving sats to a different plane

BJORN GIMLE (b_gimle@usa.net)
8 Sep 98 09:20:35 MET DST

In reply to http://www2.satellite.eu.org/seesat/Sep-1998/0003.html
(and 0005.html, 0007.html):

Re: Moving satellites to another plane.

Questions have been asked about using precession of the orbital 
plane to move an (Iridium) satellite to a different plane.

The precession of the plane is approximately
-10.0 * cos(i) / ( a*(1-e**2) ) **3.5  degrees/day, or
at Iridium inclination
-0.013345 * cos(i) * MM**(7/3) / (1-e**2)**3.5 deg/day.

Assuming a typical operational Iridium orbit with i=86.4  
MM=14.3422  a=1.1227, precession would be -0.4188 deg/day

With Ron's pre-launch elset for the Sep.08 (04) launch,
i=86.58   MM=14.796  dRAAN/dt = -0.4276 deg/day

With this small difference, it would take 3300 days to
precess the orbit to the next plane !

Obviously, a larger difference in inclination and/or
Mean Motion would be needed.

A higher MM is achieved by applying a forward thrust (velocity 
decrease). An inclination change can be accomplished by a thrust 
normal to the orbit, and horizontally, near the equator. A direct 
change of RAAN is possible near the apex, but very costly. A 
change of RAAN (or inclination) requires a velocity change of 
2*v*sin(d/2), where v is the circular orbital velocity, and d the 
angular change.

The effect of orbital maneuvres can be tested with Ken Ernandes' 
VEC2TLE program, using the Impulsive Delta V function.
The precession rate can also be checked by applying a zero 
delta-V at a specific time in the future and comparing the RAAN 
of initially co-planar orbits at the same future time.
You can also use this, or the precession formula, to verify
the slightly higher inclination of the 'spare' Iridiums, to
stay in the same plane as the operational ones.

The apogee velocity is approximately
7908 m/s * SQRT ( (1-e)/(1+e)/a )
(reverse signs for perigee).

Using this, the velocities for the circular orbit, and one with 
the same apogee height can be compared. For the operational 
Iridium, this becomes 7463 m/s. A perigee reduction to make 
e=0.02 decreases 'a' by 2%, and needs a 1% speed change, giving 
about 7% change in precession, i.e. 30 degrees in 30/0.42/0.07 
days = 1020 days !

The same deltaV, 75 m/s, can produce an inclination change of 
0.58 degrees (1% of a radian), which precesses to the nearest 
plane in about 440 days.

It seems both a lower orbit, and substantially lower inclination,
are required to shift plane in a reasonable time period.



- bjorn.gimle@tieto.com (work) b_gimle@algonet.se (home)   -
-                              b_gimle@usa.net    (temp)   -
- 59.2237N, 18.2286E, 44 m   http://www.algonet.se/~b_gimle-
- SeeSat-L / Visual Satellite Observer Home Page found at  -
- http://www.satellite.eu.org/satintro.html      -


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