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Re: AO-40: more successful ARCJET operations



Newton solution with Keprerian equation

(1)  M=MA*2*3.14/256            : Radian from MA
(2)  to=M+e*sin(M)+0.5*e^2*sin(2*M) : Initial value
(3)  mo=to-e*sin(to)            : Keprerian equation
(4)  dto=(M-mo)/(1-e*cos(to))   : e=Eccentricity
(5)  t1=to+dto                  : 1st approximate value
(6)  m1=t1-e*sin(t1)
(7)  dt1=(M-m1)/(1-e*cos(t1))
(8)  t2=t1+dt1                  : 2nd approximate value
(9)  m2=t2-e*sin(t2)
(10) dt2=(M-m2)/(1-e*cos(t2))
(11) t3=t2+dt2                  : 3rd approximate value
(12) t4=tan(t3/2)
(13) u=root((1+e)/(1-e))*t4
(14) s=2*arctan(u)              : Real anomaly
(15) p=24*3600/n                : Period(total seconds)
(16) 4*3.14^2*(a^3/p^2)=G*Q     : A law of the universal graviation
(17) a=(((G*Q*p^2)/(4*3.14^2))^(1/3))*10^9 : Semi major Axis
(18) r0=a(1-e^2)/(1+e*cos(s))   : Height from the center of the earth
(19) r=r0-6371                  : Height from the face of the earth


The solution of this algorism

                    Before      After
  Perigee height :   286.0        288.4  ....... +2.4 km
  Apogee height  : 58967.2      58966.8  ....... -0.4 km


The report of Peter Guelzow, DB2OS

                    Before      After
  Perigee height :   279.754      282.2427  .... +2.5 km
  Apogee height  : 58971.166    58971.024   .... -0.1 km


EXCEL sheet of the range analysis

http://www.ne.jp/asahi/hamradio/je9pel/a40range.zip


> Date: Sat, 23 Jun 2001 10:08:15 +0000
> From: Peter Guelzow <peter.guelzow@arcormail.de>
> To: amsat-bb@amsat.org, forum@amsat-dl.org
> Subject: AO-40: more successful ARCJET operations
> 
> Dear All,
> 
> The arc-jet thruster has been invoked on Orbit 296, MA 118-135,
> which gave about 1 hour of thrusting gas only. 
> 
> The S2 TX is OFF from MA 100-180 to spare power for the ATOS. 
> The gas generator for the ammonia draws about 120 - 130 W of power
> when cycled on by the thermostat. 
> 
> The IHU-2 is running and logging telemetry into a circular buffer
> and hold about 2.5 days worth of data. Downloaded telemetry from
> this 1h burn indicated positive power budget and everything looks
> nominally. 
> 
> The thrust on orbit 296 started at MA 121.4 and lasted for 3618s.
> The acceleration is guestimated to be 54E-6 m/s^2 ,
> and the direction of acceleration is towards alon 274, alat -2 
> (the current attitude).
> 
> Give or take the unknowns, the expected outcome of this was:
> 
>                      Before            After
>   --------------------------------------------
>   Epoch year            2001              2001
>   Epoch time       173.12145         173.16312
>   Inclination         5.2833         5.2833592
>   R.A.A.N          180.71591         180.70361
>   Eccentricity      0.815077         0.8150139
>   Arg perigee      288.69088         288.71333
>   Mean Anomaly         121.4         140.46836
>   Mean motion MM   1.2711484         1.2710861
>   Revolution             296               296
>   SMA                36003.6         36004.773
>       
>   Perigee height     279.754          282.2427   <<<  +2.5 km
>   Apogee height    58971.166         58971.024
>   --------------------------------------------
> 
> So the perigee was raised by this 1h burn by about +2.5 km, but only
> a thrust rate of 50% was used. 
> 
> Since everything went so well, the computer onboard AO-40 was 
> commanded to initiate 2h "burns" starting around apogee on orbit 297
> for the next three orbits. 
> 
> The first 2-hour burn stopped at Orbit 297 MA 142, which is 2001 
> Jun 23 0154 utc. Again, all telemetry is looking good and we may soon
> expand to 4h "burns" and possibly increase the thrust level as well.
> 
> While we haven't yet seen the latest NORAD data, some effects of the
> changing orbit should be soon noticeable. 
> 
> Indeed, we all are very happy with the successful results of the ATOS
> (Arcjet Thruster on OSCAR Satellite) so far.
> 
> Some more information about the ATOS system is available here:
> 
> http://www.irs.uni-stuttgart.de/RESEARCH/EL_PROP/PROJ/e_atos.html
> 
> 
> best 73s
>  Peter DB2OS for the AO-40 team


----------------------------------------------
Name : JE9PEL/Mineo Wakita, JAMSAT member
Mail : je9pel@jamsat.or.jp
URL  : http://www.ne.jp/asahi/hamradio/je9pel/
QTH  : Yokohama Japan, GL:PM95TJ
Date : Jun 24, 2001
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