REVOSAT

07 mars 2008

INCLINATION OF THE TRACK OF MOLNIYA TYPICAL AND MOLNIYA-1_11474

fevrier_I_and_dI_OF_MOLNIYA_TYPICAL_and_11474
fevrier_Moniya_1_11474inclination_caract
fevrier_Moniya_typical_inclination_caracteristique

The elements of Molniya typical are 40000kms*500kms*63.4°.Those of 11474 15642*433*62.7°. Molniya typical is very elliptic . Molniya 11474 is intermediate. Those two cases allow us to see the evolution of the distortion of the ground track near to the apogee.
We chose 200° as argument of perigee to obtain an apogee equal to 20° (200-180) whose slow movement could be visible over South of France.
1)Speed on orbit. The computed constant area of Molniya typical is 249*10^6.
The parameter of the ellipse 11979 kms, eccentricity=.7417
So Rho=11979/(1+.7417*cos((traj-200)*3.14/180))
As for Molniya 11474 Rho=10404/(1+.5275*cos((traj-200)*3.14/180)) .
2)V ground =Speed orbit*6378/Rho
3)SpinEarth. Earth spins 2*pi*6378 kms on equator in 24 hours so equal 2*pi*6378*cos(lat)/24 in kmh.
4)The Inclination (tan) without spinEarth is cos(lat)^2*tan(i)*(1-tan(lat)^2/tan(i)^2)^.5 see Revosat 2007.
5)Vground+SpinEarth^2=Vground^2+VspinEarth^2-2Vground*Vspin*cos(i-spinEarth)
6)di/spinEarth=(i)/V(ground+SpinEarth).

We see that at latitude~ 45°,Earth spin and V ground of the satellite are close. (1260kmh) . di of Molniya typical can reach 89° .di of Molniya 11474 can reach 31°.Molniya typical can appear ~fix in the sky. Molniya 11474 apogee height is too low compared to that of Molniya typical(40000 and 15642kms). Russians used this possibility by adjusting over a town the argument of perigee .The inclinations of the orbit being ~63.4°, the configurations were stable. See comments of NASA and ESA.

Posté par revosat à 10:26 - Observation - Commentaires  - Permalien [#]