For kicks I took the final elsets of Cosmos 398 and looked at them to get a profile of the satellite's decay. EPOCH APOGEE V(A) DA/DT HEIGHT RHO 325.562 6818.24 7.57 440.24 1.65E-19 332.266 6771.71 7.60 -6.94 393.71 2.28E-18 334.885 6745.89 7.63 -9.86 367.89 9.78E-18 339.168 6690.71 7.67 -12.88 312.71 2.19E-16 342.312 6635.26 7.72 -17.64 257.26 4.99E-15 344.695 6534.85 7.80 -42.14 156.85 1.43E-12 EPOCH PERIGEE V(P) DP/DT HEIGHT RHO 325.562 6538.15 7.89 160.15 1.19E-12 332.266 6535.12 7.88 -0.45 157.12 1.41E-12 334.885 6533.23 7.87 -0.72 155.23 1.57E-12 339.168 6528.40 7.86 -1.13 150.40 2.06E-12 342.312 6523.34 7.85 -1.61 145.34 2.74E-12 344.695 6501.54 7.84 -9.15 123.54 9.37E-12 V(A) - Velocity at apogee (km/sec) V(P) - Velocity at perigee (km/sec) DA/DT - Rate of change in apogee (km/day) DP/DT - Rate of change in perigee (km/day) HEIGHT - Satellite's height above a 6378-km spherical Earth PERIGEE, APOGEE - Expressed in km, geocentric RHO - Atmospheric density. I obtained actual measurements taken in December 94 between 120 and 200 km height, and used a best-fit exponential curve to generate the density numbers The final elset at 344.695 shows that C*398 was very close to cir- culization. It might be tempting to think that because DA/DT is increasing so much that the apogee somehow shoots past the perigee. Not true. The real story is in the convergence of V(A) and V(P). Once they converge, the orbit is fully "circularized." I use the quotes because at this point the orbit is not circular; it is actually a spiral without eccentricity. Apogee and perigee no longer exist. Once C*398 was in its spiral orbit, decay occurred very quickly. The reason for this is a combination of the non-eccentric orbit and the roughly 120 km orbit height. 120 km is a lethal height for satellites. The form of the orbit is a spiral because the drag is acting on the satellite at all points in the orbit. For every step forward in the orbit, C*398 is slowed incrementally by drag and must drop a bit. At this new lower level, rho is higher and C*398 drops even more. The classic drag equation F = 1/2 (rho)(V^2)AC d D shows that the drag force is proportional to atmospheric density and to the square of the velocity. But rho varies exponentially with height; so then does the drag force. A is the cross-sectional area; C-sub-D is the coefficient of drag. CD is typically between 2 and 10 for a supersonic object in a thin atmosphere. Once C*398 got into a low-height non-eccentric spiral orbit, the ever-increasing and relentless drag force increased to the point that the satellite broke up, either from frictional overheating or from aerodynamic structural failure. Other factors ignored here are what make precise decay prediction impossible. Rho can vary by a factor of ten at heights above 300 km or so due to solar flux and geomagnetic activity. At 120 km there are wave disturbances of very short period that vary rho by 20%. One of these random waves can accelerate decay quite a bit. Aero- dynamic lift can offset the drag force to some degree and delay decay. ---------------------------------------------------------------------------- Jim Varney | 121^ 23' 54" W, 38^ 27' 28" N | Sacramento, CA Civil Engineer | Elev. 20 ft. |jvarney@quiknet.com ----------------------------------------------------------------------------