大气阻力引起卫星轨道衰减的数值模拟

本文以德国低轨道卫星CHAMP为例，联合考虑地球扁率和大气阻力摄动的影响，对相应摄动方程进行数值积分，计算轨道根数变化，并进而计算得到卫星空间位置，由此模拟考察大气阻力引起的轨道高度衰减.模拟中使用综合考虑了太阳辐射和磁暴等多种因素影响的最新国际大气标准JB2008模式来计算热层大气密度. 选取CHAMP卫星轨道高度自然衰减（无点火提升卫星高度操作）的2005全年进行模拟；为了考察不同年份阻力系数的可能变化，对2002年1—3月处在较大高度的轨道也进行了模拟.考虑到CHAMP卫星的特殊几何构形及飞行高度的热层温度条件，取阻力系数大于2.8，并在一定范围内变化，以求得模拟与实际轨道衰减符合较好.结果表明，对于2005年，阻力系数为2.91时模拟得到的轨道高度的衰减与实际轨道衰减符合得最好，模拟与实际轨道半长轴全年的标准偏差为81m；在卫星高度稍高的2002年，模拟的最佳阻力系数为3.0；模拟所得最佳阻力系数值比传统使用的值2.2大30%以上.由于在模拟中忽略了高阶保守力分量，所得近/远地点高度没有出现实际轨道所显示的周期性起伏.

Simulation of orbit decay for LEO satellites caused by atmospheric drag

Considering jointly the perturbations due to earth's oblateness and atmospheric air drag, the LEO satellite orbit decay has been simulated for CHAMP by numeric integration on the relevant perturbation functions to derive variations of orbit elements and calculate the satellite spatial positions. In the simulation the newly proposed international standard atmosphere of JB-2008 is used to produce the air mass density, which takes both the solar radiation and geomagnetic activity comprehensively into account. The simulation is performed for 2005 when there were not either firing for lifting the spacecraft or major attitude change and thus the spacecraft orbit underwent a natrual decay. In order to inspect the possible change in the coefficient at higher altitude, the orbit in 2002 is also simulated for the first three months. In consideration of particular shape of the CHAMP spacecraft and the thermospheric condition in which the spacecraft is flying, we adopted the air drag coefficient larger than 2.8 and varying in a range to find the optimum drag coefficient. It is found that for 2005 year the simulated orbit altitude decay is consist with the real one best when the drag coefficient being as 2.91 as large. The simulated semi-major axis length shows a standard deviation in respect with observed ones as small as 81 m. At higher orbit altitude in 2002, the simulated optimum drag coefficient is estimated at 3.0. Thus the resulted coefficients are much larger than the conventionally used value of 2.2. The simulated decaying apogee and perigee exhibit no periodic fluctuations that exist by contrast in the real orbit decays, which may be due to neglecting the higher order gravity components in the present simulation.