The Inner Formation Flying System （IFFS） consisting of an freely flying in the shield cavity can construct a pure gravity outer satellite and an inner satellite which is a sphere proof mass orbit to precisely detect the earth gravity field. The residual gas in the cavity is a significant disturbance source due to the temperature inhomogeneity and relative motion of the inner satellite. The expressions of the disturbance forces were derived based on the property of rarefied gas, including the radiometer effect and the damping force. According to the current design of IFFS, heat transfer analysis of the cavity and the inner satellite was carried out, and the surface temperature distribution of the cavity and the inner satellite was given. The relative motion of the inner satellite was obtained from the formation control simulation of IFFS. Then the residual gas disturbance was calculated. The disturbance acceleration acting on the inner satellite due to the radiometer effect was on the order of 10^-11 m s^-2 and the damping acceleration was on the order of 10^-15 m s^-2.
Spacecrafts with the pure gravity environment are of great significance in precision navigation, gravity field measurement for celestial bodies, and basic physics ex- periments. The radiometer effect is one of the important interfering factors on the proof mass in a purely gravitational orbit. For the gravity field measurement system based on the inner-formation flying, the relationship between the radiometer effect on the inner- satellite and the system parameters is studied by analytical and numerical methods. An approximate function of the radiometer effect suitable for the engineering computation and the correction factor are obtained. The analytic results show that the radiometer effect on the inner-satellite is proportional to the average pressure while inversely pro- portional to the average temperature in the outer-satellite cavity. The radiometer effect increases with the temperature difference in the cavity, and its minimum exists when the cavity radius increases. When the minimum of the radiometer effect arrives, the ratio of the cavity radius to the inner-satellite radius is 1.189 4. This constant is determined by the spherical cavity configuration and independent of the temperature and pressure distributions. When the ratio of the cavity radius to the inner-satellite radius is more than 10, it is believed that the cavity is large enough, the radiometer effect is approxi- mately proportional to the square of the inner-satellite radius, and the influence of the outer-satellite cavity radius on the radiometer effect can be ignored.
