Pocketqube deorbit times: Susceptibility to the solar cycle

Nowadays, as a new kind of femto-satellite with a low cost, Pocketqube has been developed to finish the space research task within the LEO region. During its lifetime the pocketqube is exposed to a high risk of collision with space debris. Taking the solar cycle as a main factor, predicting its deorbit time and evaluating its collision probability before the launch is of great importance for the mission designers to choose a right orbit and determine the proper launch time. This article presents a combined atmospheric density model based on the data from CIRA-2012 to describe the effects of the solar cycle on air density in LEO, and shows how the model is applied to calculate orbital lifetimes of pocketqubes in essentially circular equatorial orbits below 800 km altitude. Then the classical fourth order Runge-Kutta method is utilized in integrating the first order differential equations, which express the rates of change of semi major axis and eccentricity, in order to calculate the orbital lifetimes of pocketqube in LEO. The launch date within the 11-year solar cycle has been chosen as an independent variable to present the influence on lifetime prediction and probability evaluation. The result of lifetime calculation shows that the pocketqube launched at the minimum solar activity year does not necessarily get its longest lifetime. Meanwhile if the pocketqube at some specific starting altitudes is launched at the maximum solar activity year, it may remain in orbit for the longest time period. It also demonstrates how the sensitivity of pocketqube deorbit time to the launch date varies with the initial altitudes. From the figures, it can be obtained that 450 km is the altitude at which the deorbit time is most sensitive to the launch date with the percentage amplitude of 180% over its average value. Furthermore, the collision risk from space debris whose diameter is larger than 1 mm and 10 cm are evaluated by using the same method to integrate through its whole lifetime. It illustrates that for those orbits whose initial altitude is over 700 km, no matter which date is chosen to launch a pocketqube, the debris collision risk grows sharply with the starting altitude rising. Finally, by comparison with the trend of lifetime and collision risk, the interesting thing is that at some orbits with higher altitudes, like 800km, when the lifetime of the pocketqube reaches its maximum, the collision risk inversely reaches its local minimum, which can be useful for its designers to balance these two considerations.