1. Formation Flying - T.Sugano Orbital Decay Perturbation in LEO is mainly due to atmospheric drag Orbital decay of space probes (e.g. Space Shuttle, ISS, satellites) Altitude correction “trim burns” necessary to keep probes in orbit Orbit will decay in the absence of trim burns

2. Formation Flying - T.Sugano Orbit Lifetime Estimation Estimation of the orbit lifetime of our satellite after mission Consider atmospheric drag effect only Mission orbit is assumed virtually circular for simplicity

3. Formation Flying - T.Sugano Orbit Lifetime Equation Circular Orbit Lifetime Equation (Approximation) a 0 = initial altitude S = projected area of the space probe m = space probe mass

4. Formation Flying - T.Sugano Exponential Atmospheric Model Scale height, H, obtained from tabulated data

5. Formation Flying - T.Sugano Assumptions set forth for our lifetime computation Assumptions: (Made for worst case or shortest decay) m = 50 kg (maximum); S = 0.385m 2 (spherical correction of max volume) C D = 3.0 (upper bound value in LEO probes) a 0 = 6400 + 300 km (typical altitude for STS or ISS) Δ = 150 – 300 = - 150 km (typical re-entry altitude, note the minus sign) f = 1 (ignore latitude effect; not significant (<10%)) ρ 0 = 2.418x10 -11 kg/m 3 (Table, 300 km base altitude) Unavoidable uncertainty  Scale height, H - Not constant between orbit and re-entry altitude - Take H = 30 km, so β = 1 / (30 km)

6. Formation Flying - T.Sugano Computation Result Based on the assumptions we made - T = tau_0 * 189.565 - T = (approx. 1.5 hr of initial orbit period)*(190) = 12 days LEO Nanosat at 300 km of altitude will take 12 days to decay.

7. Formation Flying - T.Sugano Conclusion Our Nanosat does not decease for 12 days Retroburn delta-V input to decelerate the Nanosat for faster decay will be costly without a compelling space debris concern(?) Unless allowed to dispose of the Nanosat in space, retrieval is rather recommended(?) Retrieval may be attained fairly easily by using robot arm of STS perhaps equipped with capture net(?)