Theory of Tumbling Bodies Entering Planetary Atmospheres with Application to Probe Vehicles and the Australian Tektites

The tumbling motion of aerodynamically stable bodies entering planetary atmospheres is analyzed considering that the tumbling, its arrest, and the subsequent oscillatory motion are governed by the equation for the fifth Painleve' transcendent. Results based on the asymptotic behavior of the transcendent are applied to study (1) the oscillatory behavior of planetary probe vehicles in relation to aerodynamic heating and loads and (2) the dynamic behavior of the Australian tektites on entering the Earth's atmosphere, under the hypothesis that their origin was the Moon.