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- W1973996874 abstract "Abstract A solution is obtained for the velocity of a body falling to earth from a point outside the appreciable atmosphere on the assumption that 1. (i) the flight path is a straight line inclined at an angle 0 to the horizontal, 2. (ii) the drag coefficient C d is constant, 3. (iii) gravitational acceleration g is constant within the atmosphere, 4. (iv) the scale height H of the atmosphere is constant. The motion is characterized by the single parameter p ∗ = mg sin θ/SC D , where m is the mass and S the frontal cross-sectional area of the body. Graphs are presented showing velocity and deceleration against height for falls from 100, 200, and 300km and for various values of p ∗ . It is shown that the deceleration is greatest at heights where the atmospheric pressure is approximately p ∗ , and that the rate of loss of energy is greatest at heights where the pressure is approximately 2 3-p ∗ (provided the maximum deceleration is somewhat larger than the gravity component along the trajectory). The maximum deceleration is shown to be approximately [e −1 (E/gH + log e p ∗ ) − 0.5152] sin θ (provided the body falls at least two to three scale heights before reaching maximum deceleration), where E is the initial energy of the body and p ∗ is measured in atmospheres. The effect is considered of refraction arising from the temperature structure of the atmosphere on the shock wave generated by a vertically-falling body. It is shown that only a part of the shock wave originating in the lower atmosphere will reach earth in the case of falls from above 120 km; but for falls from below this height, an additional part of the shock wave originating in the region of the temperature maximum at 50 km may also reach earth. Curves are plotted showing the horizontal range from the impact point at which shock waves originating in the lower atmosphere reach earth for bodies falling vertically from 100, 200, and 300 km with various values of p ∗ ." @default.
- W1973996874 created "2016-06-24" @default.
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- W1973996874 date "1957-02-01" @default.
- W1973996874 modified "2023-09-27" @default.
- W1973996874 title "Velocity of a body falling through the atmosphere and the propagation of its shock wave to earth" @default.
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- W1973996874 doi "https://doi.org/10.1016/0021-9169(57)90141-1" @default.
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