Comments by "WhatAboutTheBee" (@WhatAboutTheBee) on "Astrum"
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Formula yielding peak velocity under constant acceleration, when v0 =0 is Vpeak=sqrt(2×A×D). A=0.08 meters/second squared. D = 20,000 meters. Therefore Vpeak=56.568 meters/second. Or 126.53 mph. That's plenty enough speed.
Yet it is the deceleration at the end that kills you, not the speed. For example, 43 earth gravities (Gs) are sufficient to cause your skull to fracture away from your spine (for the curious, basilar skull fracture).
Deceleration is inversely proportional to time. Let us assume it takes two seconds to decelerate from 57 meters/second to 0 meters/second. Deceleration is V/T, yielding 28.5 m/s^2. That's only 2.9 Gs and may be survivable, particularly if you land on your feet.
If, however, we decrease the deceleration time to 0.135 seconds, we get V/T = 422m/s^2. That, of course, yields 43 earth gravities and will result in massive damage to your skeletal system.
Your video glossed over the real cause of injury. It is not the velocity. It is the sudden stop at the end, to wit, deceleration.
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@chrisdavis4230 Hi Chris. Let us Assume you shot straight up. Here on Earth, the bullet eventually slows to a stop due to gravity and air resistance. It then tumbles to the earth from that height, under a constant acceleration regime, until terminal velocity due to air resistance for the projectile is reached.
On Miranda, there is no atmosphere. The projectile is only slowed by gravity. Let us assume that the projectile never reaches escape velocity. At some point, then, the projectile comes to a stop. The height above the surface is the initial 20Km plus the displacement over the projectiles travel. Let us further assume it took an additional 30Km to decelerate to zero.
So at 50Km above the surface, we begin to fall towards the surface, under a constant 0.08m/s^2 regime. Vpeak = sqrt(2×A×D) ao we have Vpeak = sqrt(2×.08×50,000) 89.44 meters per second instead of 56.5685 m/s for the 20 Km fall. As there is no atmosphere, there is no terminal velocity.
Once we achieve escape velicity, orbital mechanics apply, and I think, not really your question.
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