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| A 'simple' Physics postulation... |
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| Ian.M:
Over the at most couple of minutes* that one *COULD* put an object into a free fall trajectory in vacuo at or near sea level, treating the Earth's orbital motion (including its 'wobble' round the Earth - Moon barycenter) as constant velocity motion in a straight line is a reasonable simplification. * Deepest mineshafts are around 4Km which gives a free fall time from the top of slightly under half a minute. One could conceivably wait for such a mine to play out, lease the shaft, vacuum seal it and pump it down and conduct the experiment from the shaft bottom. You'd need a rifle to launch the projectile, and some mighty fancy doppler laser measuring gear at the top of the shaft! For convenience: https://www.omnicalculator.com/physics/free-fall |
| TimFox:
The late Prof U Fano showed me (and the other guys) how to do quantum-mechanical calculations of macroscopic problems. To be relevant to a large-scale question, one tracks the "expectation value" of the variable in question, which is well-defined in quantum mechanics. |
| TimFox:
Going back to the original simple question about the velocity at the top of the trajectory. Stripping away the practical complications, such as air resistance and the Earth's rotation, the question goes back to the nature of "infinitesimals", which Leibnitz and others discussed ca. 1700, as calculus was being invented. In modern mathematics, the question was answered by a rigorous theory of limits, applied to the definition of derivative in the calculus. A different example of limits: consider the function f(x) = sin(x)/x , used in the reconstruction of a continuous analog waveform from discrete sampled data. (x in radians, of course) When x = 0, the function would be indeterminate (0/0 is not uniquely defined). However, applying proper limit theory (left as an exercise for the reader), the limit of f as x goes to zero (from either direction) is unity. |
| T3sl4co1l:
One that's always stuck with me is calculating the quantum number of the Earth-Sun system (applying the parameters to the hydrogenic atom). N of course is uselessly large, the neat part is calculating the wavelength of the particle (i.e., graviton) emitted in a transition from N to N-1. Can you guess the wavelength? ;D Tim |
| themadhippy:
Is the answer 42? |
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