Aardwolf. In geometry yes, but a space agency would want to know why the craft was late. Using Pi=4 solves the problem.LongtimeAirman wrote:I would say that the pi calculation is used to determine distance around the circle, not time.
Airman. Exactly. The curved-motion metric was not known. A long wait for an overdue satellite is the first clue. After noticing a delay in every orbit, one adjusts accordingly. Find the problem with the math or correct for it. In any case, Steven’s Pi=4 experiment, unless disproved, advances common understanding beyond possible ignorance, proprietary or security issues.
Time and distance are given by our relationship: velocity * time = distance. Given the time and distance measurements, we calculate the velocity, 120cm/sec. We have a constant time differential (0.1467s) and a constant distance differential (17.6cm). One can choose either time or distance as the dependent variable. To “know why the craft was late. Using Pi=4” implies you know the correct distance and velocity, as well as the new curved motion metric.
Aardwolf. If it were due to friction it would have a cumulative effect and that plot would be a curve not a straight line.LongtimeAirman wrote: There a friction slowing the ball in the circular track pi/4 when compared to the straight track.
Airman. You and I have agreed. There is no noticeable friction present. I was going for light humor, as in which is true - 1 or 2 (knowing 2 is the correct answer)? Do you believe the ball in the circular track is slower than the straight track, just not due to friction? If so, can you suggest how an initial velocity of 120cm/s is transformed to 92.4cm/s in the circular track? Why accept pi=4 in order to properly calculate time?LongtimeAirman wrote:
1. The ball in the circular track is slower than the straight track. There a friction slowing the ball in the circular track pi/4 when compared to the straight track. or
2. Both tracks are the same length when the curve is measured with Pi=4.
Airman. The forward momentum doesn’t appear to be lost in the tube (or the orbit). The pvc tube (or gravity) redirects the forward velocity vector – along with the forward momentum - each time differential. Any real loss of momentum would appear as friction.Aardwolf wrote: Forward momentum is lost in the tube as it is in an orbit. To correctly account for the lost forward momentum you should use Pi=4 to calculate the time it takes to travel around the curved trajectory.
To calculate the time for an orbit one needs to know the distance and velocity. Given the new curved motion metric, we see that we’ve been under-measuring orbital distance by pi/4. Velocity is 4/pi greater during curved motion than geometry currently assumes. Momentum depends on velocity squared and so it is also greater in curved motion than is currently assumed.
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