It's really so simple
If you accelerate a distance 400 meter with 1 m/s^2 your speed must be 400 m/s
Wrong.
second 1: start at 0 m/s, end at 1 m/s, distance traveled in one second .5 m, total distance traveled .5 m.
second 2: start at 1 m/s, end at 2 m/s, distance traveled in one second 1.5 m, total distance traveled 2 m.
second 3: start at 2 m/s, end at 3 m/s, distance traveled in one second 2.5 m, total distance traveled 4.5 m.
second 4: start at 3 m/s, end at 4 m/s, distance traveled in one second 3.5 m, total distance traveled 8 m.
second 5: start at 4 m/s, end at 5 m/s, distance traveled in one second 4.5 m, total distance traveled 12.5 m.
second 6: start at 5 m/s, end at 6 m/s, distance traveled in one second 5.5 m, total distance traveled 18 m.
second 7: start at 6 m/s, end at 7 m/s, distance traveled in one second 6.5 m, total distance traveled 24.5 m.
second 8: start at 7 m/s, end at 8 m/s, distance traveled in one second 7.5 m, total distance traveled 32 m.
second 9: start at 8 m/s, end at 9 m/s, distance traveled in one second 8.5 m, total distance traveled 40.5 m.
second 10: start at 9 m/s, end at 10 m/s, distance traveled in one second 9.5 m, total distance traveled 50 m.
second 11: start at 10 m/s, end at 11 m/s, distance traveled in one second 10.5 m, total distance traveled 60.5 m.
second 12: start at 11 m/s, end at 12 m/s, distance traveled in one second 11.5 m, total distance traveled 72 m.
second 13: start at 12 m/s, end at 13 m/s, distance traveled in one second 12.5 m, total distance traveled 84.5 m.
second 14: start at 13 m/s, end at 14 m/s, distance traveled in one second 13.5 m, total distance traveled 98 m.
second 15: start at 14 m/s, end at 15 m/s, distance traveled in one second 14.5 m, total distance traveled 112.5 m.
second 16: start at 15 m/s, end at 16 m/s, distance traveled in one second 15.5 m, total distance traveled 128 m.
second 17: start at 16 m/s, end at 17 m/s, distance traveled in one second 16.5 m, total distance traveled 144.5 m.
second 18: start at 17 m/s, end at 18 m/s, distance traveled in one second 17.5 m, total distance traveled 162 m.
second 19: start at 18 m/s, end at 19 m/s, distance traveled in one second 18.5 m, total distance traveled 180.5 m.
second 20: start at 19 m/s, end at 20 m/s, distance traveled in one second 19.5 m, total distance traveled 200 m.
second 21: start at 20 m/s, end at 21 m/s, distance traveled in one second 20.5 m, total distance traveled 220.5 m.
second 22: start at 21 m/s, end at 22 m/s, distance traveled in one second 21.5 m, total distance traveled 242 m.
second 23: start at 22 m/s, end at 23 m/s, distance traveled in one second 22.5 m, total distance traveled 264.5 m.
second 24: start at 23 m/s, end at 24 m/s, distance traveled in one second 23.5 m, total distance traveled 288 m.
second 25: start at 24 m/s, end at 25 m/s, distance traveled in one second 24.5 m, total distance traveled 312.5 m.
second 26: start at 25 m/s, end at 26 m/s, distance traveled in one second 25.5 m, total distance traveled 338 m.
second 27: start at 26 m/s, end at 27 m/s, distance traveled in one second 26.5 m, total distance traveled 364.5 m
second 28: start at 27 m/s, end at 28 m/s, distance traveled in one second 27.5 m, total distance traveled 392 m
second 28: start at 28 m/s, end at 29 m/s, distance traveled in one second 28.5 m, total distance traveled 420.5 m -- and you've run off the end of your 400 meter track, having reached a speed of less than 29 meters per second. (Actual final speed on reaching the end of the 400 meters is 28.28 m/s.)
Your guess at the speed reached by accelerating 1 m/s^s over a distance of 400 meters was off by more than a factor of 10.
If you accelerate a distance 100 meter with 16 m/s^2 you speed must be 1600 m/s
Wrong.
second 1: start at 0 m/s, end at 16 m/s, distance traveled in one second 8 m, total distance traveled 8 m.
second 2: start at 16 m/s, end at 32 m/s, distance traveled in one second 24 m, total distance traveled 32 m.
second 3: start at 32 m/s, end at 48 m/s, distance traveled in one second 40 m, total distance traveled 72 m.
second 4: start at 48 m/s, and at 64 m/s, distance traveled in one second 56 m, total distance traveled 128 m - and you've run off the end of your 100 meter track, having reached a speed of less than 64 m/s. (Actual final speed on reaching the end of the 100 meters is 56.57 m/s.)
Your guess at the speed reached by accelerating 16 m/s^2 for a distance of 100 meters was off by a factor of more than 25.
This mean you speed should increase speed 4 times in the above illustrated inner orbit.
Nope, even if your reasoning about the relation between orbital accelerations and distances, and linear accelerations and distances were correct, the numbers above show that the speed should increase 2 times in the inner orbit. 56.57 m/s is twice the velocity of 28.28 m/s (with rounding error).
But this doesn’t happen with the moon and billion other examples, even though the force of gravity increases 16 times orbit speed only increases 2 times.
WHAT is wrong?
Your calculations of the final speeds of accelerating objects after traveling given distances are wrong. The actual velocities reached in your 100m and 400m examples, when correctly calculated, show exactly a 2 times increase.
The math is cow simple and clear.
Apparently not simple and clear enough for you to have gotten it right.
I have got no explanation…only loser’s laughter
I'm not laughing, are you?
Respectfully,
Myriad