Time for object to fall length of 10m rope, assuming g=10m/s

[gabeeisenstei]

I'm still struggling with spacetime curvature. I want to know about the spacetime intervals in the following scenario:
An apple is cut loose from a tree, but is still attached by an unstretchable rope that is measured to be 10 meters by the tree observer.

(I'm ignoring all but relativistic effects. I'm also assuming that initial gravitational acceleration from the given location is exactly 10 m/s. I'm not interested in detailed calculations, just the relevant (in)equalities.)

Event1: apple cut loose from tree at t=0
Event2: clock at original apple position ticks 1 second
Event3: rope yanks on tree after apple falls rope length
Event4: rope yanks on apple


Spacetime intervals,
according to tree frame:
E1-2: distance=0, (proper) time=1s
E1-3: distance=0, time=1?
E1-4: distance=10m, time=1?
E3-4: distance=10m, time=0? or E4 sooner by S.R.?
E2-3: distance=0, time=?

according to apple frame:
E1-2: distance>10m, time<1s (so velocity of clock>10m/s ?)
(S.R. effect also slows tree clock)
E1-3: distance>10m, time=?
E1-4: distance=0, proper time=?
E3-4: distance>10m, time=0? or E3 sooner by S.R.?
E2-3: distance>10m?, time=?

 

[Passionflower]

The GR effect on the scales you propose is extremely small, do you want a calculation using Newton's or Einstein's theory?

By the way you state the acceleration in units of measure of m/s which is not correct.

You can actually use the formulas from:
https://www.physicsforums.com/showthread.php?t=552878
if you want to calculate things using GR.

 

[gabeeisenstei]

Yes I know the effect is small. If you prefer we can say that the apple is outside the horizon of a black hole and change 10 meters to something much bigger, but as I said I am not looking for the full calculations, just the inequalities.
(And yes I meant acceleration of m/s^2, attaining 10 m/s in one second.)