If the apple is stationary on the Earth, than it is being accelerated by the Earth. The Earth is pushing along objects on the Earth, so they are accelerating at G as well.
For the sake of simple math, I am having G = 10m/s2
Lets say there are two apples on a tree handing about 10 meters above the ground. Just before the first apple falls, the Earth is moving at 100 m/s. This means that the tree is also moving at 100m/s, and therefore the apples are too. Now the first apple falls. It is no longer in contact with anything (besides a small cushion of air) so it is no longer accelerating at G. The Earth is accelerating at 10 meters a second2, so it meets the apple, and it hits the ground in about one second. Now at that instant, the Earth is at 110m/s, the apple on the ground is moving at 110m/s, and the tree and the second apple hanging on it are moving at 110m/s. The second apple drops. It is no longer in contact with anything (besides a small cushion of air) so it is no longer accelerating at G. The Earth is accelerating at about 10 meters a second2, so it meets the apple, and it hits the ground in about one second. At that instant, the whole system is moving at 120m/s and is accelerating at G.
What are you confused about? The Earth is continuously accelerating, but that acceleration is constant.
I hate to bump this thread, but...
Wrong. If the Earth is moving up at 100 m/s when the first apple detaches from the tree, then the Earth will cover the 10 meters in .1 second (technically less, since it's accelerating). You're confusing acceleration with velocity.
d = 1/2at
2 + v
it
d = 1/2 (10) (t
2) + 100(t)
d = 5t
2 + 100t
10 = 5t
2 + 100t
2 = t
2 + 20t
t
2 + 20t - 2 = 0
t = (-20 + sqrt(400+8))/2
t ~ (-20 + 20.1990099)/2
t ~ .1990099/2
t ~ 0.09950495 s
This value is not even close to one second. Also, if the Earth is always accelerating at 9.81 m/s^2, then
a) wouldn't it eventually become impossible to jump? I mean, suppose that the Earth has been accelerating at this rate for even just a year. That's 31,536,000 seconds. The velocity would be 309368160 m/s. To jump, we would need to be able to accelerate at MORE than that speed. Impossible.
b) what would happen when it reached the speed of light?