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A wizard cast a spell on a ball to make it stay still in the middle of the air next to a tree, he said to the guy with him "This ball will not move from it's place not by any force in the universe", the other guy went home and the next day when he returned to that tree the ball was not there, how could that be?

(no the wizard was not wrong or lying)

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The tree moved.

One must specify what constitutes a fixed point [coordinate system] to determine whether something has moved.

One reasonable point to consider fixed is the center of mass of the universe [cmu].

Construct a ray from cmu which passes through the ball at a distance of say L units, along with two other mutually normal rays.

By OP, the coordinates of the ball [L,0,0] do not change.

Given the motions relative to cmu of the galaxy, sun and earth, the tree's coordinates will have changed.

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The ball stayed exactly where it was in space, the Earth moved away on it's journey round the sun?

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The ball didn't move as the wizard had said. The earth moved (presumably because of rotating on axis and revolving around sun) and so the ball was no longer next to the tree, but right where the wizard had commanded it to be.

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I haven't looked at other replies yet, but I think......

What we see as the position of an object is only relative to other things, usually ti the earth. However, the earth itself is always moving.

So,it all depends as to relative to which object the ball is unmoving. As the universe is expanding, the only fixed point would appear to be the origin, wherever that may be!

:rolleyes::rolleyes:

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but id go for the fact that the earth is rotating so the ball will follow a tangent path.

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One could say that the ball did not move, but the earth did, relative to the ball. But as part of the enchantment is that the ball was to remain still in the middle of the air next to a tree, and we are given that tree was in the same location the next day, either another tree spontaneously (magically) appeared to replace the tree the ball once stood by OR the ball had been moved by a force outside the universe. As magic was involved, only a force outside the universe would know the answer for sure.

Edited by Dej Mar

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The ball would be miles away in less than one second. It's a long way around the sun. The Earth has to move really fast to clear that distance in one year. It spins really fast as well.

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Because nothing any force in the world can move it, even the gravitation, so obviously the ball is still there, but the guy is moving, so do the tree, and the earth itself. The Ball is still floating at its place, no matter what happen. Maybe the guy can see it next year

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Force is term that is coined by science and according to it there are only four kinds of fundamental forces in the universe-->> gravitational,nuclear,electromagnetic and weak and other derived ones like friction,thrust etc. Now,no matter how long this list is , Magic wouldn't appear anywhere. i.e. It wouldn't be considered as force and the results that it would produce wouldn't come under those that are produced by any force . So , my answer would be that wizard again charmed the ball and it moved form its initial position. This wouldn't be taken as to be done something by result of force.

The earth moving and the ball being left behind couldn't be the answer because there was some time lapse between these incidents -->(Wizard casting the ball to stay in the midair) and ( Wizard telling the guy that "No force in this universe could move it). Since some time would have elapsed and for that time being the ball had to remain stationary there. But if the rotation of earth around its axis,its revolution around sun,the movement of our solar system around milky way and the movement of milky way in the universe were to be taken in consideration for being responsible for the disappearance of the ball, then it could have also moved in this little lapse of time.

Or, otherwise the above all movements would have to cancel each other for that time being in which the wizard said that thing to the guy, so that ball appears stationary for that time being.

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