Mr Lim told us today that the Earth actually moves when there's an impact on it. However, the movement is so insignificant that we don't notice it at all.
Therefore I decided that being a hardworking student I will try and calculate how much it takes to actually move the Earth by 1 cm.

Mass of Earth = 6.0 x 10^24 kg
Weight of Earth = 5.886 X 10^25 J

To move the Earth by 1 cm,
Energy needed
= Force X Distance
= 5.886 X 10^25 J X 0.01m
= 5.886 X 10^23 J

Therefore, since K.E. = 0.5mv²
5.886 X 10^23 J = 0.5mv²
mv² = 1.1772 X 10^24 J
v² = 0.1962
v = 0.443 m/s

=O the Earth only needs a velocity of 0.443m/s to move by 1 cm!


To calculate how much velocity an object needs to move the Earth by 1 cm:

According to the law of conservation of momentum,
For a collision occurring between object 1 and object 2 in a system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.

Therefore, m1v1 = m2v2
Assuming that m1 be a standard object weighing 65kg,
(65)(v1) = (6.0 x 10^24 kg )(0.443)
v1 = 4.09 X 10^22 m/s

Since it is difficult to achieve that speed from a low altitude, we will assume that the object impacting the Earth is a person falling from free fall.
i.e. a person weighing around an average of 65kg

As free fall is at a rate of 9.81 m/s²,
this person will have to be falling for approximately 4.17 X 10^21 s before such a speed is achieved.

To be falling for so long, this person will have to start at an altitude of 1.71 X 10^44 m.
Also, on another side note, the person in question will be falling for approximately
1.32 X 10^14 years.

That is to say that this person in question will be falling for quite some time before data analysis can be recorded.


Assumptions made:
1. There are no dissipating forces (friction).
If there were any, the person will be falling for 1.32 X 10^14 years before getting burnt out by air resistance into nothing more than ashes. Thus the experiment would be a failure.

2. The Earth's gravitational forces are able to reach a height of 1.71 X 10^44 m.
If the Earth's gravitational forces are unable to reach that height, the person will not be able to start falling, and the poor people down on Earth will be waiting for a miserable 1.32 X 10^14 years only to find out that the guy's still stuck 1.71 X 10^44 m high up in space.

3. Humans do not rot in space.
If the person rotted before he hit the Earth, all the scientists would have been waiting for 1.32 X 10^14 years only to see a skeleton fall smack into the surface of the Earth. Please note that skeletons are generally much lighter than 65kg. The experiment would then be deemed a failure as the change in the weight would generally affect the overall results. This assumption was made inclusive of the above assumptions.


Then, the Earth will move by 1 cm.


"Physics. Ah. The complexity of life."