proof of Newton's law of equal and opposite reaction: punch a table as hard as you can, does it hurt? Thats cause the table exerts a resistant force against your punch, thus equal and opposite reaction. From this we can prove the existence of a normal force and gravity since the force of gravity is what that little number is measuring when we stand on a scale and in order for us to stay on the ground and not shoot through the floor we would need to have a force opposing it, this is the normal force and as long as you are not in free fall you will have a force of gravity equal to that of the normal force. Qualifications: I live in my parent's basement mostly watching porn and contemplating my eventual demise.

The earth is actually a helix shape

Follow the instructions at the beginning of the proof

Judging from your comment i take it you didnt follow the instructions given. Newtons laws actually do hold universally, however we apply different conditions to them given the circumstances (under water, in the air, spinning around on a merry go roun)

And actually i can, i ran an experiment a while ago for a class, i can send you the data

They do, actually just finished doing this in class

Lemme see if i can write up the proof for it

So imagine the your noninertial reference frame is like a camera view moving over your inertial reference frame.

They still hold as while viewpoint is changing

We just proved the existence of these so called "fictitious" forces, if there was something you dont understand i encourage questioning

So here we can see that the force of the earth acting on the artillery shell is so minimal that it would not dramatically affect trajectory

This is due to the mass of the earth being massively larger than that of the shell

Lemme see if i can think of a better way to explain it

I have my mechanics book in front of me right now, tho i appreciate the reference