When a football is kicked, does it follow a parabolic path...?

Question

...or is the path actually elliptical? In other words, if the Earth didn't get in the way, the path of the football would be a very skinny elliptical orbit about 8000 miles long, correct? (Yeh, I realize this very small segment of the ellipse would closely resemble a parabola, anyway, but that's beside the point.)

Answer 1

I think you’re right. Gravity is indeed a central force, and bodies under a central force follow elliptical trajectories. Mathematically, in order for the path to be parabolic, the force (gravity) must be invariant in space; that is, the same in magnitude and direction. Thus, if a series of lines –representing force- are drawn on the body as it travels in space, all these lines should be strictly parallel. To the extent as we can consider the earth as flat, we may as well regard gravity as pointing downwards, perpendicularly to the –flat- surface of earth

But the earth is neither flat, nor gravity is invariant in direction. Gravity is still perpendicular to surface, but pointing to the center of the planet. The direction of the force, in this instance, changes as the body moves. Of course, this is getting overly finicky over a football. But, as you say, this is not the point.

For describing the path of a football, plainly, the “flat Earth” approach is good enough. Allegedly, not so for shelling Paris with a gun such as the “Paris railway gun”, at 70 mi from the city.

However, I cannot see how you could get Earth out of the way. If gravity were not present, the trajectory wouldn’t be elliptical, either –nor parabolic, for that matter. Nor do I how do you put a body in orbit -8 000 miles long, or whatever- without a central force.

Answer 2

It does follow a "complex" path, that is the result of various forces.
The first is the gravity, hence a perfect parabolic curve.
The second is the air resistance, that may "steeper" the curve slightly.
The third is the SPIN given to the ball. As the ball rotates on itself, the drag forces are different between two sides, giving the ball a "lift" (curve) in the direction of the lower drag (or higher "lift").
So, no, the curve is not parabolic, but complex, unless the ball does NOT spin and there is no ... well, air!
Since the spin can be at any angle in relation to the fly path, to define the curve (or flight path) of the ball, you have to take all this in consideration!
And add, as well, the influence of the small ridges on the football that creates some turbulences around the ball and modify the drag as it fly over to the right, then curves and enters the goal.
Even the shoes have been designed to give that extra spin when kicked!
They are not foot-ballers, they are now scientists that can calculate the fly path of their ball before kicking it!

Answer 3

If you remove the influence of the earth the football travels in a straight line. It's the space it moves throughthat is curved.

Answer 4

it is not true always

It depends how u kick it pls watch a Football math and see that the ball can move in an ellipticle, parabolic and circular or straight line all depends on the ecentricity

Answer 5

wen u kick a ball on earth then i agree with wat jr said.but if u r gonna remove the earth then the ball would keep flying in uniform linear motion without any orbit

Answer 6

It always depends on your frame/system of reference and where the observer is (e.g. on earth or "outside"), ignoring initial conditions.