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When you throw an object into the air, fire a cannon ball etc. we assume the trajectory to be that of a parabola, but it is in fact an elliptical path (IGNORING WIND RESISTANCE)

Think about it (ignore wind resistance), we assume that the lateral velocity is unchanging and the vertical velocity is a function of the square of the lateral velocity (ie. Y=X^2, Y being vertical velocity and X being lateral velocity. But this assumption is based on the earth being flat which it is not.

Therefore as the object moves laterally the force of gravity changes direction as the object is always attracted to the centre of the body ie. Earth, and not always in the same direction as would be required for it to be a parabola, (when you plot a parabola using Cartesian co-ordinates the axis never change direction) and distorting its path into elliptical (I’m talking about a negligible amount, to the point of splitting hairs but let’s be mathematically exact and not just approximate!)

Lets put it another way, imagine the earth being a super concentrated mass only tiny in size (a few feet in diameter say) but having equal mass, you are standing on an imaginary surface 4000 miles from its centre. The forces of gravity acting on you and the object you are about to throw are identical to that of the the earth we are all familiar with. You now throw the object into the air at an angle. It rises for a while and then falls back down but is allowed to continue through the imaginary surface towards the centre of the tiny earth, it picks up speed, flies around the tiny earth passing very close, then increases altitude and slows and comes back to the point where it was thrown from, where you catch it or watch it go up past you to go around again. This orbital path is elliptical.

I think we adopted the parabolic trajectory idea many years ago due to the simpler mathematics in calculating trajectories such as cannon balls etc. and we now assume that these trajectories are parabolic. But let us be exact, not just so close to exact that we don’t notice.

Thanks for reading and would value responses.

Keith Jump

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# Parabolic trajectories ?

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