## We All Learned Physics’ Biggest Myth: That Projectiles Make A Parabola

“For most practical applications, it doesn’t hurt anyone to treat projectiles as having a parabolic trajectory. But if you care about micron-or-better precision, or are dealing with a large structure (like a suspension bridge) that spans 100 meters or more, you cannot treat the Earth’s gravitational field as a constant. Everything is accelerated not “downwards,” but towards the center of the Earth, enabling a projectile’s true trajectory — an ellipse — to be revealed.

Studying the various effects that are at play, both external to the Earth as well as within our planet’s interior, can also teach us when and under what circumstances it’s important to make these considerations. For most applications, air resistance is a far larger concern than any effects like the various layers of Earth’s interior or dynamical friction, and treating Earth’s gravitational field as a constant is totally justified. But for some problem, these differences matter. We are free to make whatever approximations we choose, but when our accuracy suffers beyond a critical threshold, we’ll have no one but ourselves to blame.”

Throw a ball in the air, and its horizontal motion will remain constant while its vertical motion accelerates downwards at the acceleration of Earth’s gravity. Right? That’s what we all learned, isn’t it?

Well, that’s only an approximation: a very good one over short distances if you neglect air resistance, but a lousy one over long distances. In reality, the trajectory isn’t a parabola, but a tiny segment of an ellipse. You might think that if a projectile were made of dark matter, it would go through the Earth and make a perfect ellipse, but that turns out to be a myth, too!