Posts Tagged ‘projectile motion’

You probably learned about projectile motion in introductory physics class. If you throw something (a baseball, say) then its horizontal motion will remain constant, whereas its vertical motion will change under the influence of Earth’s gravitational pull. The result is a parabolic arc, right?

Well, no. Saying that projectile motion is parabolic is only an approximation.

In class, I “prove” that the motion of the baseball is a parabola, but in order to do so, I make the (reasonable) assumption that the effect of gravity is a constant. That is, I assume that the vector g (the acceleration due to gravity) always points in the same direction all along the trajectory.

This is actually not quite true, however. I’ve neglected the curvature of the Earth.

Now, this isn’t really a big deal when throwing baseballs. Suppose you toss a ball to your friend 50 m away. The vector g for you does point in a slightly different direction then g for your friend, but the angular difference is miniscule…it’s about 50/637,000,000 radians, or 0.00045 degrees. This is so small that I am comfortable pretending that the two g’s are actually parallel, and the derivation thereby leads to a parabolic arc.

But what if you don’t make that approximation? What answer do you get?

You get an ellipse. You get an orbit. And here’s the point of my post:

Every time you throw an object, the object is (temporarily) in orbit until it hits the ground.

Here’s the orbit of a thrown baseball (not to scale):


Now suppose the Earth had the same mass, but was the size of the Little Prince’s home asteroid B-612, which is as big as a house. The orbit is the same, but this time the baseball doesn’t strike the surface:


The takeaway is that all projectile motion is really orbital motion. I find this fascinating: you don’t need a fancy rocket to launch something into orbit. Your arm will suffice. It’s just that you need the Earth to not be in the way.


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