Projectile and Satellite Orbits

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Newton, in his consideration of gravity, realized that any projectile launched from the surface of Earth is, in a sense, an Earth satellite (if only for a short time).  For example, in this animation a ball thrown from a tall building sails in a modest orbit that soon intersects Earth not far from its point of launch.

If the ball were fired with a greater initial velocity, it would travel farther.  Further increasing the speed would result in ever larger, rounder elliptical paths (they would be elliptical if Earth was not in the way) and more distant impact points.  Finally, at one particular launch speed the ball would glide out just above Earth's surface all the way around to the other side without ever striking the ground.  At a greater speed the orbit of the ball will be a circle.

At successively greater launch speeds the ball would move in an ever-increasing elliptical orbit until it moved so fast that it would sail off in an open parabolic or (with an even faster launch speed) into a still flatter, hyperbolic orbit, never to come back to its starting point.

This Illustration lets you change the launch speed (but maintain the launch direction) by mouse click.  Click "+" to increase launch speed and click "-" to decrease launch speed.  Press "Start" to fire the ball.  Press "Reset" to change parameters back to default values.  The red arrow represents the velocity vector.  Click the left mouse button near the tip of the arrow and drag the mouse to change the ball's initial velocity (both direction and speed).  Click the right mouse button to stop the animation; press it again to resume.  When will the ball start to go around without striking the ground?   When will the motion become a circular motion?  Try clicking the "full" checkbox and find out what happens.



Illustration authored by Fu-Kwun Hwang and Mario Belloni.
Applet authored by Fu-Kwun Hwang, National Taiwan Normal University.