demo shown as Flash (5M byte)
Newton had observed that any projectile launched horizontally is, in a sense, an Earth satellite.
A rock thrown from a tall building sails in a modest orbit that soon intersects the earth not far from its point of launch.
If the ball were fired more swiftly to start with, it would travel further. Futher increasing the speed would result in ever larger, rounder elliptical paths and more distant impact point. Finally, at one particular launch speed, the ball would glide out just above the planet's surface all the way around to the other side without ever striking the ground.
At successively greater launch speeds, the ball would resolve in ever-increasing elliptical orbit until it moved so fast initally that it sailed off in an open parabolic or (if even faster) into a still flatter, hyperbolic orbit, never to come back to its starting point.
This java applet let you change the launch speed by mouse click.
click + to increase launch speed.
click - to decrease launch speed.
Then 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 its velocity.
Click 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? Enjoy it !
Try to click the full checkbox, and find out what will happen.