Newton’s “Cannon” or Newton’s “Mountain”

Newton’s “Cannon” or Newton’s “Mountain”
Recall Ch. 3
A projectile path is parabolic as it comes up & goes down.
Newton’s idea (in the 1600’s!)
Put a HUGE cannon on a HUGE mountain.
Shoot cannon balls (projectiles) at faster & faster initial velocities.
As the initial velocity increases, the projectiles will go farther &
farther from the starting point. Eventually, the initial velocity
will be fast enough that the Earth's curvature must be taken
into account in looking at the path. If the initial velocity
continues to increase, the projectile path will extend farther &
farther around the Earth. Finally, at some critical velocity the
path would go around the Earth all the way & eventually past
the starting point & keep on going.
It would keep on “falling” forever!
It would keep on “falling” forever!
 The projectile would ORBIT the Earth! This is
essentially what happens when a satellite is put into orbit.
Newton’s estimated critical velocity ~ 40,000 km/h!
Recall Ch. 3
A projectile is in “free fall” in the Earth's gravity.
When an object orbits the Earth, it also is in "free fall"!
Maybe it’s now easier to understand why objects in orbit are in
said to be in "free fall“?
• To keep an object in orbit, the
Gravitational Force provides the “Centripetal Force”!
F = (mv2)/r = G(mME)/r2
• Figure: Newton’s “Cannon”
showing parabolic projectile
paths becoming orbits as the
initial velocity increases.
Many web pages (11,000 hits on Google)
are devoted to this. Some have animated
illustrations, where the user can specify the
initial velocity & see the path (orbit) it will follow.
Some typical web pages: