Transcript Newton`s Cannon

Newton’s “Cannon” or “Mountain”
• Ch. 4: A projectile’s path is parabolic as it goes up & down.
NEWTON’S IDEA (in the 1600’s!): Put a large cannon on a large
mountain. Shoot cannon balls (projectiles) at faster & faster
velocities. Eventually, the initial velocity is 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 path extends farther
& farther around the Earth. Finally, at some critical velocity
(Newton estimated ~40,000 km/h!) the path would go around the Earth
all the way & eventually past the starting point & keep on going.
It would keep on “falling” forever!
 The projectile would ORBIT the Earth! This is essentially
what happens when a satellite is put into orbit.
• Ch. 4: A projectile is in “free” fall in Earth's gravity. When an object orbits the
Earth, it also is in “free fall”! Maybe it will be easier now to understand why
objects in orbit are 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. Typical web pages:
http://www.waowen.screaming.net/revision/force&motion/ncananim.htm
http://www.smaphysics.ca/phys40s/field40s/newtmtn.html
http://www.astronautix.com/lvs/newannon.htm