Newton’s “Cannon” or Newton’s “Mountain”. Recall A projectile path is parabolic as it comes up & goes down. NEWTON’S IDEA (in the 1600’s!) Put a HUGE.

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Presentation transcript:

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

Recall 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 “falling” forever!  The projectile would ORBIT the Earth! This is essentially what happens when a satellite is put into orbit. Newton estimated the Critical Velocity ~ 40,000 km/h! Recall A projectile is in “free fall” in the Earth's gravity. When an object orbits the Earth, it also is in "free fall"! Maybe now you can understand why objects in orbit are in said to be in "free fall“?

Combining Newton’s 2 nd Law with his Universal Law of Gravitation, Newton did several calculations using his idea.

To keep an object in orbit, the Gravitational Force provides the “Centripetal Force”! F = (mv 2 )/r = G(mM E )/r 2 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: