Newton's Cannon
This simulation is based on Isaac Newton's famous thought experiment, described in A Treatise of the System of the World.
Imagine that there exists another planet, weirdly similar to Earth, with an enormous mountain whose top is 100 times higher than Chomolungma (Mt. Everest) and twice as high as the orbit of the International Space Station!
At the top of this mountain is a cannon that fires horizontally. Choose the initial speed of the ball and see what happens.
Launch Speed: 2500 m/s
Welcome to Newton's Cannon, Noragulfa version. Operation of the app is rather straightforward, so your students should not have any trouble.
My purpose in writing this simulation was to give my students another way to understand that objects in Earth orbit are not in "zero gravity." For that reason there are two options that should, in theory anyway, aid in that understanding. The "Flat Earth" option allows them to link back to their experience with projectile motion and see that objects in orbit are falling, just like those projectiles. (The app starts up with Flat Earth turned on.) The "Show ISS" option adds an orbiting International Space Station. This allows them to see that the ISS is even closer to the Earth than the launch point of the ball, and maybe also that if gravity is pulling on the ball, it must also be pulling even harder on the station and the astronauts inside it.
The simulation treats the planet as a point mass situated at the center of the image. So if the ball is allowed to pass through the planet, the elliptical orbit that it follows is in a sense un-physical. The force on the ball should be adjusted to exclude the mass that is outside the ball's distance from the center. But it gets complicated, and this is meant to be simple...
If your students set the launch velocity to a high value, the ball will travel off the screen. But if they are patient, it will come back. The maximum launch velocity is purposely set to be below the escape velocity.
It would be nice to be able to drop the ball straight down, but infinite forces, adjustable step size, Runge-Kutta, blah, blah, blah. So there is a minimum launch velocity...
Newton's Cannon v1.00
© Geoff Nunes 2021-2023
I want to give a big shout out to Daniel Schroeder at Weber State University, in Ogden, Utah. I got started on programming in Javascript by following Dan's tutorial on simulating Newton's Cannon. In a sense, this entire web site is his fault.
Questions, brickbats, and requests for enhacements can be sent to doc at this website (noragulfa.com). Do not expect a rapid response.
Change Log
v2.12
Change: Impact flames now fade out after 2 seconds.
v2.11
Change: App now starts up in Flat Earth mode.
v2.10
New Feature: Option to show the ISS in its orbit.
v2.00
New Feature: Flat Eath option ends the orbit at the base of the mountain. Useful to link to student thinking back to projectile motion.
Enhancement: Silly flames when projectile lands. Because why not?
v1.10
Default behavior is now continuous orbiting. The Launch button becomes a Stop button when the ball is in motion.
v1.00
No changes yet...