Simulation created with Francisco Esquembre's Java simulation software
Spacestation Vertical throw
All motion is subject to the principle that is codified as Newton's First Law: an object that is free moving will travel in a straight line, with uniform velocity.
In science fiction movies rotation is sometimes used to create gravity inside a space station. Objects that are stationary with respect to the rotating space station will then experience a gravitational effect, as described by Newton's second law. The First Law physics comes into play when an object is thrown. If you throw an object, and you want it to land right at your feet again, in what direction do you need to aim?
When an object is thrown from some point inside a rotating spacestation, there are two contributions to its overall velocity:
If you want to hit something at the hub of the rotating space station, or just move through the hub area, then the throw must cancel all the pre-existing velocity.
The left panel shows the motion as seen from an inertial point of view. The grey straight lines can be thought of as the axes of a coordinate system that is co-rotating with the space station, or as spokes of the space station's internal structure.
The animation's controls
The input fields
When you alter an input value you will see that one or more of the other values change also. These updates are necessary to keep the simulation in an overall consistent state.
You can change any input value while the animation is playing - no need to pause it - but generally you will see some angle in the trace. After the next relaunch or bounce the trajectory will be regular again.
The extra settings
Among the checkboxes there is also a checkbox 'Extra', which opens a small window with additional checkboxes.
Method of computation
First the motion with respect to the inertial coordinate system is calculated. Subsequently the x and y values are transformed to positions relative to the co-rotating coordinate system.
The calculation of the rebounds is technically incorrect. It ought to be treated as a reflection, with the reflection angle computed to be equal to the incidence angle. Now, because of the symmetry of a circle, when bouncing around inside it the incidence angle will always be equal to the reflection angle of the previous rebound. So rather than computing the new reflection angle the angle of the original launch is reused (incidental advantage: there won't be accumulation of error.)
This simulation has been created with EJS
Also available for download: a standalone version of this applet (requiring the Java Runtime Environment but not a browser to run)
Last time this page was modified: July 17 2010