calculators

Above is a "fast airtrack" data generator (separate web version here), for use in classes interested in a modeling-workshop challenge [1] to take data, and then find a way to model what is going on. Note that the time values above have some measurement error, so that students will seldom if ever capture the same data values.

We've earlier mentioned wolfram alpha widgets for adding proper velocities and for constant proper acceleration trips in (1+1)D, although we replace them here with hopefully more reliable javascript calculators.

In fact, our relative proper-velocity calculator may be found just below (and separately on the web up here). Although in traveler-point dynamics we generally try to stick with a single map-frame (metric) and definition of simultaneity, this is not possible when discussing relative velocities with respect to different frames. As a result, we try to be very specific about whose metric, and whose clock, is being used to measure each quantity:

Below, is a one-way constant proper-acceleration trip calculator (accelerate then decelerate), to replace the Wolfram-alpha widget mentioned above. A separate web version may be found here.

In the near future, we hope to provide links to a Mathematica Demonstration simulator for (2+1)D accelerated travel between stars in our arm of the Milky Way, and a (3+1)D simulator for accelerated travel between stars with gravity in a procedurally-generated collection of stars.

In that context, look also for a page of related links that may be of interest (including on-line calculators and simulators hosted elsewhere) in the days ahead. Suggestions for links to add there are invited as well.

More technically, below is a calculator for unidirectional-roundtrips and sideways-detours which in effect begin from "turnaround". This may eventually be set up to allow for variable lightspeed and unitsets as well.

Second is a calculator for general piecewise constant proper-acceleration trajectories in (2+1)D.

Starting above with the default initial velocity of {0,1}[ly/y] in y at the coordinate origin, try coming to a halt (with 0.1 ly/y and 0.1 ly tolerance) at {1,0}[ly] in x. Your goal might be to do this in the fewest steps, in the shortest map time, in the shortest ship time, or with the least fuel (as an integral of proper-acceleration times elapsed ship-time). One might also add the requirement that the proper acceleration should be fixed at 1[ly/y^2] or 0.970043[gee].

Footnotes:

1. P. Fraundorf et al. (2001) "An experience model for anyspeed motion", arXiv:physics/0109030.