David is correct; Kepler's first law is not limited to a
statement that trajectories are elliptical, it also
requires that the Sun be at one *focus* of the orbital ellipse.
This means that some rephrasing is needed. Her is an attempt;
I am assuming the original message has already been read.
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Let them videotape the bob of a conical pendulum, looking
from below. Then ask them if the oval trajectory is an ellipse.
I am assuming they know how to determine locations of focal
points when "a" and "b" have been determined. So you can
ask them to indicate where the Sun could be, if a planet was
orbiting along the same trajectory.
Then ask them to argue (either speaking or writing) that the
recorded trajectory of the bob is very different from the
trajectory of a planet orbiting the Sun along the same ellipse.
That is how the activity can be turned into learning Kepler's
2nd and 3rd laws. One more "practical consideration" is to
use an old storm window to create a grid of coordinate lines.
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What is also worth discussing, I thing, is that in one case
the restoring force is directly proportional to 1/r^2 (pointing
toward the Sun) while in another it is directly proportional
to r' (pointing toward the origin). Both cases result in
elliptical motion. Yes, r and r' are two different distances,
for any particular location on the orbit.
Ludwik Kowalski