Re: [Phys-l] gravitational force

[Ludwik Kowalski <kowalskil@mail.montclair.edu>]

On Oct 31, 2006, at 12:53 PM, Krishna Chowdary wrote:

> On 10/31/06, Mike VanAntwerp <mvanantw@hpsk12.net> wrote:I'm looking 
> for
> ways to get students to
>
> > work with Kepler's Laws and F= G (m1m2/d^2) in a lab setting.  This is
> > for a high school class.
>
>
> I agree with JD that working with the G (m1 m2/d^2) is tough to do in 
> a high
> school lab setting.  However, I have some thoughts about Kepler's laws.
>
> (1)  If you're fine with simulations, there are tons of great applets 
> out
> there.  I've worked with some where you can adjust the semi-major axis 
> and
> measure the period, or show equal times in equal areas, etc.
>
> (2)  If you're fine with numerical stuff like on a spreadsheet, have 
> the
> students use an Euler step method and plot orbits around a 
> gravitational
> force center (essentially suggestion (1), but making their own 
> simulation).
> This is tricky because of rounding; it is hard to get closed orbits.  
> The
> advantage is that students can change the force law and see what 
> happens.
> (aside:  several people have mentioned Interactive Physics on some of 
> the
> listservs I'm on.  Is this the kind of thing you can do easily in IP?)
>
> (3)  We do an end run.  We do orbits using a spring force center:  
> attach a
> mass to a spring (we shove a ball in a slinky which works well enough) 
> and
> twirl the slinky around your head in a reasonably constant circle.  
> Measure
> the radius and the period.  Do it again, but this time twirl it faster 
> so
> that it is in a larger orbit; again measure radius and period.  You 
> can show
> that the period is reasonably independent of the radius, and then we 
> do a
> derivation to show why (essentially Newton's argument, except using a 
> spring
> force instead of gravity).  You can then show as an exercise that the
> inverse square force is the way to get the observed period to radius
> relation.

I did not use applets but the simulation program called Interactive 
Physics. Our "lab" was a simulation that I composed. It was the sun in 
the center and our planet. The x and y axes showed distances and the 
time box was showing time. Our planet was initially on the positive 
side of the x axis. Its initial velocity was always pointing up but any 
speed could be assigned.

The first task was to start with speed zero and to measure the time of 
fall
The second task was to observe trajectories for progressively larger 
speeds, till an approximately circular trajectory was found, by trial 
and error.
Students had to describe trajectories (drawing them, approximately) in 
the reports. They also had to compare the "experimentally found" v for 
which the orbit was circular. How does this compare with what was 
theoretically expected? Not bad at all, not surprisingly.

There are other things one can do. For example, freeze two moments and 
measure displacements in equal times at different locations (Kepler 2), 
or adding another planet and "discovering" Kepler 3. Explaining why 
real astronomical observations could not be made in two hours was not 
difficult.

Ludwik Kowalski
Let the perfect not be the enemy of the good.