Re: [find_orb] Determining a Tennis ball orbit through several frames

Bill J Gray Dec 14, 2011

Hi Diego,

Do you mean in Find_Orb, or more generally?

It's obviously a little bit outside the scope of "normal"
Find_Orb use, and I am virtually certain that there are
programs better suited to the purpose. In theory, it's not
very hard to do. Anyone who has played tennis has done it
in practice.

I've never tried it in Find_Orb. I can imagine someone
taking a video of a glow-in-the-dark tennis ball at night with
a camera sensitive enough to register some stars. You could then
get astrometry for the tennis ball and feed it to the program.
In theory, it would converge on the correct answer very quickly;
there would be a lot of curvature, and the trajectory should be
(mathematically) well-determined.

Alternatively, you could take pictures of the tennis ball and
do some sort of calibration relative to background objects to get
altitude/azimuth data, then convert that to RA/decs.

Find_Orb would give you an impact time, plus an orbit that
pretends that the earth is a point mass. Therefore, the orbit
would have apogee Q=6378 km or so (radius of the earth, plus
however high you threw the ball) and perigee equal to a few
dozen kilometers (assuming you threw the ball at normal
tennis-serve speeds, and assuming the ball kept falling toward
an Earth-sized black hole). The time of perigee would be about
fifteen minutes after you served the tennis ball, i.e., the
time it would take an object 6378 km from an Earth-sized black
hole to fall (almost) all the way in.

In practice, the closest objects I've tried have been meteors.
Find_Orb didn't have much trouble with them (though the times
had to be specified to high precision; fortunately, Find_Orb
provides a way around the limited precision of the MPC format).

It would, of course, help tremendously if you had data from
at least two cameras, for parallax.

Also I should mention that, at least at present, Find_Orb
doesn't account for atmospheric drag.

-- Bill