plotting orbits from photos?

On Sun, 25 Dec 2005 12:17:58 -0800, Eric wrote:

I see articles where they have taken 2 pics of an object,(eg a comet or
asteroid) and the movement from pic 1 to pic 2 is only a part of an inch as
measured on the photos. How do they calculate the orbit of an object with
so little information? I'm not looking for too much math, mostly just a
high level explanation maybe a drawing or two. Seems like you'd have to
have a lot more info before you could say where the object was and where it
was going.

You can't normally determine an orbit from just two observations; the
minimum is three. That's because an orbit is characterized by six
parameters. If they are all unknown (which is usually the case), you
need six independent known values to solve for them. Each observation
provides two (typically a right ascension and declination).

Once you have your data points, there are a variety of methods that can
be used to actually solve for the orbital parameters. The most common
are variations on a method developed by Gauss. These are typically
modified by iterative, least-squares optimizations, especially when more
than three data points are available. It doesn't matter if the orbit is
parabolic (as are many comets), hyperbolic, or elliptical- the Gaussian
methods are general for all of these. There are also a number of modern,
purely numerical approaches that lend themselves well to computers.

It should be noted that the observational data is normally reduced in a
way that compensates for topocentric position and velocity. It is also
assumed that the orbit is purely described in Keplerian terms as a
simple two-body system. One body is the unknown, the other is usually
either the Sun or the Earth, although it doesn't need to be.
Compensating for perturbations introduced by other bodies considerably
complicates things, and requires many more observations.

I don't know any way to really describe in any more detail how to
calculate an orbit without giving the math (which is moderately complex,
but not really difficult). You might try some Internet searches, looking
specifically at "orbit determination" and "method of Gauss" or "method
of Laplace".

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com