plotting orbits from photos?

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.
Eric

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 often wondered the same thing myself. Apparently initial orbital
calculations for comets assume they're parabolic at least removing
one degree of freedom from the calculations. Presumably initial
calculations for asteroids are that they are in circular orbits.

I understand that initial calculations aren't very accurate, but then
the next thing you here is that they've found the object in photos
from 100yrs back. Presumably you need total precision to get back
like that.

Hubble has just recovered a satellite of Uranus (Perfida ?) originally
seen in Voyager II photos. How they can tell whether it's taken n
orbits or (n+1) orbits in the intervening time I don't know.

Joe

--
Joseph Mack NA3T EME(B,D), FM05lw North Carolina
jmack (at) wm7d (dot) net - azimuthal equidistant map
generator at http://www.wm7d.net/azproj.shtml
Homepage http://www.austintek.com/ It's GNU/Linux!

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

On Sun, 25 Dec 2005 20:27:19 GMT, mack wrote:

I often wondered the same thing myself. Apparently initial orbital
calculations for comets assume they're parabolic at least removing
one degree of freedom from the calculations. Presumably initial
calculations for asteroids are that they are in circular orbits.

See my reply to Eric. There is a method, developed by Olbers, that
assumes a parabolic orbit. However, more general methods are usually
used, and these produce orbital elements without any initial assumption
about the type of orbit. That is, they simply produce the elements,
which determine whether the orbit is parabolic, hyperbolic, or
elliptical.


I understand that initial calculations aren't very accurate, but then
the next thing you here is that they've found the object in photos
from 100yrs back. Presumably you need total precision to get back
like that.

The initial calculations can be very accurate- it depends on how large a
section of the orbit the measurements are collected. One problem with
interpolating back in time is that the effect of perturbations can
become significant. Identifying an object in an old photo is usually one
part calculation and one part luck. Objects are seldom exactly where
they are calculated to be. Normal orbital elements assume a two-body
system. That is usually a good approximation in the short term, but not
over long periods.


Hubble has just recovered a satellite of Uranus (Perfida ?) originally
seen in Voyager II photos. How they can tell whether it's taken n
orbits or (n+1) orbits in the intervening time I don't know.

I'm not familiar with this specific case, but normally, the initial
error in calculating the orbit is small enough that it would take a very
long time before the positional uncertainty would become so large that
you didn't even know which orbit you were in.

_________________________________________________

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