 Project
Jupiter
 
V. Methods for Period
Determination
Three methods are outlined in this section, the third of which will
be used in Project Jupiter.
A. Occultation Method
One method to determine the orbital period of a satellite, if it is
regularly disappearing behind a object (being hidden, occulted) is to
measure the time interval between the occultations. While this is
possible to do, and will be used as a method in a future Quad-A project,
it will not be used in this Project Jupiter. The reason that it will not
be used here is that it requires that the observer be observing at the
exact time of the occultation, there is no latitude in the time of the
observation. Also, if clouds should obscure viewing in that particular
part of the sky when the occultation is to occur, then the observation
timing has to be restarted. Further problems consist of the magnitude
difference between the satellite and the planet disk. When the magnitude
difference is large, then the timing becomes subject to the judgment of
the observer as to when the satellite was occulted.
An additional nuance is that the satellite will disappear when either
it disappears behind the planet, or when it enters the shadow of the
planet. Unfortunately the position of the shadow of the planet changes
with time.
Alternatively, one could time the reappearances. Timing the
re-appearance is complicated because it is more difficult to time and
detect the reappearance of the satellite from behind the planet without
reference to external data sources and it is not an easy task to master.
The problem of accurate and repeatable timings is further compounded
when the planet is one of the gas giants, as the planet lacks a sharply
defined edge
( 7 ).
Because Quad-A members do not have the luxury of spending hours at
the eyepiece to catch the exact occultation time, because of the
magnitude differences in Jupiter and the satellites, and because Jupiter
is a gas giant planet, the timings of the occulations will not be used
in this project.
B. Maximum Extent Method
One definition of the period of a sinusoidal wave form is that the
period is the time between successive peaks (or valleys), as illustrated
below. The Maximum Extent Method is the application of this concept by
estimating the period when the satellite is at its maximum extent (at
its peak distance) from the planet.
By monitoring the motion of the satellite, and noting successive
points at which the satellite is at its maximum extent from the planet,
a person could infer an orbital period. This method has limited accuracy
when the orbit of the satellite is nearly in the plane of the
observation. As the satellite approaches its maximum extent the
transverse (left-to-right or left-to-right) motion slows because the
satellite motion at that time is mostly radial (away or towards the
observer). The slow transverse motion makes it difficult to determine
the time at which the true maximum occurs. The radial motion is not
detectable in the typical amateur astronomer’s equipment.
Because it would be difficult to determine when the maximum distance
from Jupiter occurs for the satellite that the observer selects, this
method has more uncertainty in determining the orbital period, and will
not be used in Project Jupiter.
C. Fitting of Data Method
A statistical/mathematical term "Fitting of Data" means seeking the
best formula that will reproduce the experimental (observed) data. If
the data and the formula answers are reasonably close ( one rarely gets
a perfect agreement ), then a person makes the assertion that the
formula correctly represents the data, and the formula may be used for
other related uses.
The Quad-A member observation data is forwarded for the fitting of
the data by an EXCEL spreadsheet created for Project Jupiter. Of primary
of interest will be the orbit period, a value that the spreadsheet is
designed to determine.
The process of finding the best formula, and hence the period, works
best if there are a sufficient data so that the chance variations in the
data are averaged out, i.e., when there is sufficient data to make
observational or measurement errors not a major factor. For Project
Jupiter the requested number of data points (observations) is from 8 to
20, for statistical reasons that will not be elaborated on here.
The process of fitting data to equations works best if there is at
least one pattern in the data is provided for analysis. For Project
Jupiter, that means that preferentially that data from at least one
complete orbit of the moon selected for observing is supplied for
analysis. Selecting the interior moons of Jupiter may not be the most
advantageous, even though they complete their orbit sooner. The orbit
time is smaller, but the data is harder to measure ( the percentage
error in the observation data will be larger). Observations over
additional orbits will, however, offset the larger percentage of
observational error.
The fitting of data method was selected for its ease in application
with a wide variety of observer equipment. Also, the method was selected
because the method can be refined in other Quad-A projects in
experiments to determine other orbit parameters.
7 For the gaseous planets, the
diameter of the planet is defined where the atmospheric pressure is equal
to 1 atmosphere.
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Project
Jupiter