Jupiter uses both observations of any of Jupiter's moons and
mathematical data derived from the observations to determine their
orbital period. From that derived orbital period data, computations
of the mass of Jupiter, the pull of its gravity, and the escape
velocity of Jupiter can be determined. The methods used in Project
Jupiter are general to any planet with a moon, and are such that
AAAA members could use their existing equipment for this project and
attain reasonable results.
The first AAAA application of Project Jupiter took place in Fall
2002. At that time Jupiter was well situated in the southern sky
early in the morning, and was high enough that even observers that
leave for work early in the morning could make a brief observation.
Nevertheless, Project Jupiter may be performed at any time when
Jupiter is suitable for viewing over a period of three weeks or
more. Project Jupiter is not date sensitive, and the Fall of 2002
was simply the first application of the Project.
Normally, an observation series like Project Jupiter is done in a
college-level astronomy course. One exciting strength of AAAA is
that its members share expertise freely. This write-up is one such
example of shared expertise that is intended to allow all AAAA
members to participate in this project, as the member need not
personally fuss with the attendant mathematics.
The Goals of Project Jupiter
Project Jupiter has five goals, each of which is worthy of the
effort involved in completing this project, and each within the
reach of members of the American Association of Amateur Astronomers,
as well as any interested amateur astronomer.
A. Develop observer's observing & logging skills
In completing this project the observer will need to schedule a
series of observing sessions, and keep a reasonable (but not
burdensome) record of the observations at location(s) of their
choice. The scheduling will promote regular observing sessions. All
of the methods used in this project will require that the observer
keep records of what is observed, and develop good estimates of the
spacings between objects.
B. Determine orbit period & compare to reference data
The orbit period of a satellite of Jupiter will be determined
from the observer's recorded data. Their data will be processed
remotely, using a method that will yield the best estimate of the
orbital period. The orbital period will then be compared with
available reference data from NASA and the percent difference to the
observer's results will be provided. The comparison is intended to
promote critical thinking of how the observations could be changed
to improve results.
C. Promote AAAA and Observing
AAAA is a unique association of amateur astronomers. Members have
differing skills, differing interests, each observes from a
different location, and each utilizes different equipment. That
diversity provides a rich AAAA resource. AAAA members are linked
together via e-mail and a quarterly newsletter. The dispersion of
the observing sites and skills is a rich asset, as AAAA members
freely help other members. Project Jupiter is, in part, to promote
AAAA and the success of the local observer. This is accomplished by
creating a press release of the individual member's participation in
D. Determine the mass of Jupiter and compare to reference
In Project Jupiter, Kepler's third law is utilized to determine
the mass of the planet which the satellite is orbiting, in this
case, Jupiter. The observer's data will be used to "weigh" Jupiter.
A minimum of non-measured data is used in attaining this goal,
illustrating the depth of information that can be derived from a set
of observational data.
E. To expand personal horizons of Quad-A members.
By participating in Project Jupiter, many members can perform a
project that may stretch their capabilities. This is expected to
lead to participation in other challenging AAAA projects.
Project Jupiter relies on the mathematical fact that the orbital
period of a satellite, moon or planet is a fundamental parameter
that is used to describe the relation of one object to another. The
orbit period is a quantifiable parameter that may be precisely
transmitted to others.
Because the orbital period may be determined with a high degree
of accuracy—how much accuracy is dependent on the skill of the
observer, the amount of time devoted to the task, and the quality
and type of equipment available—future positions of the object
observed may be made with good confidence.
When the period of an orbiting body is known, then Kepler's Third
Law of Planetary Motion and Newton's Law of Gravitation may be
combined to enable one to calculate the mass of the body being
orbited. Part of Project Jupiter is to perform those calculations.
These laws can be found in any good Physics textbook.
While Project Jupiter is designed around the planet Jupiter, the
technique is general to orbiting bodies. Its application to any
planet that has a satellite (including Earth) will yield
corresponding information about the planet being orbited.
Kepler's Laws of Planetary Motion
Project Jupiter will be using an enhanced version of Kepler's
Third Law, an enhancement that considers Newton's Law of
Gravitation. Based on his observations, Kepler developed three
revolutionary thoughts, thoughts that have withstood the test of
time and scientific scrutiny to rise to the classification of a
Kepler's 3rd Law , when combined with the Law of Gravitation,
enables us to "weigh" Jupiter in Project Jupiter. See the
sidebar on the next page for a
detailed description of the mathematics involved.
The best estimates of the orbital period of a body are attained
when a large quantity of observational data is available. In Project
Jupiter, the observer is encouraged not only to observe when the
moon of Jupiter is at its maximum separation, but also to obtain
data for the smaller separations. For the more widely separated
moons, those with longer orbital periods, each observer needs to
make their observations over at least one orbit, preferably more.
For the outer moons, the observational dates may also be more widely
spaced, providing flexibility for the observer.
Observers should generally try to make around 12 observations,
more if possible, but cover at least one complete orbit. The
observing sessions do not have to be on consecutive days and need
not be equally spaced in time. Make sure data is for the same moon.
As the moon of choice for project Jupiter nears Jupiter, its
identity may be confused with the other moons. Transits in front of
the planet reveal the different surface brightness of the satellites
themselves: Callisto and Ganymede are very dark, Io a faint grey,
and Europa is usually invisible against the bright clouds.
Therefore, visual recordings of a satellite in transit, while
possible, are not likely.
Data Gathering Methods
The participating AAAA observer may select any of four methods
while making observations, since data from any or all of them may be
directly input into the EXCEL program for analysis
The Jupiter Diameter (JD) Method uses the apparent size of
Jupiter as the unit of measure. While the apparent size of Jupiter
does change appreciably over the course of a month of observations,
the satellite separations also vary in proportion, so the JD method
is suitable for a rough unit of measure.
The Sketch Method requires the observer to make a sketch
on paper of the positions of the Moons as seen in the eyepiece.
Later the separation on the sketch is measured and is then used as
one data point in the Jupiter Project data analysis.
The CCD/Astrophotography Method is basically the same as
the Sketch Method, but with the inaccuracies of hand sketching
removed. During each observing session the observer takes an
astrophoto or CCD image(s) that record the position of the moons of
Jupiter. Later the separation on the photo/image is measured and is
then used as one data point in the Jupiter Project data analysis.
The Astrometric Eyepiece Method is used when the observer
has access to an eyepiece with a measuring reticle. The basic
techniques used here is the calibration of the reticle eyepiece to
enhance the capability to measure separations that are normally only
estimated. If an observer does not already own such an eyepiece,
rather than purchasing one, see if another member of your local
astronomy club would be willing to lend you one for this project.
Conclusions of Project Jupiter—Fall 2002
Ten AAAA members participated in a regular early-morning
observing program in the Fall of 2002. While all observations were
tabulated, the best observational data was obtained by Tim Tyler of
Angola, Indiana. The final project estimate of the Jovian orbital
1.7706 days for Io,
3.5569 days for Europa,
7.1977 days for Ganymede
16.6936 days for Callisto
The observational data was also used to calculate the mass of
Jupiter as 1.8924E27 Kg, a value within 0.3% of available reference
data, the weight of objects on Jupiter, and the escape velocity on
Jupiter. Similar accuracies were obtained for each of the values.
Due to the high accuracy of Tim Tyler's data in determining the
positions of the moons of Jupiter, the mass of Jupiter was also
obtained without a reliance on one common assumption. When that
assumption was removed, the mass of Jupiter was determined to within
2.4%, a notable achievement!