The American Association of Amateur Astronomers


Weighing Jupiter
Eugene Lanning

 Project Jupiter

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I. Purpose
II. Background
III. Orbits
IV. Period  Determination
V. Methods
VI. Kepler's Laws
VII. Observing Suggestions
VIII. Data Gathering
IX. Data Processing
X. Observer's Data Results
XI. Other Quad-A Results
XII. Conclusions
XIII. Attachments

This Project Jupiter Report was prepared by
Mizar Consulting
Eugene A. Lanning
130 Hillside Terrace
Nebraska City, NE
Member of AAAA

The American Association of Amateur Astronomers
P.O. Box 7981
Dallas, TX

Welcome to Project Jupiter

Project 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 Project Jupiter.

D. Determine the mass of Jupiter and compare to reference data.

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.

Measuring Jupiter

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 "Law".

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.

Making Observations

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 periods was:

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!

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The image of Jupiter on the Project Jupiter cover page is courtesy of AAAA member Charlie Warren of Texas. Used by permission. Jupiter and three of its moons - right to left are the moons Europa, Io and Ganymede. Callisto is not on the image. CCD Image taken February 2, 2002.

The American Association of Amateur Astronomers
P.O. Box 7981
Dallas, TX 75209-0981