X. Observer’s Data Results

A. Assumptions

1. A circular orbit adequately represents the true orbit for the selected moon of Jupiter.

2. The Meade Epoch2000™ planetarium type software program correctly provides the distance to Jupiter from the Earth (Geocentric distance) and the relative positions of the planets. Alternatively, for most observer data applications, the orbit mean-diameter for each of Jupiter’s moons is obtained from NASA data.

B. Orbit Period Determined

The data supplied data by Tim Tyler, replicated in Attachment A, was processed and is graphically shown in Attachment B. Tim’s data was gathered between September 2, 2002 and October 6, 2002 and consists of 8 observation sets. Because of poor weather conditions that developed and lingered in the observing area, on December 3, 2002, it was decided to produce this Project Jupiter Report. The use of 8 data sets, rather than the recommended 12 data sets, did not adversely impact Tim’s Project Jupiter results, as shown below.

Data obtained from the NASA website (http://nssdc.gsfc.nasa.gov/planetary/factsheet/joviansatfact.html ) provided the reference data for accuracy determinations.

The results, by moon, are:

The moon resonance parameters were also determined

C. The Weighing of Jupiter

CCD image courtesy of AAAA member Charlie Warren

The weighing of Jupiter is accomplished by using a variant of Kepler’s Third Law that incorporates Isaac Newton’s Law of Gravity. When the orbital period of a satellite is combined with an orbit diameter, then the mass of the planet being orbited may be calculated. The same EXCEL spreadsheet that estimated the orbital period performs these computations.

1. Standard Project Jupiter Analysis of the mass

Tim’s data was used to estimate the orbital period of each of Jupiter’s moons. Using NASA data for the orbital radii, the computed orbital periods yielded mass estimates for Jupiter as shown below:

The observed-weight-averaged-determined mass of Jupiter is 1.8924E27 Kg, or 316.787 times the mass of the Earth. NASA often uses the mass of Jupiter, and their value ( at http://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html ) indicates a reference mass of 1,898.6x10 24 Kg ( 317.83 times the mass of the Earth). Thus Tim’s weight-averaged data is within 0.3% of the reference data.

2. Extra Data Analysis

This section of the Report is a special addition to the standard report, produced because Tim was able to make accurate estimates of the positions of the moons. In the process of fitting of the data it was noted that Tim’s data produced the orbital radius of the moons that was very close to NASA data:

The exceptional accuracy reflects very good estimating of the distances not only on a relative scale (necessary for good Project Jupiter results) but also on an absolute scale. Because of this accuracy in estimating the moon separations, it becomes possible to perform the calculations of the mass of Jupiter without a dependence on the distance to Jupiter ( See Section X.A.2).

The use of the calibration data and the computed orbital periods yielded mass estimates for Jupiter as shown below:

The observed-weight-averaged-determined mass of Jupiter is 1.8531E27 Kg, or 310.2 times the mass of the Earth.  As noted before, the NASA reference values are 1,898.6x10 24 Kg = 317.83 times the mass of the Earth. Thus the Tim’s data weight-averaged data is within 2.4% of the reference data. Such accuracy, obtained solely through visual observing exceeds the Project Jupiter expectations!

D. Gravitational Force and Escape Velocity

The relative pull on objects on the "surface" of Jupiter 19 is computed using the classic formula

F = GmM / r2

Using NASA data for the diameter of the planet and Tim’s weight-average computed mass for Jupiter in the formula results in a weight 20 ratio of 2.47. This means that if an object on the Earth’s surface weighs 1 lb, it will weigh 2.47 Lbs on the surface of Jupiter.

The computed weight ratio is within 4.0% of NASA’s value (See http://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html ) a ratio of 2.364 . NASA was contacted regarding the large bias. The large variation is because of NASA’s treatment of Jupiter as a rotating body. Thus, the larger bias is not attributable to observer logging errors or to poor observing skills.

The Escape Velocity is that velocity such that an object may break free of the gravitational force. The escape velocity is found using the formula

escape velocity =  square root of (2GM / r)

Using NASA data for the diameter of the planet and Tim’s computed mass for Jupiter in the above formula yields an escape velocity of 59.40 Km/Sec. The computed escape velocity is within 0.2% of the value used b y N A S A , namely 59.5 km /sec (see http://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html ).