Janus was a real problem for me working on my hobby of the Solar System.
I was trying to create a formula that would use the data for ? say Saturn?s satellites in this instance ? that would confirm or disprove the published data. That is a little much to expect but I was eventually able to reconcile all of the major moons of Saturn. Janus was completely wrong based upon the data I was relying upon.
The formula weighs the basic characteristics of the moon and the ?miles mass? for Saturn (the orbited body) and the end result should confirm the moons days of orbit as observed and published by astronomers. The first problem with some objects is that they are not spheres. Janus was described as 97 x 95 x 77 Km. I had previously worked out the probable Mass of Saturn expressed in miles (the point where the planet would orbit a moon at 1 mile per second orbital velocity.) For Saturn that was taken as a Miles Mass value of 9,120,391.75 miles orbit radius for the object representing the result for all of the satellites averaged. .
Janus published data in two text books was completely off and gave me an unacceptable result for the proposed Miles Mass of Saturn that was out of line with the other Moons. The published days of orbit for Janus turned out to be OK but the orbit details did not comply. The eventual resolution was fine using the recent data published by JPL. Also a source that is useful is,
http://enclyclopedia.thefreedictionary.com. The Janus data is semi major axis miles radius 94,137.55, sidereal period days .695, orbital velocity 9.85 mps and Saturn Mass Miles, 9,118,897. This effort requires a unique finding of my creation which I call the objects significant number. The method is straightforward enough requiring us to determine the difference in the potential orbital velocity for the edge of the moon closest to the planet (the fastest) and the velocity for the edge farthest. I then deduct the slowest velocity from the fastest edge of the moon. This is dependent on the respective radius each way for the moon. We will get a value for the center point of the moon.
Janus was said to be non-spherical. I eventually used a hypothetical 59 miles radius.
Sn= 9,118,897
94,137.55 ? 59 = 94,078.5. Sn/ 94,078.5 = 96.928 unsquared = 9.8452295731
94,137.55 + 59 = 94,196.5. Sn/ 94,196.5 = 96.807 unsquared = 9.8390610821
The result # = .0061684910
Radius 59 x 6.2832 = 370.708 / # = 60,097.16 / 86,400 = .695 days. This method disclosed that some of the published data was in error when I ran most satellites in the formula.
This implies that the circumference of the satellite plays a positive part in the rotation of the object and that the significant number for the center of the object turns orbital velocity into a useful means to make other determinations about the mechanics.
jjw
