XIII. Attachments

In studying the orbit of the observed spiral the effects of the changing distance have to be mathematically removed. Only then would the laws of the orbits relate to the data.

II. Effect is noticeable for Project Jupiter

A. Apparent size vs. time

The apparent size of Jupiter will vary considerably over the time needed to collect the observations for Project Jupiter (typically about 30 days). The effect can reach 10% of the separation distances measured, so the effect of the changing distance needs allowed for in the computations.

1. The importance of the effect

To estimate the importance of the apparent size change with time, Mizar Consulting created a mathematical model of the Earth and Jupiter, each traveling in a circular orbit. The change in the apparent size was computed to be:

2. Miscellaneous notes

a. When the apparent size of Jupiter is a minimum, Jupiter is "lost in the glare" of the Sun and observing then is not recommended. The risk of a misaligned telescope causing permanent eye damage is too great.

b. When the apparent size of Jupiter is at its maximum, we say that Jupiter is at "Opposition" (opposite from the direction to the sun).

c. The effect of refining the circular orbit model to explicitly model the elliptical orbits of the planets shows an interesting effect. The ellipticity of the orbits manifests itself as a 12-year pattern in the apparent size of Jupiter:

B. Percent change in apparent size with time

The change in the apparent size, over the typical 30-day-observation period for Project Jupiter can approach 10%.

C. Impact of fitting the data

If we have not compensated the effect of the changing distance for, then the effect is that the amplitude of the moon’s orbit size grows over time (or decreases if the Earth - Jupiter separation is increasing). In Project Jupiter we assume that all of the variation in the data, when compared to the trial fit orbit, is due to fitting differences. The changing distance introduces another variable, that if not compensated for, introduces another variable that will cause an incorrect orbit period to be determined. To extract the best information from the observer’s data, least squares must include compensation for the changing distance in the determination of the orbit period.

III. Technique to remove effect

A. For each observation the geocentric distance to Jupiter is found using MEADE’s Epoch 2000 ® software, a commercially-available planetarium type software package.

B. The observed separation is corrected linearly to a base date, the first observation date and time. The linear model is a sufficient approximation of the true tangent function because of the very small angular sizes involved.

C. When the JD measuring system is selected, the apparent size change in Jupiter matches the apparent size change for the separation of the moons from Jupiter. Thus, the JD observation method inherently corrects for the changing apparent size and they need no additional modeling.