## Measurement of Latitude

As part of the long-term study of Jupiter, the observation of latitude is also important to our understanding of the behavior of the planet. We know from measurements over time what the normal latitude boundaries of Jupiter's belts and zones are, we know the normal latitude of Jupiter's currents and jet streams, and we know that these latitudinal positions can vary. While the measurement of latitude is not considered by many observers to be as easily performed as measurements of longitude, it is an area of study that amateurs are certainly capable of participating in.

During the 1800s and until about 1950, measurements of latitude could only be made visually with telescopes equipped with filar micrometers. These were precision measuring devices that were very expensive and not often available to amateur astronomers. The procedure for using a filar micrometer is fully discussed in Peek [517]. In order for filar micrometer latitude measurements

to be useful, great care and precision must be exercised in making the measurement. Furthermore, the telescope used must be equatorially mounted on a very stable mounting that is driven to compensate for the Earth's rotation. Otherwise, the image in the eyepiece will bounce around hopelessly, making an accurate measurement impossible and unreliable.

Fortunately, the procedure for making latitude measurements can also be applied to high-resolution photographs, and this has been the case since about 1948 [518]. Photographs of high resolution are required, since any blurring of the image makes it difficult to make measurements with precision.

The advent of CCD and webcam imaging has finally made it possible for astronomers, including amateurs, to make measurements of latitude from images with true accuracy. Once again, CCD cameras and webcams are making it possible for amateurs to perform scientific work that is of professional quality. Today I am not aware of very many amateurs who use filar micrometers.

Once the raw measurements have been taken, usually from images today, they must be reduced. On Earth, we refer to latitude as geographical or geocentric. On Jupiter, the corresponding latitudes are named 'zenographical' and 'zenocentric' after the Ionic genitive of the Greek 'Zeus' [519]. Some astronomers use the terms 'planetographical' and 'planetocentric'. Peek [520], Rogers [521], and Schmude [523] discuss the methods for doing this. In order to calculate the latitude from measurements, the following steps must be performed (Fig. 9.14). Measure the distance from the feature from the south pole, s, and the polar radius, r. Calculate (r-s)/r. Call this sin d, and solve for d. The next thing we have to determine is Jupiter's apparent tilt, which we designate 8'. Most almanacs give the Earth's zenocentric latitude 8 (or DE), but we need Jupiter's tilt, and so we must solve for 8'. 8' is derived by: tan 8' = 1.07tan 8. (1.07 is the ratio of Jupiter's polar and equatorial diameters, and is recently actually determined to be 1.0694.) Now we can calculate the "mean latitude" ¡5', which is: ¡5' = d + 8'. To summarize:

Because Jupiter is oblate and not a perfect sphere, there are two other definitions of latitude, and ¡5' will need to be converted into one of them (Fig. 9.14). Zenocentric latitude (¡) is the angle subtended at the planet's center between the feature and

the equator. Zenographic latitude (b") is the angle between the polar axis and the local horizon.

We can convert between the two having determined their tangents:

tan b" = 1.07 tan b' or tan b' = 1-07 tan b"-

If Jupiter were a perfect sphere, b' and b" would be identical, but on Jupiter they are not and can differ by as much as 4°.

For the purpose of making latitude measurements of Jupiter's features, we normally want to determine latitude like we would perceive it on Jupiter's "surface". Thus, we normally want to determine zenographic latitude, b".

Richard Schmude [524] expresses these calculations in a slightly different mathematical form. First compute 0, as:

where s and n are the distances between the feature and the south and north pole at the polar limb. These distances are measured with a ruler in millimeters. If 0 is negative, then the feature is south of the equator, and if 0 is positive, the feature is north of the equator. Since 0 represents latitude on Jupiter as though Jupiter were spherical, we must solve for the other calculations of latitude using the following equations:

inv tan[1.0694 x tan [inv.sin (0) + 1.0694D]] zenographic inv tan[1.9351 x tan [inv.sin (0) + 1.0694D]] zenographic inv sin 0 + 1.0694D mean, where D is the sub-Earth latitude on Jupiter. This quantity D can be found in the Astronomical Almanac [525].

In order to perform accurate measurements of latitude, the images used must be of high resolution. Images in which the boundaries of belts and zones are ill defined, or in which bright and dark spots appear indistinct, will result in measurements of which the margin of error is too great, as an accuracy of measurement within one degree is desired. The amateur astronomer who can make latitude measurements with the desired accuracy can certainly consider himself to be a more advanced amateur.

## Telescopes Mastery

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