Astronomy 1L (Lab Class) Information
Calculating the Positions of the Galilean Satellites of Jupiter
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(copy of old handout with data from early edition of "Stars and Planets"; to be updated later)
Satellite Semi-Major Axis Synodic Period Starting Angle
Io
Europa
Ganymede
Callisto
5.9 Jupiter radii
9.4 Jupiter radii
15.0 Jupiter radii
26.4 Jupiter radii
1.7698605 days
3.5540942 days
7.1663872 days
16.753552? days
49 degrees
277 degrees
300 degrees
78 degrees
(Starting Date is Midnight UT, Dec 31, 1983 = JD 2445700.0)

     Calculate the "current" date and time at Greenwich (for the time the satellite positions are wanted). Look up the corresponding Julian Date (see Appendix 11 in Stars and Planets) and add the decimal fraction of a day as necessary. Subtract the date for which the data above are correct (JD 2445700.0). This gives D, the number of days and fractional days since the starting date.
     For each satellite, divide D by the synodic period to get the number of times that the satellite has gone around Jupiter since the starting date, then multiply the FRACTIONAL part of the result by 360 degrees and add the starting angle. This gives the current angular position relative to Jupiter. (You only use the fractional part of the result because any whole number of revolutions simply returns it to the starting angle.)
     For each satellite, plot the position on a polar coordinate graph and project the position to the line of the night sky, OR take the sine of the current angle and multiply by the semi-major axis of its orbit to find its position relative to Jupiter (the +/- result corresponds to E/W positions relative to Jupiter's position; whether + is E and - is W or vice-versa might be useful to know, but doesn't necessarily tell you what things look like in a telescope; the relative position in a telescope depends upon whether the telescope reverses or mirror-images the actual sky).