On 3/15/23 11:27 AM, Maxime GOMMEAUX wrote:
I would like to have my Bachelor students estimate the orbital period
of Mars using only data from XEphem-simulated ground-based observations. I mean, from Sky view, from the Data table... and of course not from the Solar system view.
I have not being using xephem for several years, but yours is mainly an astronomy question. So, I hope I'm able to give you some advice.
The data you should look for are geocentric ecliptic longitudes of Sun and Mars. The opposition is when those longitudes differ by 180¡ã.
A Mars synodic year is the time interval between two consecutive oppositions - it is about two terrestrial years.
Since Mars' orbit has a notable eccentricity, you must expect those intervals are not constant, but fluctuate from one opposition to another. So in order to get a reliable mean synodic year an average must be taken over a series of oppositions.
In other words, you take the interval between one opposition and - say - the tenth following it. Dividing 10 into that interval you get a mean synodic year over 10 periods.
Once a mean synodic year is obtained, it's a simple matter to get Mars' sidereal year. The formula is:
1/Tsid(M) = 1/Tsid(E) - 1/Tsyn(M)
where
Tsid(M) = Mars' sidereal period
Tsid(E) = Earth's sidereal period
Tsyn(M) = Mars' synodic period.
I hope this helps. Greetings
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Elio Fabri
