The Trojan Math Challenge Progress

I received some info to solve my Trojan Math Challenge. But the deeper I go into the rabbit hole, the more frustrating it gets. I haven’t even got to try the formulas I found. So far I’m still struggling with the fact that different sources work with different data.

One of the values I need to have in order to introduce the time into the equation is the last date at which a certain object (asteroid or planet) was at its perihelion. The perihelion is in this case the moment where the object is nearest to the sun. The JPL Small-Body Database Browser gives a time of the perihelion passage in JED (days since 12:00 January 1, 4713 BC). I can use that and the orbital period (day to make one orbit) to calculate the last perihelion with ease.

So I have all the data I need for the Trojans. BUT I also need Jupiter. Actually, I want to check my program with the Planets first before I move on to the Trojans. Unfortunately, I can’t find the next perihelion passage time for Jupiter or any other planet. Neither the Jupiter Fact Sheet nor the JPL data sheet list that. You would think that there is MORE data on the planets than on some dinky asteroids.

Wolfram Alpha says Jupiter’s last perihelion was May 20, 1999 but that seems to be somewhat imprecise. I would feel better having a JED value.

Weird enough, the Jupiter Fact Sheet gives a Mean Longitude for Jupiter (34.40438). I have no idea what time this is referring to. I guess it’s not the current Longitude as the page looks static. So it could be the Longitude at J2000, the currently-used standard epoch, defined by international agreement. But if it is, why does the JPL fact sheet give a slightly different Longitude value (34.39644051) aren’t they referring to the same thing?

That’s the same kind of bullshit I run against every time I get into this kind of projects. The last time I wanted to map the orbits of the irregular moons of Saturn and Jupiter and it was simply impossible to determine what plane the inclination values were referring to in the different sources. Sometimes it was the ecliptic, sometimes the mother planet’s equator, sometimes some weird mathematical constructs. You could never really tell. You could also never tell how to derive one from another.

I’m frustrated, I’m going to kill a Great Jagi now.

Krystian Majewski

Krystian Majewski was born in Warsaw and studied design at Köln International School of Design. Before, he was working on a mid-size console project for NEON Studios in Frankfurt. He helped establish a Master course in Game Design and Research at the Cologne Game Lab. Today he teaches Game Design at various institutions and develops independent games.

6 responses to “The Trojan Math Challenge Progress”

  1. sirleto

    thanks for your update.

    i will try to get that java aplett running,
    as soon as i can mess with the code, i try to add the JPL list of trojans into it … only problem i can see now (there will be more soon, i’m pretty sure ;) is how to find all trojans in JPL… is there some kind of list? i don’t find apropriate links to it …

  2. sirleto

    ah okay, found it myself:

    niiiice ;-)

  3. Krystian Majewski

    I checked that Java applet. The problem there is that they are doing a ton of unit conversions to prepare the calculations. And they are spread all over the place. Since none of the code is commented it’s quite difficult to understand what they do exactly. But I can probably salvage some code from it. For example, I recognized a neat bit of code to calculate the True Anomaly from the Mean Anomally. That’s one problem I don’t have to deal with anymore.

    I will just ignore the problem of data for now and do an orbit visualization tool.

  4. sirleto

    i just used the applet now, adding loading of trojans and rendering “all of em”

    i would love to upload it only as a toy – but as usually i am stuck with java file rights / permissions … i can’t put it on webspace and have the trojans file loaded … so i can send it to you via mail if you want …

    here is a first screenshot:

  5. Krystian Majewski

    You show-off. But yeah, having it locally would could help. I need to have some kind of reference to check if the stuff I come up with makes any sense.

  6. sirleto

    ah – always this totaly unintuitive complicated java crap …

    i can “run” it from eclipse (dev environment) but i’m to stupid to start the aplett without it … so i can send you what i have but to get it running probably requires another java expert or a full eclipse installation…

    *argh* do you have any experience with java / java apletts?


The Game Design Scrapbook is a second blog of group of three game designers from Germany. On our first blog, Game Design Reviews we describe some games we played and point out various interesting details. Unfortunately, we found out that we also need some place to collect quick and dirty ideas that pop into our minds. Hence, welcome to Game Design Scrapbook. You will encounter wild, random rantings. Many of then incoherent. Some of them maybe even in German. If you don't like it, you might enjoy Game Design Reviews more.


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