[Deprecated] Scale Top-Down Model of the Kebol System

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UPDATE: New thread created for 3D model that does everything this model does and more.

Original post below:

I've been exploring optimization solutions lately for my interplanetary communications network, and was having a hard time wrapping my head around some of the math and picturing the system in my head. So I did some research and learned some equations and relationships and found a nice free graphing software to bring it all together. I worked out the polar coordinate equation for each planet's elliptical orbit and plotted it. What came of the exercise was a scale model of the Kerbol System, viewed from the top down, with all planets' orbits represented accurately in terms of:

• major and minor axes
• foci (Kerbol in the correct position)
• eccentricity
• longitude of ascending node (how a planet's orbit is tilted relative to a reference direction)
• argument of periapsis (where the Pe is located; given relative to the longitude of the ascending node)

(As far as I can tell, imgur album embedding is broken at the moment--please correct me if I'm wrong--so forgive the screen-captures.)

^Model overview

^Inner planets

^Tidied up a little (disabled grid-lines, too)

^Just Kerbin, Jool, and Eeloo nicely visualized

The only thing this tool doesn't properly portray is orbital inclination, as that would be in a third dimension. I may look into that soon. We'll see.

To use:

1. Download and install GeoGebra on damn-near any platform, or use the web app
3. Open, explore, modify... enjoy!

At the moment, it's a fairly bare-bones item, with only the most essential information included, but it may just end up growing into something more substantial, whether for my own use, or at the request of the community.

I don't know if any licensing is necessary here, but  if it is, let's say.... MIT (referring only to the .gbb I've shared. GeoGebra has its own licensing policy).

A few notes for clarity:

• Scale is in megameters (1Mm = 1,000km = 1,000,000m
• Visibility of elements can be turned on/off in the left pane. This can help with crowding when zoomed out past the inner planets.
• Π is used to denote the location of the ascending node (normally I would use ☊ but GeoGebra does not support it)
• Ω denotes the longitude of the ascending node (an angle)
• ω denotes the argument of periapsis (an angle)
• γ is used to denote the reference direction, along the x-axis (normally I would use ♈ but GeoGebra does not support it)
Edited by Syntax
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Nice model. I'm a Geogebra user too and often start dealing with geometrical problems (including some KSP orbital stuff) first modelling there, it allows me to get the correct relationships before I turn to strict math. Though, my models always are built from geometric elements, I put equations directly in Geogebra only when can't find an easier geometric solution (therefore, e.g., my way to draw an elliptical orbit in 3D goes to define the orbital plane, the cone (given center, axis and aperture angle), and intersect the two).

Looking forward to see your model in 3D space!

P.S.: yes, better show a license, the model is your creation and worth having recognition (MIT is fine for that purpose). Even if the forum rules only make a license mandatory for add-ons.

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hrm... this is cool. I've seen GeoGebra in use before for stuff like dark side transits. I have a flight tracker that displays planet positions on a weekly basis for the entire system and a daily basis for the inner system. Right now I have a macro program that generates them for me so it's not a huge deal in terms of upkeep but lately I've been considering replacing it with a dynamic application that lets people see the current location of things for that day but then also look back and even forward in time. It would also be easier to manage when I start having more than just planets orbiting out there. So @Syntax and @diomedea would GeoGebra be a good solution for this?

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11 hours ago, Drew Kerman said:

hrm... this is cool. I've seen GeoGebra in use before for stuff like dark side transits. I have a flight tracker that displays planet positions on a weekly basis for the entire system and a daily basis for the inner system. Right now I have a macro program that generates them for me so it's not a huge deal in terms of upkeep but lately I've been considering replacing it with a dynamic application that lets people see the current location of things for that day but then also look back and even forward in time. It would also be easier to manage when I start having more than just planets orbiting out there. So @Syntax and @diomedea would GeoGebra be a good solution for this?

Hey DK. You actually showed me something about GeoGebra on the web that I was completely unaware of. I had previously been limiting myself to the Windows desktop application, and was largely ignoring its web capabilities. Those worksheets are a game changer for me.

I've been exploring your KSA project, as I hadn't heard of it before, and I have to applaud you for your passion and dedication! That's quite the undertaking you've... erm... undertaken...  As for using GeoGebra for your purposes, it seems to me (from my limited understanding of what's going on in that macro) that it would/could be a good fit. Variable sliders for mean/true anomaly, elapsed time, focused planet, etc, might be the sorts of tools you'd want to leverage most. As my model evolves over the next few weeks/months, you can feel free to use/modify it for your own purposes (with acknowledgement, please), but you certainly seem capable of building your own should you wish. Long story short, I think exploring GeoGebra as a possible solution would be worth your while.

Does that help?

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Thanks @Syntax, that does help. I will continue to keep an eye on what you're doing but in the meantime I'm going to see how well I can understand the Matlab graphing code from KSPTOT. I was able to use the source to reverse-engineer a JavaScript version that does all the orbital plotting for my flight tracker. Since GeoGebra seems similar in terms of how it can plot things, I'm curious if I can do the same thing here. You may consider taking a look as well. I'd be interested to hear what @Arrowstar thinks of this, he may have a better idea of whether his Matlab code is worth referencing for this application. I'm really annoyed Matlab itself doesn't have any sort of web viewer like this for their figures that you can save. That would have made my life so much easier!

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1 minute ago, Drew Kerman said:

Thanks Syntax, that does help. I will continue to keep an eye on what you're doing but in the meantime I'm going to see how well I can understand the Matlab graphing code from KSPTOT. I was able to use the source to reverse-engineer a JavaScript version that does all the orbital plotting for my flight tracker. Since GeoGebra seems similar in terms of how it can plot things, I'm curious if I can do the same thing here. You may consider taking a look as well. I'd be interested to hear what Arrowstar thinks of this, he may have a better idea of whether his Matlab code is worth referencing for this application. I'm really annoyed Matlab itself doesn't have any sort of web viewer like this for their figures that you can save. That would have made my life so much easier!

I think MatLab is probably a lot more powerful than Geogebra, but also a lot less accessible, both in terms of learning curve and plain old availability. Geogebra makes sharing a lot easier and doesn't really have code... just the language of math and some rudimentary input syntax. That's what I appreciates about GeoGebra.

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• 3 weeks later...

Hey folks. Just wanted to offer an update on my progress since I've been completely silent for a few weeks. I've been plugging away at a 3D model of the system and learning how to represent the planets' and moons' changing positions over time. What I have right now is a product that is very nearly done (80%) and more than anything else just in need of a bit more tidying and polishing. I've been a bit busy lately and haven't had the time to work on this that I'd have liked, and I'm not yet sure how the next couple weeks are going to play out for my schedule. But rest assured, the 3D model is coming. And @Drew Kerman, I think you'll be quite pleased with the results

Not yet sure if I'll post the finished product as an update to this topic or a new one altogether; the 3D model is a much more substantial, and frankly significantly different piece of work from the initial file I posted. In either case, I'll place an update in the OP.

Edited by Syntax
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• 2 weeks later...

3D model completed and released! New thread created! Wheeeeee!

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