Title, I tried converting the coordinates from here to rectangular but it seems off.
2 Answers
At the bottom of your linked web page is the sentence:
If you need really accurate data for a planet or asteroid, try the JPL HORIZONS System. (These guys were navigating spacecraft through the solar system when I was still playing with GI Joe!)
...which is indeed an excellent answer to your question!
A step-by-step example of how to obtain "rectangular coordinates of the solar system planets" using Horizons can be found in this answer.
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I could not find a good live imagery of planetary positions. Also try this question in Astronomy SE.
http://www.astrosoftware.com/cpnew/software/sirius/features/skymap.html works well.
The examples in the question and the comments are valid ways to track the planets. I do see plausibility in converting the coordinates into a visual grid.
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jpl-horizonstag: https://space.stackexchange.com/questions/tagged/jpl-horizons and see if those give you some insight. See how far you can get by trying things yourself, and reading those questions and answers. The (or at least a) goal in stackexchange is to build a set of searchable questions and answers. Look around, and take the tour while you're at it. – uhoh May 01 '17 at 14:39