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What kind of software, operating system, database, processor, architecture, antenna used for communication back to Earth, basically what computer does it use.

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You've asked 6 questions there, of which at least two seem unrelated to the title so I'm going to ignore them.

This document describes the "Integrated Science Instrument Module". The OS is listed as VxWorks, and the processor architecture is just described as "PowerPC". A separate presentation, "Lessons from 30 Years of Flight Software" mentions it explicitly as a RAD750.

This is not the only computer though. There's also the "Command And Telemetry Processor" or CTP, which handles spacecraft-specific operations like "pointing in the right direction". It also is the bit that deals with communication between Earth and the instrument package. Unfortunately, I seem to be quite unable to find anything out about the CTP, other than there was a faulty one that was replaced by Northrop Grumman before the telescope was launched. The odds that it also runs VxWorks on a radiation-hardened PowerPC chip are good (because nearly everyone does that sort of thing, as it happens) but I can't get any confirmation of that so it remains a guess.

The software running on it is (unsurprisingly) a bit old and weird. According to JWST: Maximizing Efficiency and Minimizing Ground Systems:

The JWST science operations will be driven by ASCII (instead of binary command blocks) on-board scripts, written in a customized version of JavaScript. The script interpreter is run by the flight software, which is written in C++. The flight software operates the spacecraft and the science instruments.

The thought of proprietary early-noughties javascript will no doubt delight any software engineers in the audience. Event-driven James Webb Space Telescope Operations says that it is called "NOMBAS ScriptEase". There's more information in "Event-driven James Webb Space Telescope operations using on-board JavaScripts", for which I don't have a more reputable free source. This runs on top of VxWorks, though I can't tell if it runs on the CTP or the ISIM computer.

Being developed in the early noughties, there was lots of enthusiasm for XML as a storage and interchange medium. James Webb Space Telescope XML Database and CCSDS XTCE goes into more detail (and includes delightful quotes like "XML is the ASCII of the future"). CCSDS stands for "Consultative Committee for Space Data Systems", and XTCE "XML Telemetric and Command Exchange".

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    $\begingroup$ This sounds almost like a software stack for a stereotypical "enterprise" software project, which, coincidentally, also tend to be late and over budget. $\endgroup$ Jul 16, 2022 at 10:31
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    $\begingroup$ Not a downvote, this is a just sayin' comment. Just because it's in ASCII does not mean that it is human readable or writable. Assembly language is written in ASCII, as is good old eXcremental Markup Language. $\endgroup$ Jul 16, 2022 at 12:32
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    $\begingroup$ When I first started working in this industry it was a bit shocking how out of date flight computers, etc., were. It's no longer shocking to me that a "state of the art" flight computer is a scaled down 20+ year old architecture. The widely-used RAD750 is kinda-sorta like a PowerPC, but compared to a 1998 PowerPC (which was desktop state of the practice 24 years ago, not even state of the art), a RAD750 runs at half the clock speed, has very limited main memory, and has even more limited cache memory. $\endgroup$ Jul 16, 2022 at 12:49
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    $\begingroup$ @DavidHammen - sure, but it is space qualified. Rad hard (even “just” space rad hard) is hard, and a very niche market to boot. $\endgroup$
    – Jon Custer
    Jul 16, 2022 at 14:06
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    $\begingroup$ According to Nombas, the decision wasn't so much to use the JavaScript language as to leverage an onboard scripting engine, and Nonbas ScriptEase happened to be 1) extremely well tested (allegedly), and 2) implemented in C (not C++!), the latter which likely resulted in a smaller runtime and easier integration with VxWorks. According to Event-driven James Webb Space Telescope Operations the goal of using onboard scripting was to reduce the overall complexity and cost of ground operations. $\endgroup$
    – dhinson919
    Aug 6, 2023 at 4:12

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