I concur with Hohmannfan's response. This answer addresses the wider issue of computers in satellites.
Who needs a computer?
I don't think there is anything about the mission that you have described in the question that actually requires any "digital computer" at all. It might seem as if image handling and navigation are highly demanding in computing terms, but that is largely because we are accustomed to the idea of a world enabled by high-level software.
I think it is a good starting point in terms of systems engineering education to actually step through the processes involved and ask oneself "what is the most basic implementation possible?", particularly in terms of "what decisions absolutely must be taken on board, rather than by ground command?". Designers of missions in the 60's through 80's often came down on the side of "no computer needed". Its only since the weight, performance and cost of such things has come down that we take it for granted.
All of the logical decisions that need to be made on a satellite could in principal be made by discrete logic gates. Its an engineering judgement as to when the "digital finite state machine" so created has become so complicated that it would be better replaced by a CPU/address bus/data bus architecture.
As an aside, its not obvious that there is any clear dividing line between discrete electronics and a "computer" in the modern sense. This article regarding Pioneer 10 hints at the in-between possibilities.
Much of the computation for the mission was performed on Earth and transmitted to the probe, where it was able to retain in memory up to five commands of the 222 possible entries by ground controllers. The spacecraft included two command decoders and a command distribution unit, a very limited form of processor, to direct operations on the spacecraft.
Furthermore, decisions relating to progressive quantities - sensor outputs and control loops are in the first instance analysed in control engineering terms. How they are implemented is again a design choice and the old world was full of analogue computer elements.
There is the launch environment and then natural radiation once in orbit. The latter includes ESD damage (see here) as well as radiation dose and displacement damage. One interesting anecdote is that the progressively higher performance computers using physically smaller gates and switching times are more vulnerable to these effects than their older cousins. When it comes to ESD, shielding doesn't help when there are peripheral bits of the circuit on the spacecraft skin. The designers need to take it carefully.
By the way, thank you @uhoh for the link, that was interesting.