There is a lot to be said for extending the life of a mission that has mostly been paid. The incremental cost of data is low.

However, there are other resources that are used in extending mission life of deep space probes. The antennas used for communication are a crucial resource, and an antenna used for one probe is not available for use with another probe that explores entirely new areas of space utilization (lost opportunity cost). The whole system must be examined for how useful it is to get a relatively small amount of new information that can be gleaned from an existing probe vs the unique information obtained from a new probe. Eventually, we get diminishing returns on our probes, unless they can examine new and unique areas rather than the same place over and over. It is one reason for assigning lifetimes to each mission. It allows for planning for future missions, knowing when certain amounts of resources will be freed for other use.

The lack of resources is a real problem, and it is one of the faults with depending upon government with limited budgets for funding and performing our science. Government has priorities that do not necessarily match our own priorities.
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Perhaps it would be beneficial to go back to the method of conducting and funding science that we had a hundred years ago, where We the People individually funded general scientific research and government funded only the research that benefitted government. Were we to do it that way, we may once again get many of the advancements in technology that we had gotten between 1800 and 1960. The only new technology we got in the last two-thirds century is additive manufacturing (3-D printing). The society-changing cell phone and smart phone are combinations of existing technologies, and the fundamental technologies of lasers and integrated circuits were invented in the 1950s.

Another advantage for We the People to fund science individually rather than depend upon government-funds is the ready availability of private money vs the limited availability of taxpayer money (government priorities being what they are):
‘There is far more capital available outside of NASA [for use by commercial space marketplace] than there is inside of NASA.‘
— paraphrased from an interview with NASA Administrator Bridenstine on the Ben Shapiro radio show on Monday 3 August 2020.

The Victorian Age was an age of dramatic change in our knowledge and use of Mother Nature’s phenomena, and little of it was government funded. Who knows, we might even get launch vehicles that can put payloads into orbit for significantly less than $10,000 per pound, if We the People do our own rocket development instead of relying upon government to make incremental improvements in launch technologies.

Talk about more bang for the buck!

With We the People funding our own science, We can decide when we have reached diminishing returns. We can also decide to increase the available resources so that the diminishing returns are not as stressful to our resources. That way, we can get more out of our probes, each data point costing less than when government runs science.

Aside from the dollars involved, it seems to me that there is also an “opportunity cost” — or would that be a “lost opportunity” cost — in terms of ending Juno’s mission. As Robert puts it, “While new knowledge can certainly be gained if it remained operations for three more years, the amount of knowledge will be relatively small.”* Or, in other words, how cost effective might it be to secure this new knowledge? But what if (yes, I know, some folks HATE what ifs) something were to occur in the Jovian system like the Shoemaker-Levy cometary impact in 1984? In such a case, what is the “cost” of *not* having Juno there? Likewise, the years long gap in the close-up monitoring of the Jovian system until the arrival of Europa Clipper and Juice. What is the price / value of continuity?

*Following a similar line of reasoning, when will it be “time” to shut down the Mars rovers Curiosity and Perseverance? When will it not be “worth it” to keep them going?

Finally, I like Jay’s idea, and clickbait prone sloppy thinker that I am, I would like to learn more about 3I/ATLAS even if it turns out to be nothing more than a “normal” comet from another solar system. Here, the cost to benefit ratio / bang for the buck would seem to be very high indeed if Juno can be repurposed, and the cost of failure (should Juno explode) would be trivial.