the medical marketplace is ... a mess. Let's go to space instead.

Good idea. When the conversation turns to healthcare, I "prepare for badness."

Oxygen's role in Earth's plasmaspheric currents. As far as I'm concerned, the only justification for delving into such a thing is cuz it's purdy cool. In the next couple centuries we may pull from studies like this one in developing technologies to harvest energy from or navigate around near-Earth space, but good luck convincing a private entity to invest in something that it likely won't survive to utilize.

So you have described two benefits.

One, we get satisfaction from having a better underderstanding of the universe. That's a real benefit, even if it is not a tangible product. Joy and wonder via books, television, and movies are things people happily pay for.

All taxpayers pay to study the plasmasphere. How many enjoy the benefit? I also find space exploration and science fascinating, but I am unaware of this research, and don't even know what the plasmasphere is. Are you confident that a large proportion of taxpayers will enjoy the benefit of a better understanding of the plasmasphere? If not, is it fair to make them pay to provide pleasure to the plasmasphere special interest group?

Two, we may one day be able to harvest energy from space thanks to this research. This is clearly a benefit, distant in the future though it may be. Business and government often have to weigh efforts that pay off sooner vs. those that pay off in the long term. Mitigating the effects of climate change is an example: money not spent on malaria eradiaction today can be used instead to reduce the harmful effects of climate change in 100 years.

How do we make these choices? With lots of difficult assumptions, of course, and also with a discount rate.

Suppose I have the choice of spending $100 on goodies today or investing $100 with a fairly certain expectation of gaining $200 in ten years. If I am indifferent between these options, my discount rate is about 7% per year (the article says "something around seven percent is what the US Office of Management and Budget recommends for a pretax rate of return on private investments").

Let's assume that plasmasphere research today will certainly enable us to harvest energy from space in 200 years. Let's also assume that the value (in today's dollars) of that energy harvest will be one trillion dollars. Using the formula provided, 1/(1+r)^t, we calculate a discount factor of 1/(1.07)^200 or about 0.000001. So the value today of the trillion-dollar benefit we expect in two centuries is about a million dollars.

If our assumptions are true about the value and certainty of the energy harvest, we should not spend more than one million dollars in total now for the research (here ignoring the joy dividend). Probably the 7% figure comes from the idea that you can earn at least that much by investing the money in something other than research, then in 200 years you just buy the energy from Elon Musk.

Conspiracy theorists aside, you'd probably be hard-pressed to find many people who feel like the Apollo missions were a waste of money.

Surely not a waste. We got Tang, and better dialysis techniques. And a lot of thrill. Is it wrong to put a price on these benefits? Is it impossible to spend too much on a good thing?

The correct way to evaluate an investment is with cost-benefit analysis. Benefit analysis alone is not enough.

Lots of people will say they support NASA when they imagine other people are paying for it. If you could calculate how much each person actually contributes, and give them the option of spending that money on something else, how many would still chip in?