Slowing down 16 Psyche using an enormous solar sail to reach the inner planets

Question

I am writing a sci-fi story and would like my science as hard as possible. I was thinking of using the solar sail as a kind of sea anchor. Slowing down, the asteroid would move down to the inner planets, where the metals would fetch a higher price than in Jupiter orbit. In my story it would take more than a century to reach Mars and the whole solar sail is a scam to keep the miners placid. It won't slow the asteroid appreciable, and the owners use an array of rail guns to launch extremely accelerated slugs of metal to slow down the asteroid. My question is how big a solar sail should be to slow down an asteroid? My protagonist discovers the scam when he tries to calculate the size of the solar sail. Alas, I am unable to do the calculation myself.

Answer 1

First up, the answer for 'how big does the solar sail need to be' is always 'enormous' but lets see roughly HOW enormous.

Using impulse delta V calculations for a solar sail will get results that are too low, but it is quick so we have a look at maps like this and see that we need between 1 and 1.5 kilometers a second to do an asteroid belt/Mars transfer. If we want to do this maneuver in 10 years we need thrust that gets around 5*10^-6 meters per second (5 micro meter per second) since we have lots of seconds to work with. F=ma gives us a needed thrust of 115 Tera Newtons since 16 Psyche is heavy.

The performance of solar sails is best right in close to the sun, and a lot of studies assume operation around Earth/Venus rather than out near Jupiter. Using the Earth orbit math from here indicates 9 micro Newtons per meter at Earth orbit. Using 1 μN per square meter getting 115 TN total needs a sail 10 million kilometers on a side. The gap between the orbits of Mars and Jupiter is around 500 million km to give this some scale.

This calculation ignores a LOT of things, starting with the mass of the sail, the non ideal thrust axis and using impulse delta V calculations for continuous thrust however the answer 'big enough that physically fitting between Mars and Jupiter is a problem' remains valid.

This number may seem implausibly large, but if solar thrust was substantial 16 Psyche would have already blown away given the long lifetime of the solar system.

In terms of the story this scam would seem unlikely to work since even with poor prior assumptions the needed sail area is just clearly immense. Solar sail projects often design with less 10kg of payload on a 100*100 meter sail.

What might make the plot work is that stated scheme is a team going out, processing the asteroid into sail material and sending economically meaningful amounts of material to be re-processed into other things on arrival (eg sail IS the payload). They launch sails that are visible, and take longer to arrive than planned (because they were 'so rich'). When decades latter they do start arriving they are instead found to be light weight inflatables, performing poorly be design not because they are heavy.

Would suggest the plot aspects of how fake sails are identified are more on topic in world building SE.