Because the requirements are not that hard, there is more chance that a private company that would be able to develop a rocket to do this if it was part of their business plan. The only question is "How reusable is it really?" Do you need to replace a heat shield after each launch? Do the engines really only last 50 launches? But even with maintenance it should still be far cheaper to operate than an expendable launch vehicle (ELV).
The closest thing to the SSTT rocket may be the X-34 reusable rocket that was a NASA project valued at $85.7 mil. It seems this project was canceled when NASA wanted to change the design after it was already signed off without paying any more for the changes. This rocket is 18,000 lbs empty, and generally much bigger than the SSTT rocket proposed here. It may be that a small missile is closer to what I am thinking of.
NASA has Cost Estimating Guidelines and an online cost estimator. If I use this online estimator and put in "Launch vehicle stage", "750 lbs", and "Quantity 15", I get $240 mil.
Just to put an initial number out I am going to estimate $200 mil for development.
Note that, even with an ELV, the air launch/tether is still interesting.
The tether is mostly a big rope and some ballast, which seems like it should be cheaper to develop per pound than the average satellite. We need some solar cells, ion-thrusters, and probably an separate small rocket. However, it has not been done before, so it might not be cheaper per pound to develop. A rule of thumb is that satellites cost about as much to make as they do to launch. If we use this rule then we could estimate the cost of the tether system at $60 mil.
So making and launching the tether could be about $120 mil total.
Another idea is to just start out with a small ballast and send up small payloads to add to the ballast. As the ballast gets bigger the payloads can get bigger. This would still be much less expensive than regular launches, especially toward the end when you could use full payloads.
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