To be clear, the only medium class launch vehicle the National Aeronautics and Space Administration (NASA) has operated for us in its satellite and spacecraft launches is the Long Tank Thor/Delta family of vehicles which were derived from the Thor IRBM. All other medium and large class satellite launches were contracted to the United States Air Force on the Titan, Atlas, Thor-Agena/Delta, and Minotaur vehicles or have been performed using commercial launch services such as Orbital Sciences Corporation Pegasus and Taurus vehicles, SpaceX Falcon 9, or in joint venture on various Russian and European launchers. NASA did operate the crewed version of Atlas-Mercury and Titan-Gemini rockets as well as develop the Apollo and Space Transportation System (‘Space Shuttle’) launch systems, and does built and launch sounding rockets for atmospheric research. However, as Chronos notes, the hardware of all of those systems were actually built by aerospace contractors such as Rockwell, Convair, Glenn L. Martin, Rocketdyne, Pratt & Whitney, Grumman, Hughes, IBM, McDonnell-Douglas, et cetera. (I’d list them all but even the prime contractors would be an enormous list of companies which have sense absorbed into one another.)
Most of the people actually turning wrenches and putting together hardware at NASA are, in fact, contractors from private companies; from the mid-Nineties onward, the United Space Alliance, a joint venture of Boeing and Lockheed Martin (which is separate from the United Launch Alliance that manages the EELV program) did essentially all of the maintenance, upgrades, and pre-launch integration and servicing of the Shuttle system. Even the systems engineering and software, which were traditionally areas where NASA did a lot of the actual work, have transferred over to contractor responsibilities. I’ll note that having a private contractor did not drive down the costs of Shuttle launches, which continued to increase through the life of the program due to various factors including aging of the Orbiter vehicles, parts obsolescence, reduction in the frequency of missions, et cetera.
The question of the o.p. is actually two separate questions; one is whether a private company could provide crewed spaceflight services, and the other is whether NASA could be directed to use those services to transport members of its astronaut corps to a mission. The first is yes; since the passage of the Commercial Space Launch Act of 1984, codified as 51 USC 509 private operators, licensed by the FAA for launch operations, have been able to provide commercial spaceflight services to both other commercial entities and to NASA and government agencies such as the Air Force. This law was enacted specifically to allow NASA to use commercial providers for various services. In 2015 the Spurring Private Aerospace Competitiveness and Entrepreneurship (SPACE) Act of 2015 was passed which, among other things, encourages the development of commercial space flight systems, encourages government agencies to use commercial services, and extends indemnification for “extraordinary hazards” to operators.
NASA is, of course, using the ongoing Commercial Resupply Services (CRS) contracts to purchase resupply services to the International Space Station. It has also supported the Commercial Orbital Transportation Program (COTS) from 2006 to 2013 to develop both resupply and crew transportation, downselecting to SpaceX (Cap C–pressurized cargo and return) and OSC (Cap B–pressurized cargo and disposal) for crew resupply. The Capability D component was not exercised, but NASA has supported the Commercial Crew Development (CCDev) program for crewed delivery, downselecting to Boeing, Sierra Nevada Corporation, and SpaceX under Commercial Crew Integrated Capability (CCiCap). As of 2015, Boeing completed all contract milestones, Sierra Nevada completed 10 of 13 contract milestones, and SpaceX completed 13 of 18 contract milestones for their respective systems. NASA awarded Boeing and SpaceX with contracts to provide crew transportation services to the ISS pending certification of the crew vehicle, and in the case of SpaceX, the Falcon Heavy launch vehicle. (Boeing will use a crew-rated version of the Atlas V launcher.)
So, private companies can and in fact are trying to develop the capability to provide crewed launch services, both for NASA (the only US government agency with an operating crewed space program) and to other parties (foreign governments, private companies, and individual space enthusiasts). In fact, other than the FAA licensing process and International Traffic in Arms Regulations restrictions, there is very little the US government could do to prevent a commercial entity from offering crewed launch capability (although the FAA restriction is absolute; it could prevent a US-registered company from operating anywhere, even outside of US soil).
Could NASA be directed to use commercial services? In theory, NASA is an independent agency reporting to the executive branch. The President of the United States appoints the NASA Director who has plenary authority over the agenda of the agency and the programs that it undertakes. Congress, however, approves the NASA budget as part of discretionary spending and could add or remove line items for specific programs. (It can technically delve into finer detail but rarely does.) Members of Congress cannot compel the NASA director to do anything other than by budget allocations. As a practical matter, NASA does what appeases powerful members of Congress, such as selecting contractors in key Congressional districts, so that it doesn’t run political roadblocks with budgetary allocations, so realistically the President may set the overall agenda but Congress funds specific programs and other areas of discretionary spending.
However, NASA has a very proprietary interest in seeing to the safety of its astronaut corps and reliability of the vehicles it depends on for mission success. The standards for a crew rated vehicle are much higher than an uncrewed launcher, and I suspect they would be highly resistant to being directed to use an uncertified system or one with significant unresolved risks, especially after the experience of Challenger and Columbia. A lot of the cost and effort of crewed launch vehicles is in meeting a higher standard of development testing and integration verification testing. A private space program run by a commercial entity may not have such concerns and be willing to adopt a far more liberal risk posture. I have a hard time seeing NASA accepting the use of the Falcon Heavy as currently designed, and in particular the cryogenic propellant densification, for crewed launches. Obtaining certification and being approved to execute a NASA contract would mean satisfying this standard.
This begs a separate question, however, of what a crewed space program is supposed to accomplish. Although NASA was originally chartered with advancing crewed spaceflight and, very early in its existence, landing a person on the Lunar surface for the purposes of national prestige, its overarching mission is the advancement of space and aviation technology, and development of scientific understanding of the Earth, Sun, planetary science, and the wider universe beyond our solar system. These are not objectives that a commercial entity would engage in for profit but they are nonetheless very important for advancing human knowledge and protecting ourselves from space hazards such as solar storms and potentially hazardous impactors. A partnership between NASA and commercial providers could free NASA to focus more upon the science and exploration aspects as well as technology development instead of the mundanities of operating launch vehicles. But expecting commercial entities to take over the mission objectives of science and exploration at some expectation of return on investment is really not practical in the foreseeable future, and will not be until there is a sufficient space infrastructure that exploration can be done inexpensively and as an aside to commercial operations such as resource extraction and fabrication.
There is another implicit point that needs to be addressed: the notion that a commercial entity will necessarily be cheaper because “of course it will, it’s private enterprise”, especially if it is a firm fixed price (FFC) contract. Setting aside that nearly all of the hardware that flies to and in space is built by commercial entities–often on FFP procurements–it should be understood that costs grow dramatically beyond estimates for two fundamental but practical reasons; one is failing to understand the complexities of the system or state of technology and having to spend additional money to develop new capability; the other is the dreaded “requirements creep”, where program requirements keep being modified throughout the program requiring redesign or retesting. (The F-35 program is an example of the latter, as the design went from an inexpensive fair weather interceptor to a do-all, be-all replacement for the much more sophisticated F-22.)
Either way, the fundamental problem lies in evaluating proposals for adequate technical basis and managing the resulting contract. FFP is thought by some to be a panacea for poor contract management because regardless, the contractor is on the hook to complete the work even if it ends up eating into their profit margin. The reality is that nobody every loses money on an FFP contract, because they’ll get up to the final milestones, admit that they need more funding, and hold the agency hostage to getting an end product until they get it. The Bradley Fighting Vehicle, the Terminal High Altitude Area Defense system, and the F-35 are all examples where the program went way over budget and the government kept pouring in money to get a finished product. The result is that the proposal evaluation process often looks more at the cost volume than technical volumes and the cheapest contractor who meets the basic acceptance criteria wins, even though they do not demonstrate an adequate technical basis to do the work. This is a game contractors play with RFPs. If a hypothetical provider claimed they could put build a lunar base for US$10B, and managed to get to critical design review and do a proof of concept before running out of funds, the government would very likely just extend the contract, especially if it meant that more money went to critical Congressional districts. This is true whether NASA is the procuring agency or whether another separate contract administrator is involved.
For those venerating so-called “New Space” companies and their ability to perform these kinds of tasks much more cheaply through the exposition of buzzwords like “commoditization”, “flat management structure”, and “capabilities-based architecture”, I’ll point out that even the most successful entrant into commercial spaceflight to date, SpaceX, has essentially doubled their costs from original estimates, has missed every stated capability milestone on their schedule, and has experienced several failures and near misses due to incomplete development testing or evaluation of the design. This is not to fault SpaceX for the technical capability, and they’ve demonstrated some significant accomplishments but I would not uncritically accept any claims about what can be done for cost and schedule without substantial technical evidence and proof-of-concent demonstration.
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