A Grand Tour deep space probe that needs an entire Saturn V to launch it would be a sight to see!
We have on the site trained rocket engineers and other aerospace types who know a lot more than I do. If we polled them, most would, based on my past raising these questions anyway, dismiss the idea of such a giant probe. "What do you need all that mass for?" they generally ask. (To give an idea how much mass I am talking about--Saturn V sent about 45 metric tons, plus somewhat over 10 tons in the form of the spent mass of the third stage, on a trajectory to the Moon. The thing is even a minimum energy orbit from low Earth orbit to the Moon's orbit is already very close to Earth escape velocity,a and Apollo used a still more energetic orbit that required just slightly more injection velocity. They did this to save some time, but mainly to enable a "free return orbit." This orbit was still just under escape energy and, were it not aimed to encounter the Moon, would the the Apollo far out past the Moon's orbit and eventually return to LEO--since it did encounter the Moon it would loop around Luna and come back much sooner. For reasons too technical for me to get into here, you can't do that with a minimum energy Hohmann transfer orbit--but the differences between such a minimal transfer orbit, the faster ones Apollo used instead, and an escape parabola orbit were quite small compared to the just under 3 km/sec addition to the LEO parking orbit speed the Saturn V upper stage would achieve on its second burn. They could easily have sent Apollo on an actual escape orbit, had there been any sane reason to do so, with very minor trimming of its mass. Now, for an interplanetary mission, you need more velocity than just Earth escape, you need to put it in a hyperbolic faster trajectory that gives the probe significant speed versus Earth's orbit around the Sun--although for close targets like Venus and Mars, that extra boost is modest. I'd have to either look up the actual trajectories of OTL Pioneers and Voyagers to figure out just how much extra delta-V a Grand Tour launched in the early Seventies windows would require. It would require the probe to be a lot smaller than 45 tonnes, to be sure; proposed manned flyby missions of Venus and Mars projected something like 30 tonnes, and at a guess the deep space probe would be somewhere between 10 and 20.
But the Voyager probes mass 773 kg, just over 3/4 of a tonne! Pioneer 10 was 258.8 kg. The Voyagers used a Titan IIIE/Centaur, and using the Silverbird launch calculator, I infer that the "C3" of the escape hyperbola was 17 (km/sec)^2. (C3 is a parameter from hyperbolic geometry as applied to orbital dynamics with an inverse square central force, in this case relative to Earth, and is proportional to the orbital energy). Plugging the same target C3 into the calculator's Saturn V data, I get a 35 tonne payload! I'm not at all sure I did that right, but even at half that, clearly a probe built to be launched by a Saturn V would be some 20 times more massive than the Voyagers.
Hence the "sticker shock." To be sure, a deep space probe is cheap compared to human spaceflight, but if we take the cost of the Voyager program and multiply by 25, let alone by 50, we are going to be quoting some serious money for Congress to spend. Now I'm sure that if you handed a specification like that to JPL or the scientific community in general, after a number of tenure positions open up due to scientists dying of heart attacks or strokes at the vast generosity of it all, they'd scramble to figure out ways to use the tremendous mass to accomplish great capability--but I suppose that if we were able to get the results we got from a 3/4 ton probe, it seems fair to guess that we won't get 50 times the data value from 50 times the mass, whereas the price tag would assuredly be 50 times as much. Maybe we'd save some money since such a huge bus allows for some engineering savings, perhaps.
I've never had much luck getting a sensible dollar breakdown, year by year, of any NASA program. Obviously you have to pick a base year and adjust for inflation. NASA reports the two-probe Voyager program has cumulatively cost under $900 million, in recent dollars I presume, but that includes a share of the deep space telemetry costs and data processing costs during encounters, which though modest per year obviously adds up over the decades. Clearly the cost as of launch and successful injection onto its interplanetary trajectory was lower, in modern dollars, and lower still in dollars at the time of launch bearing in mind the large amount of inflation since then. (Inflation has been at a modest and mostly stable rate, but it adds up exponentially).
If we multiply that by 50, I'm pretty sure Congress will balk at the cost, even though the pre-launch costs can be spread out over half a decade--the window used by Voyager opened in the late 70s, which gives the probe designers some time. (I think that the very best window opened earlier, and it would have been hard to meet it, certainly with such a grandiose thing as a Saturn V sized probe--maybe with generous funding, a good probe launched on a Titan derivative, or Saturn 1B type rocket, massing around a tonne or less, could be launched earlier).
You should look at the OTL NASA budget.
This Popular Science article shows that in 2014 dollars the budget zoomed up to nearly $45 billion/yr around 1968, but then plummeted down to the current level averaging around 18 billion where it has been pretty stable, give or take $5 billion or so, since.
Now then, this could be blamed on Nixon, but actually Nixon was reasonably supportive of space; LBJ undertook some of the decisions to cut costs (such as mothballing the Saturn production lines) and it was bipartisan opposition in Congress that led to the fall. Note that indeed from the mid-Seventies to mid-80s it was down to around $15 billion, not much over 1/3 the peak, and it was later in the late Reagan, Bush the First, and early Clinton years that it reached a higher plateau over $20 billion, falling again to hold at typical $18 billion until late in Bush the Second's years, held higher for a while in the early Obama years and falling again to $18 billion now.
I suppose if RK can engineer major savings of Vietnam costs by getting out fast, and if his liberal/progressive approach results in a stronger economy, he may be able to reduce the rate of fall and hold NASA funding at say 2/3 the peak level, say $30 billion/yr--but realistically, he is going to face some very stiff opposition on this no matter how much he invokes the sacred name of his brother. $25 billion a year, more realistically an average of a 30 billion level held for a couple of years declining down to $20 billion, and holding at that level--some 10 percent more than the overall average, and considerably more by a factor of 4/3 than the decade of '75-85 OTL--may be the more realistic achievement.
Now relative to OTL that is a lot of money kept for NASA, but relative to the timeline's own past, it is a drastic decline, by more than 50 percent by 1975. From our point of view, he is increasing NASA relative to OTL, but ITTL he is merely resisting a drastic decline that he can't stop. He won't look like a winner.
For him to actually increase the budget would involve tripling it relative to OTL. I'd like to see it, but I don't see how he does it.
Anyway there has to be some sort of program all this money pays for. Extending Apollo to some medium-term temporary Moon bases is something that was planned (more honestly, wished for in detail by NASA planners, but not approved by Congress). Some sort of program to develop cheaper launch capability is definitely in the cards, and ate up most of that measly $15 bill a year in the '75-'85 decade.
If RK backs off from extending the Moon missions beyond Apollo 20, what he is left with for manned space is some combination of something along the lines of achieving the Shuttle's goals OTL, and having a space station program. A few Saturn V type vehicles can certainly launch a few Skylabs, but then we'd also need a parallel crew vehicle to get crews to them. Of course Apollo exists, but this is where we need smaller launchers such as Saturn 1B, and 1B as it was had to lighten the Apollo loads by skimping on Service Module fuel--not that the fuel it omitted would be needed for an orbital mission! Still making more Apollos means overkill for orbital missions, and yet having a vehicle that is only good for 3 crew. Actually there were plans to cram 5 astronauts into an only slightly modified Apollo CM, but they would be very crowded unless there were an additional space for them to occupy, and providing that space would involve some costly and long-term engineering. I trust you are familiar with Eyes Turned Skyward which developed some very exciting modifications of Saturn and Apollo tech, but it took time. To take a different approach, I might suggest that since the Apollo Service Module does not need the massive propellant load required for Lunar missions for mere orbital missions, instead of developing a smaller SM as done in ETS, we could convert a portion of its volume to habitable space, accessed by a hatch in the heat shield of the CM. But that too is a major redesign that, if planned in 1969, might not become available until well after 1972--and that is a fast development time I suppose. On budgets around $25 billion instead of falling to 15, the work might be done quickly perhaps, but it will need to be tested out. And a different medium launcher than Saturn 1B would take some years to develop as well--continuing with new build 1Bs as well as Saturn Vs would be the only way RK is going to see new post-Lunar missions in his first term, and it is hardly clear yet he even gets a second term.
Besides something like OTL Shuttle, there would be many possibilities for somewhat cheaper costs to launch to low Earth orbit. One is to simply soldier on with already developed vehicles like Saturn 1B, and hope that extensive use of them brings down the unit costs through shaking down the tech and economies of scale in production. But this would not be very popular in 1969! In fact the fashion was that NASA ought to develop some kind of reusable Shuttle, and most proposals floating around were considerably more grandiose and optimistic than the OTL approach chosen, which was a compromise between the sort of development budget anticipated for a "proper" and fully reusable Shuttle, and the even deeper budget cuts Nixon's Budget office wanted to recommend. If Kennedy is grandstanding for NASA to get what it wants, a more grandiose Shuttle design could easily eat up all the extra $5-10 billon Kennedy might win for the agency, and leave it desperately thirsty for yet more funding--for in hindsight, the modern consensus is that anything more ambitious than OTL's version of the Shuttle would have broken the bank and yet failed to be a success.
There are yet other approaches though. Yet another timeline by one of ETS's authors (e of pi) and Polish Eagle, currently on hiatus but running within the past year, called "Right Side Up," points to one of the mistakes OTL Shuttle suffered from in hindsight, which is the perspective, not so clear then, that the expensive part of a launch vehicle is the massive first stage. The OTL Shuttle used the solid boosters for this and these were supposed to save money by being reused, but in fact the cost of trying to recover and refurbish them is said to equal the cost of simply making new ones for each launch and disposing of them. Everyone was focused on the upper stage being the thing to make reusable, but in fact upper stages on rockets are generally a small fraction of their launch mass, whereas if one could recover and reuse the massive first stage, very large cost reductions might result even if everything else is expendable.
Trying to approach this problem as a clean sheet, with the benefit of hindsight, I suspect a sensible plan would have been to develop a standardized strap-on liquid fuel booster rocket, attached in varying numbers to a disposable hydrogen-oxygen central stage using the J-2S engine. Unlike the OTL Shuttle, the plan would be for this central stage not to burn its engine(s) until it reached a great height on the boosters. The J engines were excellent in vacuum but poor at sea level and much of the high cost of developing and maintaining OTL Shuttle Main Engines was to enable them to be lit on the ground. So, I envision developing a kerosene-oxygen, or even (in my wilder dreams) kerosene-hydrogen peroxide, standard strap on booster engine, designed so that two of them are about right for boosting a central stage very similar to Saturn V's upper stage with a single J-2S engine, for a payload in the ballpark of 20 tonnes. The two liquid booster engines would parachute to a splashdown in the ocean, be recovered, checked out, refurbished and reused; the upper, central stage would be disposed of and burn up in the atmosphere after putting its payload into orbit.
Optimistically I'd think if Kennedy approved that, he could see it operational before his first term ends. I suspect the trained engineers would deny that though. Anyway if it were developed, on whatever time scale, the outcome is a flexible launch system that can be expanded to Saturn V sizes or beyond by using more boosters and bigger central stages with more J engines.
But such a thing would not have any champions I fear.
One cool idea for repurposing Saturn V tech was to modify the massive first stage so that the outer 4 of the 5 F engines, here a further evolved version than the F-1A, would be mounted on a droppable ring. The rocket would launch on all 5 F engines, and after a lot of propellant were burned up, the outer 4 engines would drop off, to parachute to a spashdown and to be recovered and refurbished for reuse, while the largely depleted stage goes on supplying the 5th engine with propellant. It was said this could put a lot of mass into orbit without using any upper stages at all, or upper stages could be used for more payload. With 4 of 5 engines and their mounting ring recovered, costs might well come down, and again the system is flexible--use no upper stages for modest payloads, and various sizes of upper stages for bigger ones, up to something in the same 120 tonne ballpark as Saturn V.
There were loads of other Saturn derivative ideas OTL.
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Elvis Presley as a politician would resemble Reagan in a number of ways, but was Elvis nearly as right-wing as Reagan was? I suppose he might come down as a bit of a cultural conservative, perhaps, more of a hard hat than a hippie to be sure-but I doubt he would embrace Reagan's hard-core positions along the lines of "the magic of the marketplace will solve our problems, therefore stop taxing the rich" and "government is the problem." I'm pretty sure he'd be much more of a pragmatic New Dealer type, and out of step with the fashion of the late 70s and 1980s to believe deregulation and privatization was always the way to go. Mind, I can easily see him being swept along by those currents, and embracing them perhaps, but he seems more like a Reagan Democrat than a Reagan--and I bet he would run as a Democrat. I don't believe he'd acquire nearly the level of right wing support Reagan did, but would capture a broad swathe of lower-class moderates. Much depends on decisions he makes, whether he comes across as culturally progressive enough not to be seen as an enemy of African-Americans or gay rights or feminism, but conservative enough to reassure people who are alarmed at the rate of the progress of these movements but not deeply committed to stopping them cold. I think he'd get a fair amount of evangelical support--again not the hard right of the Moral Majority perhaps, but lots of grass-roots Born Again types who might not be roped into the right wing in the ATL. His biggest negative, aside from any possible actual buffoonery he might perform as governor (I am assuming he grows into the office of governor of Tennessee and performs credibly, any flakiness being offset by outside the box thinking that works) is that people will think it is silly for a crooner to run for President--not having the OTL experience of Reagan, at least as much of an intellectual lightweight, becoming the beloved icon of millions.
In many ways his career if successful would be reminiscent of Reagan's, and if elected America will be something of a global laughingstock for a while--unless he turns out to be an effective President!
I'm not his biggest fan at all, but by golly, could he possibly be worse than Reagan? If he is, it will be because his campaign gets captured by the same people who backed Reagan OTL. And actually I think they will miss the Elvis bus, because they will be backing Ronnie.