Business Insider's (long) article SpaceX's biggest rival has a 'genius' plan to cut its rocket launch costs more than 70% contains the statements sourced from ULA's CEO Tory Bruno:
Vulcan should lift 40 tons (nearly three school buses) into low-Earth orbit. That's less than SpaceX's Falcon Heavy, which can lift more than 70 tons — nearly five school buses — for one-fourth the price. But Bruno said there are big differences between the two systems that will make Vulcan competitive.
The key difference is the rocket's upper stage. Falcon Heavy currently uses a rocket-grade RP-1 kerosene as fuel, but it can freeze in space after a few hours. Vulcan's upper stage will use cryogenic oxygen and hydrogen, which are more resilient to the punishing temperatures of space.
LH2 and LOX have about the same molar density, but the stoichiometry requires twice as many moles of LH2. If the tanks are end-to-end, it would mean the LH2 tank intercepts close to twice as much geometrical exposure to the environment as the LOX tank. However, the Enthalpy of vaporization of LH2 on a molar basis is only one quarter that of LOX (see LH2 and LOX).
Further, at 1 atmosphere for example, LH2 boils at around 20K while LOX boils at around 90K. That means without active refrigeration, the heat loading would have to be of the order of $(4.5)^4$ times lower if LH2 was used (assuming passive radiation for cooling), which would be a real challenge in sunlight.
There are two three parts to this question. If I have to split them I will but it's possible an answer can address both at the same time.
- Is ULA likely to consider putting the 2nd stage LH2 tank inside the LOX tank (or at least be surrounded by it coaxially)?
- Unless the second stage is going to Jupiter or beyond, isn't the heating from Sunlight boiling the LH2 a more challenging problem than "freezing" of the RP-1? (See Does the NK-33 engine require subcooled kerosene so cold that it turns to wax? for some density vs temperature plots.)
- In order to keep the LH2 cold for months, would the 2nd stage end up looking a little bit like the the JWST with those large metallized polymer layers deployed to block the Sun?
Temperature of a Spherical Cow in Space:
Spherical cow as illustrated by a 1996 meeting of the American Astronomical Association, in reference to astronomy modeling. From here: "The image was created by Ingrid Kallick for the program cover of the 1996 annual meeting of the American Astronomical Association. An earlier version was created for the National Center for Supercomputing Applications. The artist gave permission for use to the University of Wisconsin Department of Astronomy. The STScI subsequently used the image. http://www.ikallick.com"
Equilibrium temperature happens when average power in equals average power out, or $\bar{P}_{in} - \bar{P}_{out}$. Averaging should be done over short term variations in attitude relative to the Sun and take into account eclipses for most orbits near the Earth, Moon, or another planet.
$$\bar{P}_{in} = I_{Sun} (1-a) \ \pi R^2$$
$$\bar{P}_{out} = \sigma \epsilon T^4 \ 4 \pi R^2 $$
where $a_{vis}$ is the visible light albedo, $e_{ir}$ is the infrared emissivity (both should really be weighted averages over the appropriate wavelength ranges; @Tristan's and @Puffin's comments explain this better than their associated answers do), $\sigma$ is the Stefan–Boltzmann constant (about 5.67E-08 W m^-2 K^-4), and I is the intensity of sunlight, and for 1AU is the solar constant and about 1360 W/m^2. Solving for the average equilibrium temperature of said cow gives:
$$T \sim \left( \frac{(1-a_{vis})}{e_{ir}} \frac{I_{Sun}}{4 \sigma} \right)^{1/4}$$
For an average visible-light albedo of 0.95, and an average infrared emissivity of 0.95. this turns out to be about 130 Kelvin at 1 AU, and about 110 Kelvin near Mars, and because of the fourth-root, this varies only slowly with any of the parameters. It seems that space is much more LOX-friendly than LH2-friendly, and only moderate Sun-shielding measures would be necessary to get the LOX down below boiling at 1 atmosphere pressure, like simply having the 2nd stage face the Sun end-on, because cows are not actually spherical.
But what about the RP-1?
If the albedo of a hypothetical "LOX compartment" were 0.1 instead of 0.95 (if it were 18 times more absorbing of sunlight), the temperature would rise by the fourth root of 18, or about a factor of two (see my thoughtful (and unnecessarily down-voted) tutorial on the use of power laws in physics). That would put the RP-1 up near a balmy 273 K or 0C, "sub-cooled" and ready to go! This can be confirmed by the plot of equilibrium temperature of temperature for a spherical blackbody around each of the planets (ignoring eclipses and planetary albedo) found in this answer.
