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Gravity on Saturn's moon Titan is much weaker and the atmosphere is far denser than either Earth's or Mars', which Starship seems to have been designed for. Could an unmanned Starship do an Earth-Titan (and return?) tour nonetheless?

Coming from interplanetary transit orbit, braking in Titan's atmosphere is probably much harder than in Mars'. Also, maximum aerodynamic pressure (max Q) during restart might be more than in Earth's atmosphere. On the plus side, one of the propellant components (liquid methane) is readily available on Titan's surface, changing mass calculations.

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    $\begingroup$ Glad you said "unmanned." That would be a long voyage! $\endgroup$ Oct 2, 2019 at 23:31
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    $\begingroup$ Methane is a rocket fuel that's burned stoichiometrically, so the mass savings may not be as great as you think. Oxygen is required in a 4:1 ratio. $\endgroup$ Oct 2, 2019 at 23:59
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    $\begingroup$ @Hohmannfan There is water-ice as well. Energy for electrolysis might be a problem though. $\endgroup$
    – HannesH
    Oct 3, 2019 at 0:03
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    $\begingroup$ @HannesH In long-term confinement humans are less stable than Kerbals. $\endgroup$ Oct 3, 2019 at 1:45
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    $\begingroup$ Titan's atmosphere is extremely deep due to the low gravity, so there will be a very long stretch with very thin atmosphere. Dynamic pressure seems unlikely to be an issue (especially near terminal velocity when the vehicle rights for the landing burn), heat soak from the relatively moderate but unusually long period of heating may be a problem instead. $\endgroup$ Oct 3, 2019 at 12:18

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Getting There:

In general there is "the quick way" and "the efficient way" to get to the outer planets. The trade-off is between the capability of the launch vehicle and the time-of-flight to reach the destination. For the mid 2020's timeframe I looked for "the quick way" using a Jupiter gravity assist (though Jupiter is not in the ideal phase with Saturn but it still helps):

KPIs Arrival Dates TOFs

(Personal work)

Here we see typical C3s of about 120 $km^2/s^2$, arrival $v_{\infty}$ of about 7 km/s, and time-of-flights of about 6-7 years. For reference here is the relationship of C3 to $\Delta V$ from an assumed 250 km parking orbit with Starship's "empty" and "full" payload $\Delta V$ values marked:

delta v and C3

(Personal work)

The "efficient way" takes more work to find so I am stealing from the Dragonfly mission. This uses a series of Earth and Venus gravity assists to reach Saturn. It has a significantly lower C3 of about 20 $km^2/s^2$, similar arrival $v_{\infty}$ of about 7 km/s*, and a time-of-flight of about 9.5 years.

*I personally checked out the proposed trajectory and found an arrival energy of about 7 km/s and the paper's Titan interface velocities are consistent with a value slightly higher than this, though it is not explicitly stated.

Dragonfly Trajectory

(From Christopher et al.)

Titan Entry:

Because Titan orbits Saturn the spacecraft can encounter it with significantly varying velocity depending on if the spacecraft approaches "from behind" (prograde, minimum relative velocity) or "from in front" (retrograde, maximum relative velocity). Interestingly, the minimum (prograde) entry speed at Titan with a Saturnian $v_{\infty}$ of about 7 km/s is about 5.4 km/s, less than the Huygens probe at 6.1 km/s (despite coming from interplanetary space versus from Saturnian orbit). This is where Starship's entry system comes into play:

Coming from interplanetary transit orbit, braking in Titan's atmosphere is probably much harder than in Mars'

 ~6 km/s entry velocity is approximately Mars' entry like speed, but at a less massive body with a significantly cushier atmosphere, making the affair easier in some aspects. I think this slide from The Dragonfly Entry and Descent System, Wright et al. (NTRS entry #20190028683) really emphasizes the drastic difference between Mars and Titan EDL:

edl timelines

(Source: The Dragonfly Entry and Descent System, Wright et al. (NTRS entry #20190028683))

The capabilities of the spacecraft's entry system determines just how "retrograde" (how fast) it can approach Titan (higher speeds the more oblique/retrograde you encounter Titan).

In general, for a given entry speed, a steeper entry flight path angle will result in higher peak deceleration (g-force), higher peak heating, and lower heat load (time-integrated heating). This can be seen in another figure from Christopher et al.:

Titan entry KPIs

(From Christopher et al.)

The heat flux & heat load values from the above figure are comparable with that of a Martian direct entry and slightly lower than a typical LEO entry meaning entry at Titan is actually easier than at Mars or Earth (heating & inertial loading wise). A few observations to note:

  • the "stronger" your entry system, the faster you can afford to encounter Titan, opening up different landing locations (Titan is tidally locked to Saturn) and enabling a faster interplanetary journey to Saturn (see first figures, top right; higher Saturnian $v_{\infty}$ from earlier arrival maps to higher Titan encounter velocities, though strongly dependent on how "prograde" you encounter Titan)
  • typical LEO or Martian direct entries have much lower entry flight path angles ($\gamma$ in above figure); about 5° and 15° respectively so a "shallower" entry at Titan could further reduce the "entry burden" on the spacecraft (lower peak heating and peak deceleration).

Landing:

maximum aerodynamic pressure (max Q) during restart might be more than in Earth's atmosphere

"Maximum aerodynamic pressure during restart", or perhaps better understood as "terminal velocity near Titan's surface", would be much less than on Earth. At terminal velocity the drag force is equally balanced by the gravitational force:

$$F_G=\frac{\mu}{r^2}=F_D=\frac{1}{2}\rho V^2 \cdot S \cdot C_D$$

Titan of course masses much less than Earth (about 2% as much) and has a higher surface atmospheric pressure (analogous to density). $S$ will be the same value on Earth or Titan and $C_D$ is not likely to be appreciably different (Reynold's number is the same order of magnitude, ~$10^7$). The terminal velocity aerodynamic pressure then is solely dependent on the force of gravity at the surface which at a ratio of about 7:1 means the terminal velocity aerodynamic pressure is about 7 times lower on Titan than on Earth.

However, the more pressing (pun intended) consideration is the static pressure and its effect on Starship's engines. This may not be a big deal though as SpaceX has shown it can test fire the vacuum variant of Raptor as sea level.

I estimate a terminal velocity for Starship on Titan of maximum 30 m/s depending on how much propellant & payload there is (~820 t mass: half propellant, 100t payload, 9 by 50 m surface area, $C_D$ of 1, Titan surface density of ~5 kg/m^3). Compare this with ~90 m/s for an Earthly Starship (in a lighter configuration). This means the landing probably costs less than 100 m/s in $\Delta V$, not very much.

Launch from Titan:

Titan's atmosphere is quite soupy. Consider that at an altitude of 30 km on Titan (i.e., higher than the SR-71 Blackbird flew on Earth) the atmospheric density is comparable to sea level on Earth. That being said Titan is also quite light. I made a crude launch sim from Titan and estimate around 4 km/s of $\Delta V$ is needed to escape into Saturnian orbit. For return to Earth a required departure energy similar to the Saturnian arrival energy discussed before can be expected (~7 km/s $v_{\infty}$). This requires a Saturnian departure burn of about 5 km/s post Titan escape.

This ~9 km/s already most likely exceeds the $\Delta V$ capabilities of even an empty Starship.

In Conclusion:

Starship readily has the propellant capacity to launch towards and land on Titan. EDL on Titan is a snail-like process compared to the "7 minutes of terror" landing on Mars and reasonably comparable (heating wise) to an Earth or Mars entry that Starship is (presumably) designed for.

References:

 1. Scott, Christopher & Ozimek, Martin & Adams, Douglas & Lorenz, Ralph & Bhaskaran, Shyam & Ionasescu, Rodica & Jesick, Mark & Laipert, Frank. (2018). Preliminary Interplanetary Mission Design and Navigation for the Dragonfly New Frontiers Mission Concept.

 2. The Dragonfly Entry and Descent System, Wright et al. (NTRS entry #20190028683)

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