Starship surface heating on Mars landing

Mars atmosphere is much thiner than Earth's

And then how much will Starship heat on a Mars landing comparing to a landing on Earth?

• SpaceX with Red Dragon was contemplating a strange approach, dive deep into the atmosphere and fly a lifting body in the dense atmosphere to better decelerate. They did not report heating numbers in the presentation I saw. NASA Likes to go in direct. SpaceX was planning to take it sporty. (Uhoh - no citations needed in a comment!) Nov 30, 2020 at 16:11

Starship Earth LEO & Mars Return:

My answer to Starship reentry velocity on return from Mars: What are the options talks about the Starship Mars to Earth return entry case. It draws heavily on my answer to What is the heat shield refurbishment procedure for a crew Dragon capsule? to inform the heating analysis. Here is the key plot for this case, assuming a best case scenario inertial entry speed of 11.4 km/s, with a LEO reference on the right:

(Personal work)

The bottom "heat shield strain" plots are explained here and the performance limits are specific to PICA, which SpaceX improved upon in PICA-X. Existing evidence (of admittedly questionable current-ness) points towards "Starbrick" TPS being something akin to PICA-X, see here (it's apparently ablative) and here ("leverages ablative heat shield materials developed for Dragon vehicles").

The best case direct interplanetary entry speeds require Starship to dissipate 16x more heat than a LEO entry!

Starship at Mars:

SpaceX gives a Martian entry speed of 7.5 km/s, presumably inertial (emphasis added):

Starship will enter Mars’ atmosphere at 7.5 kilometers per second and decelerate aerodynamically. The vehicle’s heat shield is designed to withstand multiple entries, but given that the vehicle is coming into Mars' atmosphere so hot, we still expect to see some ablation of the heat shield (similar to wear and tear on a brake pad).

Which it is important to note is higher than a typical Mars direct entry:

Mission: Entry Speed (km/s): Source:
MPF 7.26 (inertial) Ref. 1
MER-A&B 5.4, 5.5 (inertial, respectively) Ref. 1
Phoenix 5.6 (inertial) Ref. 1
MSL 5.8 (relative) Ref. 2
InSight 5.8 (inertial) Ref. 1
M2020 5.3 (relative) Ref. 2

(Mars surface rotation speed is ~250 m/s at the equator, re: difference between inertial and relative)

Perhaps this is an (unintended) result of wanting to get to Mars faster.

Another factor working against Starship is its large mass. Depending on Starship's fuel/payload mass its ballistic coefficient, $$\beta$$, can range from a minimum of a few hundred to a maximum of a few thousand $$\frac{kg}{m^2}$$. Higher $$\beta$$ values necessitate steeper entries (larger entry flight path angle) which lead to higher inertial loading and higher peak heating. For reference, US Mars entry vehicles have had ballistic coefficients of ~60 (MPF, Phoenix, Insight, Ref 1), ~90 (MER-A&B, Ref. 1), & ~120 $$\frac{kg}{m^2}$$ (MSL, M2020, Ref. 3).

This leads to problems alluded to in this answer and I think this is what @geoffc's comment is referring too. I also think this is the presentation (Ref. 4) Geoff is referring to that contains this slide about Red Dragon:

The strategy is to point your lift vector down until the vehicle is "about to crash into the surface" (for lack of a better description) then pull lift up to allow more time to decelerate in the denser lower atmosphere. This is what is seen in this (relatively old) Starship animation. I have crudely tried to replicate the trajectory shown in that animation to analyze the heating (similar methods from this answer adapted to Mars):

The "heat shield strain" plot (right) shows that the direct Martian entry is much closer (heating wise) to a LEO entry than a Mars return Earth entry/lunar return entry.

Note though that these heating analyses are about an order of magnitude accurate estimation, when applied correctly (i.e., blunt, sphere-cone entry vehicles, which Starship is not).

References:

1. Korzun, A. et al. "Aerodynamic Performance of the 2018 InSight Mars Lander," (2020) NTRS ID: 20200002812

2. Edquist, K. et al. "Mars 2020 Reconstructed Aerothermal Environments and Design Margins" (2021) NTRS ID: 20210024709

3. Noyes, C. "Robust Optimal Entry Guidance for Future Mars Landers DISSERTATION," (2021) (archived link)

4. A. A. Gonzales et al., "Mars Sample Return Using Commercial Capabilities: Propulsive Entry, Descent and Landing," 2014 IEEE Aerospace Conference, 2014 NTRS ID: 20140013203