Entry Study: Earth vs Mars (They Really Are Different)

I used Apollo data located from various on-line sources to determine an effective density ρ,  a “nose radius” value Rn ,  and a ballistic coefficient β for the Apollo capsule at its entry to Earth’s atmosphere.  This involved using data from Hoerner (ref. 1) and Miele (ref. 2) for the hypersonic drag coefficient C_D of the capsule,  based on blockage area A at zero angle of attack.  My result was very close indeed to the ballistic coefficient reported from other on-line sources,  as indicated in Figure 1 below (all figures are at the end of this document).  

I chose a diameter of 1 m and a higher density (no human occupation spaces needed) to estimate a mass,  blockage area A,  and ballistic coefficient for a probe design similar to the earlier smaller landers sent to Mars since Viking.  I used a CD value found on-line for that “typical” Mars heat shield shape,  that being a cone 20 degrees off flat,   with a small nose radius to blunt the otherwise sharp conical shape.  This is also shown in Figure 1 below,  and results in a ballistic coefficient very similar indeed to those reported on-line for those smaller landers.

For this study,  I used the same mass and afterbody aeroshell shape,  but substituted an Earth-type blunt heat shield for the Mars-type slightly-blunted conical shape.  That gave me two different ballistic coefficients and Rn values to use for such a probe-like entry vehicle,  at otherwise the very same size.  One is a slightly-blunted conical “Mars type” heat shield,  the other a very-blunt-indeed “Earth type” heat shield.  All of this is summarized in Figure 1 below. 

What I did with these two slightly-different designs is run both of them for entries at both Mars and Earth,  using a spreadsheet based on references 3,  4,  and 5. 

For Mars,  I presumed direct entry and landing,  typical of many landers sent there,  but off a faster transfer than min-energy Hohmann transfer.  About the fastest might be something similar to a 2-year period abort orbit at average planetary distances from the sun,  resulting in a speed at entry interface near 7.4 km/s.  I simply assumed a nominal entry interface angle below local horizontal of 2 degrees. 

For Earth,  I presumed entry from low circular Earth orbit (LEO),  which would result in a sped at entry interface pretty near 7.9 km/s.  Again,  I simply presumed a nominal entry interface angle below local horizontal of 2 degrees.  This entry speed and the Mars entry speed are not the same,  but they are fairly comparable,  in the sense that heat shields which work for entry from LEO should also work for direct entry at Mars.

I re-ran only the Earth heat shield model at Earth for a higher entry speed of 11 km/s,  to model the effects of coming back from the moon (or something comparable),  instead of just from circular LEO.  There was no point to running the Mars heat shield model that fast,  as it already had higher convective heating.  This could extend to entries off of extended elliptical orbits about the Earth. 

Figures 3 and 4 below show the spreadsheet and plotted results for the probe with a Mars-type heat shield,  entering direct at Mars.  Figures 5 and 6 below show the spreadsheet and plotted results for a probe with an Earth-type heat shield,  entering direct at Mars.  Figures 7 and 8 below show the spreadsheet and plotted results for the probe with a Mars-type heat shield,  entering from LEO at Earth.  Figures 9 and 10 below show the spreadsheet and plotted results for a probe with an Earth-type heat shield,  entering from LEO at Earth.  Figures 11 and 12 below show the spreadsheet and plotted results for a probe with an Earth-type heat shield,  entering from near escape at Earth. 

I already had data for Apollo returning from LEO and from the moon,  showing essentially the effect of ballistic coefficient β upon what is otherwise the same proportion of nose radius Rn to heat shield diameter D,  and speed at interface.  That compares with the probe data with an Earth-type heat shield entering near escape.  The Apollo data from the moon are given as Figures 13 and 14 below,  and the Apollo data from LEO are Figures 15 and 16 below.   

I did accumulate and cross plot some results,  given in Figure 17 below.  Top left is end-of-hypersonics altitude plotted versus speed at entry interface.  This is annotated to indicate which vehicle,  its ballistic coefficient,  and which mission (Earth or Mars).  Top right is peak total stagnation heating rate versus the speed at the peak heating point.  This is annotated to show which vehicle,  which mission,  and the percentage split in peak heating rate convective – radiative.  Lower left is estimated peak stagnation pressure on the heat shield versus speed at the peak deceleration gees point.  It is annotated to indicate vehicle and mission.

Only two of these show clear differences between entries at Mars versus entries at Earth.  The altitude at end-of-hypersonics is distinctly lower at Mars,  traceable directly to the thin atmosphere.  So is the estimated stagnation pressure on the heat shield,  same cause.  Atmospheric densities on Mars are comparable to those on Earth at altitudes very much lower than at Earth.

There is a ballistic coefficient effect:  higher ballistic coefficient penetrates further along the slant path before slowing down,  which results on a lower altitude at end of hypersonics.  This effect is actually larger at Earth than at Mars,  surprisingly enough.

Bear in mind that this stuff is somewhere around 5% accurate,  maybe a little worse here because the entry speeds are slightly different for the probes of this study and Apollo.  Do not read very precise trend evaluations from it!  But the sense of these trends is quite real!

Figure 1 – Where the Data Came From,  and How They Were Used

Figure 2 – Nominal Entry Conditions,  As Used In This Study

Figure 3 – Spreadsheet Data for a Probe with a Mars Heat Shield,  at Mars

Figure 4 – Plotted Results for a Probe with a Mars Heat Shield,  at Mars

Figure 5 -- Spreadsheet Data for a Probe with an Earth Heat Shield,  at Mars

Figure 6 -- Plotted Results for a Probe with an Earth Heat Shield,  at Mars

Figure 7 -- Spreadsheet Data for a Probe with a Mars Heat Shield,  at Earth

Figure 8 -- Plotted Results for a Probe with a Mars Heat Shield,  at Earth

Figure 9 -- Spreadsheet Data for a Probe with an Earth Heat Shield,  at Earth

Figure 10 -- Plotted Results for a Probe with an Earth Heat Shield,  at Earth

Figure 11 – Probe with Earth-type Heat Shield,  Near Escape Speed at Earth, Spreadsheet

Figure 12 – Probe with Earth-Type Heat Shield, Near Escape Speed at Earth, Plots

Figure 13 – Apollo Lunar Return Spreadsheet (compare to probe/Earth type/near escape)

Figure 14 – Apollo Lunar Return Plotted Results (compare to probe/Earth type/near escape)

Figure 15 – Apollo LEO Return Spreadsheet (compare to probe/blunt/LEO)

Figure 16 – Apollo LEO Return Plotted Results (compare to probe/blunt/LEO)

Figure 17 – Results Compared

References

#1. Angelo Miele,  “Flight Mechanics Vol. 1 Theory of Flight Paths”,  Addison-Wesley,  1962.

#2. Sighard Hoerner,  “Fluid Dynamic Drag”,  self-published,  1965.

#3.  H. J. Allen and A. J. Eggers,  “A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth’s Atmosphere at High Supersonic Speeds”,  NACA Technical Report 1381,  44^th Annual Report of the NACA 1958,  Washington D.C. 1959. (unclassified)

#4.  C. G. Justus and R. D. Braun,  “Atmospheric Environments for Entry,  Descent,  and Landing”,  MSFC-198,  June,  2007. 

#5.  SAE “Aerospace Applied Thermodynamics Manual”,  1969. 

Note that this study used the methods of references 3, 4, and 5 in a spreadsheet described in detail in another posting on this site:  “Entry By Hand”,  1 May 2026.  

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Search code DDMMYYYY format      01062026

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