Third Spacex Tanker Study

Update 3-26-21:  this third tanker study identified the best approach to refilling the lunar mission Starship on-orbit.  This approach maximizes tanker operations in low circular orbit,  and minimizes them to one refilled fly-along tanker sent to the elliptical departure orbit. 

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This article presents work that follows up on the lunar mission results already posted in Ref. 1 and Ref. 2.  The first was a Spacex tanker study aimed at refilling a lunar landing mission Starship directly in the elliptical departure orbit required to make a lunar landing mission feasible.  The second was a two-stage refilling operation,  with a full refill of the mission Starship in low circular orbit,  and a more modest top-off in the elliptic departure orbit,  from tankers sent directly there. Those orbits were defined in Ref. 3.  The reverse-engineering of vehicle performance characteristics to support this was presented in Ref. 4.

This third study conducts all refilling operations but one in low circular orbit,  where tanker capacities are the highest.  The mission Starship is fully refilled there,  and then sent to its elliptic departure orbit,  and topped off there.  All tankers are initially sent to low circular orbit,  where they fully refill the mission Starship,  and partially refill only one tanker!  That one tanker goes with the mission Starship to the elliptic departure orbit,  where it tops-off the mission vehicle before returning to Earth directly from that orbit.  This approach got the tanker flight requirement down to only one more tanker than would otherwise be required for a full mission Starship refill at max payload in low circular orbit!

Orbits Considered

For clarity,  the elliptic departure orbits being considered are 300 x 7000 km altitude,  and 300 x 10,000 km altitude.  The low circular orbit is 300 x 300 km altitude.  Lunar missions flown from the lower-apogee orbit can take a max 75 metric tons payload to the lunar surface,  with 0 tons payload returned to Earth.  From the higher orbit,  59 tons can be landed on the moon,  with 32 tons returned.  Bear in mind that these elliptic departure orbits penetrate deeply into the Van Allen radiation belts,  whose “base” is nominally about 1400 km altitude.  That definitely means that cargo must be radiation-hard,  and any crew/passengers must have a good radiation shelter,   in order to perform these lunar missions. 

Tanker Options Considered

As indicated in Ref. 1,  there are two possible tanker configurations:  (1) a dedicated tanker design with extra tankage volume in the forward spaces,  and (2) an ordinary cargo or crew Starship flow at zero payload,  so that there is unused propellant aboard upon arrival.  These are based upon comments made by Mr. Musk in his public pronouncements,  and presume the same inert vehicle mass of 120 metric tons as I used,  in reverse-engineering Starship/Superheavy performance in Ref. 4. 

Flown to the low circular orbit,  and withholding only a dry-tanks landing allowance of 9.02 tons propellant,  the deliverable-propellant capacities of these tanker options currently calculate as 232.00 metric tons for the dedicated design,  and 192.51 tons for the ordinary Starship flown at zero payload.   Those capacities are dramatically lower still,  when flown to higher-energy orbits!  They are max capacities:  you can always fly with less,  but never more! 

Calculations

The refill requirements from elliptic departure for the mission Starship were computed in Ref. 1,  and are repeated here in Figure 1 below.  That figure shows both the direct refill in elliptic,  and the two-step refill and top-off requirements.  It is quite easy to see the dramatic difference!  These refill requirements in elliptic orbit are substantially larger than the capacities of the tanker configurations,  when flown directly to the elliptic orbits.  That is exactly why the second study in Ref. 2 got the results that it did,  despite doing the initial full refill of the mission Starship in the low circular orbit.   

I did simple hand calculations with a calculator to determine the departure mass from low circular orbit for the one tanker that accompanies the mission Starship to its elliptic departure orbit.  Those are based on the top-off requirements of the mission vehicle in the elliptic departure orbit.  Those top-off requirements are shown on the right-hand side of Figure 2,  as well as the left side of Figure 1.  Note that due allowance was made for the landing reserve propellant,  while still carrying full deliverable payload. 

A Starship fully refilled in low circular orbit arrives in its lunar departure elliptical orbit only a little less than full,  despite it being early in the burn when you use lots of propellant for little effect.  That is because the mass ratio MR required for the orbit-changing burn is actually rather modest.  This was figured for 3 vacuum Raptor engines at full thrust in vacuum.  That’s enough to be an impulsive burn,  so the orbital mechanics delta-vee is the mass ratio-effective delta-vee for the maneuver (factor = 1.000).  Mass ratio data are given in the middle of Figure 2,  along with the propellant loads upon arrival that allow topping off the mission Starship,  while still retaining a landing reserve. 

The tanker propellant loads needed in low circular orbit are shown on the left of Figure 2.  The refill quantities are less than the propellant load by the landing reserve.  Depending upon which lunar departure orbit and which tanker version,  you add the tanker refill quantity to the mission Starship refill quantity,  to determine the total propellant that must be delivered by tankers to low circular orbit. 

The resulting procedure to run the lunar landing mission is simple.  Note that “ord” refers to an ordinary Starship used as a tanker by flying at zero payload,  and “ded” refers to a dedicated tanker design with extra tankage capacity in the forward spaces,  beyond the regular 1200 metric ton capacity.

Procedure:

Step 1. – Launch the mission Starship plus 7 ord (or 6 ded) tankers to low circular orbit.

Step 2. – Refill the mission Starship from the first 5 ded (or 6 ord) tankers,  leaving the 5th (or 6^th) with a partial load still aboard,  while always withholding landing reserve in all tankers.

Step 3. – Put that partial load in the next-to-last tanker into the last tanker,  to fill it with enough propellant to reach the elliptical departure orbit,  plus just enough to cover the mission Starship refill,  while still maintaining the tanker landing reserve.

Step 4. – The mission Starship plus that one partly-refilled tanker,  go to the departure elliptical orbit,  while the other (empty) tankers return to Earth using their landing reserves.  Their entry speed will be about 8 km/s.

Step 5. – The last tanker tops-off the mission Starship,  there in the elliptical departure orbit,  then returns to Earth using its landing reserve.  Entry speed will be about 9 km/s. 

Step 6. – The mission Starship,  being now fully refilled in its elliptic departure orbit,  can then carry out its lunar nearside landing mission,  including return to a free entry at Earth,  and landing with its landing reserve.  Its entry speed will be about 11 km/s.

The tanker and refill quantity data are summarized in Table 1 below,  just ahead of the figures.  All are at the end of this article.  How these lunar landing missions compare to others is shown in Figure 3. 

Remarks

The reader should bear in mind that these results are not from computer trajectory or orbital simulations run on a computer!  These are the results of simple hand calculations made from simple equations,  sometimes semi-automated with a spreadsheet,  and sometimes not.  For such,  the use of empirical “jigger factors” is necessary to get realistic results.  Those derive from experience in the field.

The reader should also bear in mind that the two-way mission to a lunar landing requires significantly more delta-vee than the one-way flight to Mars.  There is potentially propellant manufacture capability on Mars,  but not the moon.  This has an exponential effect on vehicle mass ratio. 

The assumptions in common here with all the references cited are:

#1. Vehicle “weight statement” is inert mass + payload mass + propellant mass = ignition mass

#2.  Vehicle inert mass presumed to be 120 metric tons,  regardless of type

#3. Engine performance factors are per Ref. 5,  converted to metric

#4. Effects on performance due to throttle setting are presumed linear,  from min to max

#5. Kinematic delta-vee values are factored-up “appropriately” to obtain mass ratio-effective values

#6. Delta vee factors are experiential judgements that account for gravity losses,  drag losses,  and any hover or divert effects during landings

#7. For purposes of eastward launch,  the surface circular velocity is used as the kinematic velocity to attain,  in order to include potential energy effects into the rocket equation calculation

#8. For purposes of eastward launch,  the surface circular velocity (or higher) gets factored by 1.10 to account for gravity and drag losses at 5% each

#9. If launch were polar,  the eastward velocity due to Earth’s rotation at the launch latitude would be added to the surface circular (or higher) velocity (add two rotation velocities if westward launch)

References (all are located on this site)

#1. G. W. Johnson,  Spacex Tanker Investigation,  dated 17 March 2021.

#2. G. W. Johnson,  Second Spacex Tanker Study,  dated 21 March 2021.

#3. G. W. Johnson,  Reverse-Engineering Estimates:  Starship Lunar Landings,  dated 15 March 2021.

#4. G. W. Johnson,  Reverse-Engineering Starship/Superheavy 2021,  dated 9 March 2021.

#5. G. W. Johnson,  Reverse-Engineered “Raptor” Engine Performance,  dated 26 September 2019.

The easiest way to locate references on this site is to use the navigation tool on left-of-page.  You will need the year and month it was posted,  and the title.  Click first on the year,  then on the month.  If need be,  click on the title.  It would be wise to scrawl all this reference date and title information onto a piece of scrap paper,  before starting that research.

               Table 1 – Summary of Third Study Results 

Figure 1 – Mission Starship Refill Requirements

 

Figure 2 – Tanker Refill Requirement to Go From Circular to Elliptic and Top-Off Mission Vehicle

Figure 3 – Comparing Lunar Missions to Other Possible Missions

Second Spacex Tanker Study

Update 3-26-21:  this second tanker study looked at refilling the lunar mission Starship in low circular orbit,  where tanker Starship capacities are high,  then topping it off after moving it to the departure orbit,  with more tankers sent directly to that orbit.  That reduced the number of required tankers,  but not by enough to be truly practical.  The strategy explored in the third study (also posted here) turned out to be the most effective one.

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In Ref. 1,  I defined two elliptical orbits from which a Spacex Starship could be sent fully-fueled on a lunar nearside landing mission,  be unrefueled on the moon,  and return to a free entry landing trajectory at Earth.  Payloads sendable to the moon this way are far smaller than payloads deliverable to low circular Earth orbit,  because payload capacity to the higher-energy orbit is reduced,  as well as the inherently-smaller payload capacity for the lunar flight. 

It makes sense to use the elliptical orbit at which Starship payload capacity to that orbit matches the Starship lunar mission capacity.  Some 75 metric tons can be sent to the moon,  with zero return payload,  from an elliptical orbit that has 300 x 7000 km altitudes.  Some 59 tons can be sent to the moon with a 32 ton return payload,  from an orbit that is 300 x 10,000 km altitudes.

Both elliptic orbits have apogee altitudes that penetrate well into the Van Allen radiation belts.  Thus cargoes delivered this way must be radiation-hard,  and any crew or passengers will require effective shelters from serious radiation exposure.  The “base” of the Van Allen radiation belts is considered to be about 1400 km altitude,  outside the South Atlantic Anomaly. 

In Ref. 2,  I determined the deliverable propellant quantities from two potential Spacex tanker configurations:  a dedicated tanker design with extra tankage volume in the forward spaces,  and an ordinary Starship flown fully fueled,  but at zero payload,  so that it arrives with significant unused propellant.  The scope of that study looked at the 300 x 300 km altitude low circular Earth orbit,  and the two possible elliptical lunar mission departure orbits that “sort-of” bound the problem. 

Deliverable tanker “payload” with either configuration was considerable in low circular orbit,  but a lot less when sent directly to either of the two elliptical orbits.  This is because the higher energy orbits require a whole lot more propellant just to be reached.  In all these scenarios,  the dedicated tanker design carries somewhat more deliverable propellant than the ordinary Starship flown at zero payload.

This basic information is summarized in Figure 1 below.  All figures are located at the end of this article.  The two elliptical lunar departure orbits and associated lunar payloads are in the upper part of the figure.  The tanker delivery capacities are shown for both tanker configurations,  at each of the three orbit locations,  in the lower part of the figure.  In each case,  the Starship/Superheavy tanker vehicle is flown directly to the target orbit location,  as is the cargo/passenger Starship/Superheavy vehicle. 

Two Waves Of Refueling On-Orbit

The small tanker propellant delivery capacities to elliptic orbit versus the large capacities to low circular orbit suggested a two-step refueling operation for the lunar-bound Starship:  a full-capacity refill in low circular orbit,  followed by moving it to the elliptic orbit,  with another refill there.  This would apply to either lunar mission scenario. It could be done with either tanker configuration.  Hopefully,  fewer tanker flights would be required than by direct one-step refueling in the elliptic departure orbit.

To support this two-step refueling operation,  I had to figure out what the refill requirements would be upon arrival in the target elliptic orbit,  and also the low circular refueling requirements when carrying the smaller lunar payloads.  The elliptic refill requirements I hand-calculated,  and these are summarized in Figure 2.  The low circular refuel requirements at lower payloads,  I figured with one of the Starship spreadsheet models.  Those results are Figure 3 for the 75 ton payload from the 7000 km apogee orbit,  and in Figure 4 for the 59 ton payload from the 10,000 km apogee orbit.

Calculating Numbers of Tanker Flights

Then I calculated the number of tanker flights required to carry out these operations (first the low circular refill,  then second the elliptic refuel after moving there).  In each operation,  the requisite tankers are flown directly to the orbit where the refill will take place. The limiting number of tanker flights is the refill requirement divided by tanker delivery capacity,  but the only such number that makes any sense is an integer!  You always hold back the tanker landing reserve from deliverable propellant. 

If there are decimals,  you must round up to the next-larger integer!  That is because you cannot carry more deliverable propellant than the max capacities these calculations have identified,  but you can always carry a little less than max capacity. 

Intermediate Results

The refill requirements in low circular orbit for the lunar-bound Starship are just about 1050 tons of propellant,  depending upon which mission and payload we are talking about.  The tanker capacities to low circular orbit are right at 200 tons per vehicle,  give or take,  depending upon whether the tanker is the dedicated design or the ordinary Starship flown as a tanker.  Those numbers and the rounded-up integer numbers of flights are given in Figure 5.  Note that the delivered tanker loads are just not very far from the max capacities of the tankers,  as also given in the figure.   We are looking at 5 dedicated tankers,  or 6 ordinary tankers,  to accomplish this,  for either lunar departure scenario.

The second refueling operation is illustrated in Figure 6.  The refill requirements are far smaller,  but then so are the max tanker capacities!  Again,  you round up the decimals to the next larger integer number of tankers.  Those results show 3 tankers (of either type) are needed for the 300 x 7000 km orbit that supports 75 ton lunar landings,  with 0 tons return payload.  The more demanding 300 x 10,000 km orbit requires 5 tankers of either type,  but that scenario supports a 32 ton return payload,  with 59 tons landed on the moon.  It is the higher-energy orbit.

Ultimate Results

A summary comparison of these results versus the direct staging in elliptical orbit,  and versus operations only to 300 x 300 km circular  are given in Figure 7.  That figure this summarizes the results of the first tanker study and this second one. 

The max payload deliverable to low circular orbit is quite a bit more at 171 metric tons.  That is why 7 ordinary or 6 dedicated tankers are needed to fully refill the Starship there.  That’s a Ref. 2 result.

Another Ref. 2 result is the single refueling operation conducted with Starship and tanker flights directly to the lunar departure elliptic orbit.  That is also indicated in the figure,  which shows some 21 ordinary or 19 dedicated tanker flights to refill the Starship carrying 75 tons to the moon from the 300 x 7000 km orbit.  The Starship carrying 59 tons from the 300 x 10,000 km orbit requires 17 ordinary or 15 dedicated tanker flights to fully refill.  Those high tanker flight numbers are not very attractive!

The two-refill operation approach analyzed in this article (with the first wave of tankers sent to low circular orbit,  and the second wave of tankers sent to the departure elliptic orbit) does indeed reduce the number of tanker flights.  For the 300 x 7000 km departure with 75 tons to the moon,  the first wave is 6 ordinary or 5 dedicated tankers to circular,  followed by the second wave of 3 ordinary or 3 dedicated tankers to the elliptical orbit,  for a total of 9 ordinary or 8 dedicated tankers to support the mission.  For the 300 x 10,000 km departure (59 tons to the moon),  the first wave is the same 6 ordinary or 5 dedicated tankers,  and the second wave is 5 ordinary or 5 dedicated,  for a total of 11 ordinary or 10 dedicated tankers to support that mission.  That is a substantial improvement,  but still unattractive.

Remarks

Readers need to be aware that these calculations I have made are not any sort of simulations run with any sort of computer programs.  These are the kind of calculations I would make,  if I sat down at the kitchen table with pencil,  paper,  and a pocket calculator (or even a slide rule).  These have been semi-automated with spreadsheet software,  but are essentially the same very simple calculations made with simple models,  plus the engineering art of selecting the right “jigger factors” to get realistic results. 

For those readers too young to know what a slide rule is,  see Ref. 3.

Plans

The improvement achieved with two-step refilling is attractive,  and the disparity between tanker capacities in low circular versus feasible lunar departure orbits is large.  That suggests refilling not only the lunar mission Starship in low Earth orbit,  but also 1 or maybe 2 tankers.  The mission Starship plus the 1 or 2 refilled tankers would then move to the elliptical departure orbit,  where those tankers would top-off the mission Starship.  As time and opportunity permits,  I will look at this method of employing these assets,  to see if the total number of supporting tanker flights can be reduced further.

References (all are located on this site)

#1. G. W. Johnson,  Reverse Engineering Estimates:  Starship Lunar Landings,  dated 15 March 2021.

#2. G. W. Johnson,  Spacex Tanker Investigation,  dated 17 March 2021.

#3. G. W. Johnson,  THIS Is a Slide Rule!,  dated 16 March 2019.

Figure 1 – Selected Results From the First Tanker Investigation

Figure 2 – Determining the Refueling Needs Moving From Circular to Elliptical With Lunar Payloads

Figure 3 – Determining the Refueling Needs in Circular with Lunar Payloads:  75 ton

Figure 4 – Determining the Refueling Needs in Circular with Lunar Payloads:  59 ton

Figure5 – Tankers Required to Refuel Lunar-Bound Starships in Circular Orbit (First Refuel)

Figure 6 – Tankers Required to Refuel Lunar-Bound Starships in Elliptical Orbit (Second Refuel)

Figure 7 – Comparison of First Investigation Results with Results of Second Study

 

Spacex Tanker Investigation

Update 3-26-21:  This first study looked at refueling a Starship sent directly to its elliptical departure orbit with tanker Starships also sent directly to the same orbit.  That turned out not to be the best way to do the required on-orbit refilling for lunar missions.  The third study (also posted here) turned out to be the best way. 

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This article is based on published comments by Elon Musk that (1) there will be a dedicated tanker design for on-orbit refueling operations with Starship,  but (2) initially the “tanker” will just be another Starship. 

In the first case (dedicated tanker design),  there will be additional propellant tankage volume in the forward spaces,  where the cargo bays and or passenger accommodations are located,  in the other designs.  The propellant in that extra tankage volume is the “payload mass” ferried to orbit.  It computes directly as any other payload in rocket equation and the 2-body orbital mechanics approximations to performance that I have been using for these estimates. 

For that second (initial) case,  the only thing that makes sense is the fly the ordinary Starship-as-tanker to orbit with zero payload but a full propellant load.  It will have unused propellant upon arrival to orbit,  in excess of that needed to land.  That excess can be transferred to the target Starship. 

For both tanker cases,  there is no need to support an abort to the surface with payload aboard,  because excess propellant mass can be vented to space prior to any deorbit burn.  Thus,  the tanker landing can be made to the “dry tanks” standard with zero payload,  in either case.  That reduces the propellant reserve for landing that must be withheld from any on-orbit refueling operation.

When I investigated lunar missions with the Starship in Ref. 1,  I looked at a variety of orbits,  from 300 x 300 km altitude circular,  through a variety of elliptic orbits all sharing the 300 km perigee altitude.  I found that the 300 x 7000 km altitude orbit,  and the 300 x 10,000 km altitude orbit,  might prove feasible for Starship lunar missions,  depending upon the payload to and from the moon.  The 300 x 300 km altitude circular is of general interest for all sorts of applications.  Those three orbits are the scope considered in this article.  This article also presumes that all refueling is done in the departure orbit.

General Operations In 300 x 300 km Circular (Excluding Lunar Landing Missions)

When I reverse-engineered orbital performance of the Starship/Superheavy in Ref. 2 (and to support Ref. 1),  I obtained payload capabilities and staging velocities for Starship/Superheavy,  under the assumption that the Starship landing reserve of propellant be sufficient to support an abort to surface with the full payload still aboard (a dry-tanks landing at full payload). 

That is not necessary for any Starship design used as a tanker.  Tankers can always vent propellant overboard prior to the deorbit burn,  down to only that required for a dry-tanks landing at zero payload. Which situation is exactly why the propellant-as-payload and landing reserve numbers for the tankers are different from those for the target ship,  to the same orbit.  Data are given in Table 1.

                              Table 1 – 300 x 300 km Altitude Results

Vehicle                               target                   dedicated            ordinary

Payload, m.ton                 171                       232                       192.506

Vstaging, km/s                 2.23                      2.21                      2.375

Land. Res., m.ton             21.876                 9.019                   9.019

Full refill req., m.ton       1178.124            --                             --

Tankers to refill                --                           5.08                      6.12

In the data table,  “target” means the Starship vehicle to be refueled on-orbit.  “Dedicated” means a dedicated tanker Starship design with extra tankage volume in the forward section.   “Ordinary” means another cargo or passenger Starship operated with zero payload in the forward section,  whose deliverable “payload” is merely the excess propellant not used reaching orbit,  less the landing reserve.  “Full refill” means filling to the capacity,  currently thought to be 1200 metric tons.  The number of “tankers to refill” is for a full refill,  and is the max refill requirement divided by the deliverable propellant from a tanker vehicle.  For planning purposes,  you should round up any decimals.

Not all missions flown from this orbit require a full refill to max capacity.  Mars missions can be flown from this orbit,  but lunar landing missions cannot. 

Lunar Landing Missions From 300 x 7000 km Elliptic Without Return Payload

Lunar landing missions are too demanding in terms of total delta-vee to be flown from the low circular orbit,  without any refueling on (or near) the moon.  The same is true of Mars missions,  although there are materials on Mars from which propellant can be made,  unlike the moon. 

Departing from a sufficiently-elongated elliptic orbit with a high-enough perigee velocity lowers the departure delta-vee sufficiently to make an unrefueled lunar landing mission feasible with a filled-to-capacity Starship,  at some reduced payload.  The higher-energy elliptic orbit also reduces the payload that can be carried up to orbit from Earth.  It makes sense that payload ferried up is also payload carried to the moon.  The elliptical orbit where these payloads are equal is preferred for the mission. 

See the data in Table 2,  bearing in mind that these results for the target vehicle were partially just read from a graph in Ref. 1,  not specifically supported by precise calculations.  Imprecision is inherent.

                              Table 2 – 300 x 7000 km Altitude Results

Vehicle                               target                   dedicated            ordinary

Payload, m.ton                 ~75                       83                         73.4

Return payload, m.ton     0                          --                             --

Vstaging, km/s                 ~2.23                    2.22                      2.275

Land. Res., m.ton             ~14.9                    9.019                   9.019

Full refill req., m.ton       ~1185.1               --                             --

Tankers to refill                --                           14.28                   16.15

Also,  the presumption here is that the tankers fly directly to the same elliptic departure orbit as the target vehicle.  No other scenario was considered at this time.  That does not mean that there are no other scenarios!  One possibility for future investigation is refueling in low circular orbit,  then moving the target vehicle to the departure orbit,  along with 1 or 2 more tankers to fully refill it just before departure.

Lunar Landing Missions From 300 x 10,000 km Elliptic With Max Return Payload

There is one other nuance to consider:  how much payload can be returned from the moon?  The 7000 km apogee altitude is associated with a higher payload to the moon,  but a zero return payload,  per Ref. 1.  The 10,000 km apogee altitude is associated with a lower payload deliverable to the moon,  but a nonzero return payload,  again per Ref. 1.  See the data in Table 3.  (Again,  the presumption here is that all of the tankers rendezvous with the target vehicle in the elliptic departure orbit.) 

                              Table 2 – 300 x 10,000 km Altitude Results

Vehicle                               target                   dedicated            ordinary

Payload, m.ton                 59                         64                         57.657

Return payload, m.ton   32                         --                             --

Vstaging, km/s                 2.23                      2.215                   2.263

Land. Res., m.ton             13.456                 9.019                   9.019

Full refill req., m.ton       1186.544            --                             --

Tankers to refill                --                           18.54                   20.58

“How I Did It” for the 2 Different Tanker Choices

These tanker versions of Starship and the “regular” cargo or passenger Starship all share exactly the same “model” of the Superheavy booster.  That booster’s flyback for recovery is modeled first,  and in reverse.  The touchdown is figured as a dry-tanks landing,  with engine cutoff just as the on-board propellant zeroes.  Then the entry burn is modeled,  and finally the boost-back burn.  That quantifies the propellant still on board at staging. 

The capacity less the propellant-still-on-board at staging,  is the booster propellant available to reach staging velocity.  The way I set this up,  you iterate the imposed staging velocity until the overall mission’s remaining propellant is a small positive fraction of a ton.  That result is also affected by the payload in the Starship weight statement.  The Superheavy booster sees the fully-loaded Starship upper stage as its “payload”,  which affects how much propellant is needed to reach staging velocity.

The Starship upper stage analysis begins with the landing.  For the cargo/passenger vehicle,  I require a dry-tanks landing with the full payload still aboard,  as a way to support an abort to surface without the chance to unload payload.  For the tankers,  the dry-tanks landing is made with zero payload aboard.  This is because with the dedicated tanker design,  the “payload” is propellant that can be dumped to space before the deorbit burn.  For the “ordinary Starship-as-tanker”,  loaded payload is zero.  The excess propellant in the regular tanks can be dumped to space before the deorbit burn.

You analyze the effects of the landing and the deorbit burn,  to determine the propellant reserve that must be aboard,  at the time of the deorbit burn.  That reserve is larger for the cargo/passenger vehicle,  and smaller for the tanker (of either kind). The propellant available for the ascent burn is capacity less the landing reserve. 

For the dedicated tanker design,  I use exactly the same analysis as for the cargo/passenger Starship.  You burn the available propellant,  and see what delta-vee that gets you.  You set the payload to that value which gets you the right delta-vee.  Your “payload” is the transferable propellant.

For the ordinary Starship-as-tanker,  you set payload to zero,  always.  The calculation finds out how much propellant is required to reach the correct delta-vee.  That is the required ascent propellant.  The capacity less the ascent propellant,  and less the landing reserve,  must be a non-negative number.  That is the unused propellant available for transfer while on-orbit. 

Future Plans

I want to look more closely at doing a full refill of the target vehicle in the low circular orbit,  then moving it and 1 (or 2) more tankers to the elliptic departure orbit.  That would be an attempt to reduce the number of tankers required to effect a full refill at departure for a lunar landing mission.  Scope would be for the 300 x 7000 km orbit with 75 tons to moon,  and 0 return payload,  plus the 300 x 10,000 km orbit with 59 tons to the moon and 32 tons returned.  That might have a large payoff,  given the large disparities in the number of tanker flights needed for the low circular orbit,  versus either of the lunar-departure elliptical orbit choices.

Final Comments

These numbers were created with essentially pencil-and-paper hand calculations for the rocket equation and the combination of 2-body solutions for the orbital mechanics.  The only way to make such calculations realistic is the judicious use of appropriate factors to increase the theoretical delta-vee requirements,  and a judicious approximation to combine 2-body orbital mechanics models in lieu of a real 3-D trajectory program in a computer.  That art is summarized in Refs. 3 and 4. 

These numbers were also created with the best available data regarding the propellant capacities and inert masses for the Starship and Superheavy stages,  and for the performance characteristics of the sea level and vacuum versions of the Raptor engine.  More of that was available on the Spacex website in prior years than is there now.  Much of this now has to be obtained from online sources like Wikipedia. 

I did my engine performance figures from information that used to be posted on the Spacex website,  and is no longer posted there.  They do still post propellant capacities for the stages,  but not the inert masses (and they never did).  Inert masses came from Wikipedia. 

The results are very sensitive to such data,  particularly the stage inert masses.  Increases in inert mass must come directly out of payload capability.  What I have is “in the ballpark”,  but still subject to change,  especially as Spacex has begun flight testing of the Starship vehicle,  and soon the Superheavy booster.

These results indicate some phenomenally-attractive capabilities with this basic vehicle design.  Those are enough to warrant solving both the known,  and the still-unknown,  problems with this design,  which problems will become more-and-more evident as flight testing proceeds.  Those include (but are not limited to) ullage/slosh problems inside un-bladdered cryogenic propellant tanks,  propellant leaks leading to engine bay fires,  and a totally-inadequate design concept for the landing legs (both stages,  but more especially the second stage). 

References (all are articles published on this site)

#1. G. W. Johnson,  Reverse-Engineering Estimates:  Starship Lunar Landings,  15 March 2021.

#2. G. W. Johnson,  Reverse-Engineering Starship/Superheavy 2021,  9 March 2021.

#3. G. W. Johnson,  Fundamentals of Elliptic Orbits,  5 March 2021.

#4. G. W. Johnson,  Back of the Envelope Rocket Propulsion Analysis,  23 August 2018.

Update 3-18-21:

In response to a comment,  I have added 6 figures that are the images to the spreadsheet worksheets that I used to model these vehicles.  The inert masses for both stages are there,  along with full engine performance figures,  and choices for number of engines and  thrust settings.  Figures 1-3 are for the ordinary Starship-as-tanker to 300x300 circular,  300x7000 elliptical,  and 300x10,000 elliptical.  Figures 4-6 are for the dedicated tanker design for 300x300,  300x7000,  and 300x10,000.  

Figure 1 -- Ordinary Starship as Tanker, 300 x 300 km Circular

Figure 2 -- Ordinary Starship as Tanker, 300 x 7000 km Elliptic

Figure 3 -- Ordinary Starship as Tanker, 300 x 10,000 km Elliptic

Figure 4 -- Dedicated Tanker Design, 300 x 300 km Circular

Figure 5 -- Dedicated Tanker Design, 300 x 7000 km Elliptic

Figure 6 -- Dedicated Tanker Design, 300 x 10,000 km Elliptic

Reverse-Engineering Estimates: Starship Lunar Landings

This article picks up where Ref. 1 left off,  looking at direct lunar landings using a Starship refueled (fully) in Earth orbit.  That might require a lot of tanker flights,  something not investigated here or in Ref. 1.  The methods and assumptions mostly conform to those given in Ref. 2.  A brief list of selected orbital data is given in Fig. 1,  which includes the results initially determined for Ref.1.  All figures are at the end of this article. 

I chose to analyze a min-energy Hohmann transfer to the vicinity of the moon,  instead of the Apollo figure-eight orbit.  The Apollo trajectory,  while a slightly-shorter transfer time,  is more suited to entering low retrograde orbit about the moon.  The Hohmann trajectory is closer to the real 3-body result for a direct landing on the lunar near side.  The trajectory and related data are given in Fig. 2.  The variations in lunar distance from Earth are included,  labeled as “close”,  “average”,  and “far”. 

The actual mission uses a slightly-different return trajectory from the moon.  It is a min-energy Hohmann transfer ellipse,  but it is one that grazes the Earth’s surface at perigee.  That ensures a direct atmospheric entry and landing upon return to Earth.  Entry interface speeds are very near 11 km/s.  The rough locations for midcourse and terminal course corrections are shown with red stars in Fig. 3. 

The course correction burn delta-vees are figured from cross ranges at remaining-distances,  and speeds,  using the small angle approximation.  These are in Fig. 4,  and totaled into outbound and return course correction budgets for delta-vee.  Approximately,  dV = (V) (cross range)/ (remaining distance).

Fig. 5 shows the basic approaches to and from the moon,  viewed with respect to the moon,  plus where the gravitational loss factor comes from.  There is no drag loss factor at the airless moon.  This stuff gets used figuring the factored (mass ratio-effective) delta-vees to land,  and to take off. 

The landing and takeoff details have to include engine selections,  because for the touchdown and liftoff immediately adjacent to the moon’s surface,  the thrust vector control (TVC) capability afforded by the sea level Raptor engines is simply required!  The bulk of these burns can be accomplished with the vacuum Raptor engines,  farther from the surface,  at higher specific impulse.  This means there must be a shift from vacuum to sea level engines near the end of the landing burn,  and a similar shift from sea level to vacuum engines after the start of the takeoff burn. See Fig. 6. I guessed “the last 0.5 km/s”. 

Fig. 7 contains a multitude of useful data regarding burn delta-vees.  The departure burn from Earth orbit onto the transfer trajectory is not only figured for “close”,  “average”,  and “far” lunar distances,  but also for multiple choices of elliptical orbits about the Earth.  The landing burns and the takeoff burns at the moon depend only upon lunar distances, and not upon choice of Earth elliptic orbit.  Delta-vees are totaled in this figure as a measure of how demanding the mission is,  although with different engine specific impulses,  these are not values one can use to design vehicle mass fractions. 

The “right” way to estimate performance is with a burn record spreadsheet as illustrated by the image in Fig. 8.  This one has inputs for the vehicle weight statement that include separate entries for outbound and return payload.  The relevant engine performances for the two engine types are included as inputs (yellow-highlighted),  complete with max and min power setting data.  A linear model is computed between max and min settings,  for both thrust and specific impulse. 

There are 4 burns listed for the outbound journey,  and 4 more for the return journey.  There is an Earth orbit departure burn,  starting from max propellant load,  a burn representing the 2 course corrections,  the vacuum-engine portion of the landing burn,  and the sea level-engine portion of the landing burn.  For the return,  there is takeoff using the sea level engines,  then departure using the vacuum engines,  a burn representing the 2 course corrections,  and the terminal landing burn after atmospheric aerobraking entry,  with the sea level engines.  There are inputs for each of these 8 burns,  for the user’s selection of how many engines and what throttle setting to use (highlighted yellow).

Significant information or outputs are highlighted blue or green.  Lots of data are simply built-in,  including the worst-case delta-vees related to lunar distance effects.  That means the payloads indicated can be carried,  or perhaps very slightly more,  but never less.   The departure delta-vee associated with the elliptical orbit about the Earth is the main variable here,  besides outbound and return payload.  That departure input is also highlighted yellow,  located top right of worksheet.  Adjacent to it are records of the various inputs appropriate to the various elliptic orbits,  plus a results record for the payloads obtained with each of these departures.

The way this worksheet functions is a user iteration of outbound and return payloads (and the number of engines and their thrust settings),  until the propellant remaining at end of mission is a nonzero fraction of a ton.  Thrust setting affect specific impulse,  but it and the number of engines affects thrust/weight far more.  These thrust/weights need to meet the green-highlighted requirements shown.

I took the accumulated payload results (in the form of zero return payload) vs elliptic orbit apogee altitude,  and combined them with the payloads deliverable to those same orbits from Ref. 1,  and cross-plotted them below the vehicle performance analysis in this worksheet.  All of that is shown in the figure.   The curves cross at about 7000 km apogee altitude,  at about 75 tons delivered (with zero return payload).  The 10,000 km apogee altitude is associated with 59 tons delivered to orbit.  Using those 59 tons as the outbound payload to the moon from that 300x10,000 km orbit,  I found there was just enough propellant to bring 32 tons of payload back from the moon,  and then to land with it.

The 59 ton outbound with 32 ton return from 10,000 km apogee is depicted in Figure 9.  The 75 ton outbound with 0 ton return from about 7000 km apogee is depicted in Fig. 10.  The latter is more approximate,  being just read from the cross plot graph,  but it is “in the ballpark”.  Thus it would seem to be feasible to deliver significant tonnages to the moon with this Starship/Superheavy system,  but not the “100+ tons” advertised on the Spacex website for low Earth orbit and Mars.   The lunar mission is more demanding than the Mars mission,  because there is no refueling on the moon for the return.

Regardless,  the 7000-to-10,000 km apogee altitude is well within the Van Allen radiation belts!  The cargo delivered from orbits like this must be radiation-hardened.  Any crew (or passengers) will certainly require an effective radiation shelter somewhere aboard the vehicle. 

I did not investigate the tanker problem:  on-orbit refueling of Starship to the 1200 metric ton max propellant load!  Be aware that many tanker flights will be required,  especially since far smaller payloads (or transferable propellant) can be delivered to these high-apogee elliptic orbits. 

References (all located on this site)

#1. G. W. Johnson,  Reverse-Engineering Starship/Superheavy 2021,  dated 9 March 2021. 

#2. G. W. Johnson,  Fundamentals of Elliptic Orbits,  dated 5 March 2021.

Figure 1 – Summary List of Selected Data for Elliptic Orbits About the Earth

Figure 2 – Hohmann Min-Energy Transfer to the Moon for Direct Landings

Figure 3 – Actual Lunar Transfer and Return Orbit Data

Figure 4 – Figuring the Course Correction Budgets

Figure 5 – Direct Landing Approaches and Departures at the Moon

Figure 6 – Working Out Engine Selections and Delta-Vees for Lunar Landing and Takeoff

Figure 7 – Departure and Arrival Delta-Vees as a Function of Earth Orbit Choice and Lunar Distance

Figure 8 – Spreadsheet Image of Performance Estimator with Orbit Results Plot

Figure 9 – Pictorial Results for Direct Lunar Landing Mission with Return Payload

Figure 10 – Pictorial Results for Direct Lunar Landing Mission with No Return Payload

Reverse-Engineering Starship/Superheavy 2021

Update 3-14-21:

This and similar earlier articles were done to help define what the Spacex "Starship/Superheavy" design might be capable of achieving, once all its evident problems are solved.  While prototypes have begun to fly,  the design is obviously still quite immature.  Landing on a reinforced concrete pad is still a severe problem.  Landing on dirt is obviously completely out of the question.  Slosh and ullage in the propellant tanks still seems to be a problem,  as are leaks and unwanted engine bay fires.  Spacex has a long way to go before this design will be ready.   Yet its potential looms quite large.  So the massive effort that is needed would seem to be worth it. 

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I recently updated my reverse-engineering estimates for what a Spacex “Starship/Superheavy” vehicle can accomplish flying to circular low Earth orbit (LEO) from eastward launch.  These are based on the best available information about the vehicle from the Spacex website,  the Spacex user’s manual for flying on this vehicle,  what some observers have published for inboard profile details,  and what Wikipedia shows for details like inert masses. 

There is still a big difference between the Starship test flight prototypes Spacex is flying,  and its proposed orbital transport design.  This shows up in the inboard profile,  and in the landing legs.  The prototypes are presumed to be heavier in construction,  since data is still being obtained.  The hull forward of the propellant tanks is mostly empty,  whereas in the proposed transport vehicles,  those spaces are rigged for all-cargo,  passengers plus some cargo,  or extra tanks for a tanker version. 

Figure 1 compares the prototypes and the proposed versions,  giving the relevant data as appropriate.  All figures are at the end of this article.  Prototypes are flying on 3 sea level Raptor engines,  while the proposed flight vehicle has 3 sea level and 3 vacuum Raptor engines,  for a total of 6 engines.

Figure 2 gives similar pertinent data for the Spacex Superheavy booster design.  It depends upon the source as to how many sea level Raptor engines power this stage.  Currently Spacex says 28,  but in the recent past I have seen numbers as high as 33,  or even more (37 in one older presentation).  This is a critical issue for acceptable kinematics right off the launch pad.  Mr. Musk himself has said (in his Boca Chica presentation in front of a prototype) that he wants to see liftoff thrust/weight ratio close to 1.5. 

I have already reverse-engineered the performances of the sea level and vacuum Raptor engines.  This includes the full intended rated chamber pressure,  as well as throttled-back performance,  which is lower.  These numbers are included here as Figures 3 and 4.  The effects of altitude are included specifically,  at both max and min chamber pressure.  These engines share exactly the same powerhead.  They differ only in the expansion area ratio of their exit bells.  In the predicted performance tables listed in the figures,  shaded cells indicate flow separation due to excessive backpressure. 

The basic mission data are given in Figure 5.  The Superheavy booster gets flown back from the stage point,  while the Starship upper stage continues on to orbit.   The numbers are for an eastward launch.  The circularization burn for final orbit entry of the Starship upper stage is presumed included in the factored velocity requirement to orbit. 

The booster,  much lighter without the upper stage,  thrusts to kill the downrange velocity,  and for a little bit more speed,  both up-range and upward.  The idea is a net 45 degree upward trajectory,  coasting back toward the launch site on a more-or-less parabolic trajectory.  This will convert by drag to a downward fall toward “entry”,  which is really just hitting denser air and seeing larger wind pressures.  There is an entry burn to reduce speed down to near Mach 1 at fairly low altitude,  with subsequent fall to the landing burn from a presumed Mach 1 terminal velocity in the dense air.

There is a deorbit burn,  followed by hypersonic aerobraking,  with the Starship upper stage.  Once the entry hypersonics are over,  the vehicle assumes the “belly-flop” attitude to limit downward velocity.  At low altitudes,  broadside drag limits the fall velocity to quite modest values,  as already seen in prototype flight tests.  Near the surface,  the vehicle “flips” to vertical attitude by means of engine thrust (and aerosurface action),  and then lands retro-propulsively,  as the prototypes currently do.  

Figure 6 indicates how the gravity and drag losses were estimated,  and how they were apportioned among the various burns during the mission.  The booster ascent is initially vertical,  and bends near horizontal upon reaching the staging altitude,   which is essentially exoatmospheric.  I used the simplest means of estimating the gravity and drag loss totals,  and apportioned all the drag loss and most of the gravity loss to the booster stage burn.    This is in accord with the best recommendations of Ref. 1.

Figure 7 indicates exactly how the parabolic ballistic trajectory of the booster flyback was estimated.  The requisite horizontal and vertical velocity components,  which are equal at 45 degrees,  were determined from the required range (merely an educated guess here).  The net burn delta-vee sums this horizontal and the magnitude of the staging velocity,  for the horizontal component.  The vertical component is alone.  The “ideal” or kinematic delta-vee is the vector sum of those components.  To that,  the gravity loss estimate is added (there being no drag loss at altitudes that high). 

Figure 8 indicates the details of the booster flyback entry and landing burns,  including the assumptions made.  A potential energy difference to the presumed entry altitude is added to the kinetic energy coming out of the parabolic arc.  That is the kinetic energy at entry altitude in the absence of any drag loss.  Converted back to velocity,  the difference between that and the desired entry speed is the “ideal” or kinematic delta-vee for the entry burn.  This gets the estimated gravity loss added to it for the mass ratio-effective delta-vee.  The terminal speed at the surface,  factored up,  is the landing burn delta-vee.

Figure 9 summarizes which engines get used for each of the burns,  and what the estimated performance of the selected engines are,  at those conditions.  Note that the booster uses sea level Raptors,  sometimes at sea level,  sometimes in vacuum,  and an average of those two during its ascent toward the stage point.  For the entry burn,  I used the 50 kft (15 km) altitude performance values.

The upper stage spacecraft uses its vacuum Raptors during its ascent from stage point to orbit.  It uses a vacuum Raptor for the deorbit burn.  The landing burn is made with sea level Raptors operating at sea level.  Full thrust settings were presumed.

The figure indicates where vehicle thrust/weight ratio ought to be 1.5 (or more) to get acceptable kinematics in vertical flight against gravity.  It also indicates where the Spacex user’s manual (Ref. 2) says that vehicle accelerations should not exceed 6 gees.

One worksheet in the spreadsheet does the entire analysis.  Its image is given in Figure 10.  User inputs are highlighted yellow,  with significant results highlighted blue.  Pertinent comparison data are highlighted green.  This spreadsheet requires user iteration to achieve “closure”.  There are two variables that must be optimized:  the stage point velocity,  and the payload carried by the Starship upper stage.  Spacex advertises “100+ tons to LEO”.  This analysis indicates 171 tons might be feasible.

Instructions are on the worksheet;  these require first determining the stage point velocity such that the required ascent delta-vee equals what the stage can deliver.  That presumes zero propellant remaining after the booster flyback,  entry and landing.  You do this with some “reasonable” payload in the Starship upper stage. 

Once that is done,  you maximize the payload carried in the Starship,  such that its ascent delta-vee capability just matches the requirement.  This is done such that deorbit,  entry,  and landing results in zero propellant remaining,  when landing with the full payload.  That last covers the abort requirement if payload cannot be delivered and unloaded on orbit.  This is a highly-constrained analysis,  not general.

You may or may not have to readjust stage point velocity,  then payload,  to fully converge the analysis.

There are inputs for the number of Raptor engines operating in each stage for each of the pertinent burns.  The resulting estimated thrust/weight ratios are computed from these engine number selections and the appropriate thrust performances.  The best guesses for thrust/weight criteria are listed alongside those results. 

Results and Conclusions

This analysis indicates that Starship/Superheavy might be capable of delivering as much as 171 metric tons of payload to a low Earth orbit from an eastward launch.  Spacex claims “100+ tons”,  and these results indicate significantly more than that might well be feasible.  The previous analysis (Ref. 3) got a somewhat-lower payload number (still greater than 100 tons) for the same circumstances. 

This calculation determines the propellant requirement for Starship to deorbit and land,  and limits payload capability of the Starship to make sure there is propellant on board sufficient to make the landing.  It does this under the assumption that the full payload is carried back down to the landing,  in order to cover an abort possibility where payload cannot be offloaded before a descent is required.

Similarly,  the propellant required for the Superheavy booster stage to execute the flyback,  entry,  and landing is determined.  Then the staging velocity capability of the Superheavy is determined such that there is enough remaining propellant to land.  That determines the stage point velocity for the mission.  This is done with the ignition mass of the loaded Starship as the “payload” of the Superheavy.

These results are based on certain guesses for stage inert masses.  If there is growth in inert mass beyond that assumed,  it must come straight out of payload capability.  It is also based on maximum propellant loads for each of the stages.  Carrying less propellant reduces payload capability.  Or,  looked at another way,  reducing payload carried reduces the required propellant load.  That analysis is not done in this spreadsheet!  This is not a generalized performance-prediction analysis!

Possible Future Analyses

Sending Starship to an elliptical Earth orbit instead of low circular,  has been touted as the way to use Starship/Superheavy for trips to the moon and back,  without any refueling on the moon.  The velocity requirement to reach such an orbit is higher,  reducing the lunar payload capability below the estimate here.  That mission is challenging enough that return payload likely needs to be reduced,  or even zeroed.  This spreadsheet could be used to determine what payload might be delivered to that elliptic orbit.  The lunar mission itself needs to be analyzed separately,  not with this tool. Same for Mars.

References

#1.  Fundamentals of Elliptic Orbits,  dated 5 March 2021,  by G. W. Johnson,  located at http://exrocketman.blogspot.com  

#2.  Starship User’s Guide,  revision 1.0,  dated March 2020,  downloaded from Spacex.com as pdf

#3.  2020 Reverse-Engineering Estimates for Starship/Superheavy,  dated 25 May 2020,  by G. W. Johnson,  located at http://exrocketman.blogspot.com

Figure 1 – Best Available Data for “Starship”

Figure 2 --  Best Available Data for “Superheavy”

Figure 3 – Best Reverse-Engineered Model of the Sea Level Raptor

Figure 4 – Best Reverse-Engineered Model of the Vacuum Raptor

Figure 5 – Circular Low Earth Orbit Mission Characteristics (160-600 km Altitudes)

Figure 6 --  How the Gravity and Drag Losses Were Estimated

Figure 7 – Details for the Booster Flyback

Figure 8 – Details for the Booster Entry and Landing

Figure 9 – Engine Performance Assumptions For the Mission

Figure 10 – Spreadsheet Results for Mission Performance Estimates

Update 9 March 2021:

I copied and edited the worksheet to represent a 300 x 1400 km elliptic orbit.  Those changes are shown in Fig. 11.  The results are given in Fig. 12.  Payload reduces to 144 metric tons,  staging is unchanged.

Figure 11 – Orbit and Input Data Changes for 300 x 1400 km Elliptical Orbit

Figure 12 – Spreadsheet Results for 300 x 1400 km Elliptical Orbit

Looking at even higher elliptical orbits,  and assuming radiation dangers to cargo and crews can be addressed,  I found that about a 300x4000 km orbit reduces payload to about 103 metric tons,  with the same staging point.  Orbit data are in Fig. 13,  results are in Fig. 14.  

Figure 13 – Data Regarding the High Elliptical Orbit

Figure 14 – Results for the High Elliptical Orbit

Note that Spacex promises payload delivery of “100+ tons”.  What I found for the high elliptical orbit is pretty close to that figure.  The lower elliptic orbit has a higher max payload figure,  and the low circular orbit a higher max payload still.   This is summarized in Fig. 15.  Note also that radiation protection becomes a serious issue for apogees above 1400 km,  which puts the spacecraft in the Van Allen belts.

Figure 15 – Overall Results Summary for the 3 Earth Orbits

 Update 3-13-2021:

While pursuing use of Starship to perform unrefueled lunar landing missions,  I needed to analyze some higher-still elliptical orbits for Starship/Superheavy to reach.  These were a 5000 km apogee altitude,  a 10,000 km apogee altitude,  a 20,000 km apogee altitude,  and a 30,000 km apogee altitude.  Those results from the spreadsheet are given in Figures 16,  17,  18,  and 19,  respectively.  The trend is quite clear:  less and less payload can be delivered to orbit,  as the orbit apogee altitude increases. 

Bear in mind that the “base” of the Van Allen radiation belts is about 1400 km altitude (lower for the South Atlantic Anomaly).  All these orbits penetrate quite far into the radiation belts.  Radiation hardening of cargo,  and radiation shelter protection for any crew,  are simply required.    

Bear also in mind that all of these orbits (this update and earlier) were computed under the assumption that an abort back to the surface be feasible,  with full payload still aboard.  That does raise the landing propellant budget,  and it raises the landing thrust requirement.  

Figure 16 – Results for 300 x 5000 km Elliptical Orbit

Figure 17 – Results for 300 x 10,000 km Elliptical Orbit

Figure 18 – Results for 300 x 20,000 km Elliptical Orbit

Figure 19 – Results for 300 x 30,000 km Elliptical Orbit

 

The overall trend summarizes as the following table:

Orbit (km altitudes)                       max payload (metric tons)

300 x 300                                          171

300 x 1400                                        144

300 x 4000                                        103

300 x 5000                                        92

300 x 10,000                                    59

300 x 20,000                                    30

300 x 30,000                                    17

For those interested,  this spreadsheet I used to estimate Starship/Superheavy performance to these orbits is named “SS SH 2021”,  for my 2021 reverse-engineering estimates of Starship/Superheavy.  These calculations include booster flyback and recovery,  plus Starship deorbit and landing (recovery).  Each destination orbit has its own worksheet.  These are named (so far) as follows:

Orbit                                                  worksheet name

300 x 300                                          circ LEO

300 x 1400                                        ellip LEO

300 x 4000                                        high ellip

300 x 5000                                        5k apo

300 x 10,000                                    10k apo

300 x 20,000                                    20k apo

300 x 30,000                                    30k apo