Starship to Mars: faster than Hohmann transfer trajectories

[Twark_Main]

4) I agree that an aerocapture followed by a landing is probably safer for crewed missions than direct-to-EDL, but then you have periapse-raising delta-v, and a small entry burn.  I can't tell if that's included in their 200m/s "non-optimal Oberth effect" number or not.

You don't need these burns.

If you’re not coming straight in, then your periapse is down in the atmosphere. In theory, you could finish landing at the next periapse. In practice, the post-aerocapture orbital parameters aren’t known well enough to do that without a correction maneuver.

Correction, maybe.

What you proposed is raising the periapsis and then lowering the periapsis again.  This is (unnecessarily) digging a hole and filling it back in again.

6) My model is circular, with both planets in-plane, but that should make my model more optimistic, not less.  In order to get down to a speed of 7km/s at a 55km periapse altitude, I need an Earth departure angle (vs. Earth's orbital direction) of 42º, and time of flight is 3.7 months (112 days).  That's still terrific, but it's not as terrific as they're getting.

Technically a circular coplanar model isn't strictly more pessimistic (especially when it comes to arrival velocity, and especially at the better-than-average windows where Mars's radial motion is helping you), so I'm inclined (no pun intended) to trust the real orbits and poliastro.

Circular coplanar is usually more optimistic, not pessimistic.

Nope, not always true when it comes to the arrival velocity (hence why I say it's not "strictly" optimistic).

My model works by letting you allocate the delta-v budget how you like, letting you plug in a departure angle, using that to compute your angular momentum, which gives you your perihelion and your departure true anomaly. Now you can compute your arrival true anomaly by setting r = Mars, which gives you ToF, arrival angle, and arrival vInfinity, thereby avoiding needing a Lambert solver.

Solution: use a real Lambert solver. 

[sdsds]

Maybe given RTN coordinate system a try.

Hmm, good thought. Thanks!

FWIW the attached image shows where I got a few years back on optimal broken plane transfers. They're just difficult to visualize properly, at least in this inertial frame. (Note the z-axis scale exaggerates the inclination of Mars quite a bit.)

[TheRadicalModerate]

If you're not coming straight in, then your periapse is down in the atmosphere. In theory, you could finish landing at the next periapse. In practice, the post-aerocapture orbital parameters aren't known well enough to do that without a correction maneuver.

Correction, maybe.

What you proposed is raising the periapsis and then lowering the periapsis again.  This is (unnecessarily) digging a hole and filling it back in again.

That's the price of aerocapture.  You dive into the atmosphere and, when you come back out, you raise the periapse to make sure you're in a stable orbit.  If/when you decide to land, you have to lower it again.

If you're certain enough of your nav and can afford to scrub all the velocity off at once, do a direct EDL.

[Twark_Main]

3) Most likely, we need to go even lower, at the same speed, to get denser air.  This increases the negative lift we need by a little bit, because the centrifugal acceleration increases faster than the gravitational acceleration does, but we're only changing the radius by small percentage.  (Mars is small, but it's not small in relation to the altitudes we're using.) The extra lift is almost negligible.

But denser air at the same velocity is going to heat up more.  It's not terrible:  The heating rate is proportional to the square root of the density.  But the heating rate that melts the vehicle is down there somewhere.

To do a better solution, we'd need to find the density that gives us the extra (negative) lift we need, reverse lookup that density to find the altitude, and then iterate until the centrifugal acceleration converges.  Then you have to decide if you can live with that heating rate.  If not, you can't enter that fast.

Bottom line:  The charts below are probably fairly accurate in terms of G forces on the crew and vehicle, but the altitude will be lower, and peak heating will be higher. 

Thanks, exactly what I was hoping for!

If we line up the G-forces for the Moon Return to the Mars Entry, the Mars Entry as a max velocity of 6.5km/sec if we limit our selves to the same G-force as a Moon Return entry of 11km/sec.

Less than I would have expected.  Ouch.

It seems like we have enough information to examine this, if we take the benchmark of Starship as return-from-Moon at 11km/sec, we can solve these two equations where we set F to be equivalent for our Mars and Earth entries and solve for p

F  pv²
q_dot  p^0.5 x v³

 p_earth * v_earth² =  p_mars * v_mars²

p_mars / p_earth = v_earth² / v_mars²

which is 11² / 6.5² ~= 3.  We need three times the density on Mars to get the same force (and thus same acceleration).

at 60km, 0.0001 kg/m³ means we need 0.0003 kg/m³  on Mars

so relative q_dot on Earth is 13.31 and relative q_dot on Mars is 4.76, or 2.8x less heating on Mars

if you plug in a constant force or pv² = constant, you get density is inversely proportional to velocity squared, and if you plug that into the q_dot proportional equation you get q_dot  v²

in other words we can do entry on Mars faster than 6.5km/s, but the limit won't be heating it'll be G-load.

It's a shorter soak on Mars in terms of G-load and heating, so that might help us go a little faster.

3Gs seems reasonable, given that on launch our astronauts experience that, so that corresponds to 7.25km/sec.

Does this math account for the fact that Mars has a much smaller radius than Earth?

I would've expected to find a factor of 0.533 somewhere in there, but I may have missed something.

[Twark_Main]

If you're not coming straight in, then your periapse is down in the atmosphere. In theory, you could finish landing at the next periapse. In practice, the post-aerocapture orbital parameters aren't known well enough to do that without a correction maneuver.

Correction, maybe.

What you proposed is raising the periapsis and then lowering the periapsis again.  This is (unnecessarily) digging a hole and filling it back in again.

That's the price of aerocapture.  You dive into the atmosphere and, when you come back out, you raise the periapse to make sure you're in a stable orbit.  If/when you decide to land, you have to lower it again.

That's only one type of aerocapture.  Aerocapture in general has no requirement to enter (and then leave) a stable orbit.

If you're certain enough of your nav and can afford to scrub all the velocity off at once, do a direct EDL.

If you're certain enough of your nav and can't afford to scrub off the velocity all at once (eg because you want to get as much performance out of the hardware as possible, or reduce risk as much as possible), then you can do a aerocapture with no orbit raising and lowering burns.

[Vultur]

But haven't some crew vehicles pulled much higher Gs?

Also, are we talking peak G load or sustained? For peak, I think New Shepard is fairly high and they fly very elderly passengers.

The crew will have spent 3-4 months in microgravity before landing. Unlike a return to Earth, they�ll have no ground support staff to help them adjust to gravity after they land.

The good news is that they�re only in 1/3G. But they�ll want to be pretty conservative about crew health.

IDK. During the g load of reentry, people will presumably be well strapped in. Breaking bones or whatever shouldn't be possible, even after microgravity effects, unless something is done very very wrong. So what difference does it make they've been in microgravity before that? They are not exercising or needing to move under the Gs.

(And yeah they are dealing with much lower gravity on Mars, so I don't think deconditioning from microgravity would be as significant as we'd expect from Earth experience.)

I would also expect people going to Mars to be relatively young (say under 50 and probably median age 30 or less) and quite healthy.

[TheRadicalModerate]

If you're certain enough of your nav and can't afford to scrub off the velocity all at once (eg because you want to get as much performance out of the hardware as possible, or reduce risk as much as possible), then you can do a aerocapture with no orbit raising and lowering burns.

If you wish to descend to pendantry crush-depth, sure.  But for short-ToF trajectories (the topic), I can't imagine a case where you're deep enough into the atmosphere to capture (i.e., exit below escape speed), but you're willing to do subsequent aerobrakes using that deep periapse.  You're pretty much guaranteed to enter on the next periapse.

If you're that strapped for delta-v, then use a longer ToF, with a lower-energy transfer.

[Twark_Main]

If you're certain enough of your nav and can't afford to scrub off the velocity all at once (eg because you want to get as much performance out of the hardware as possible, or reduce risk as much as possible), then you can do a aerocapture with no orbit raising and lowering burns.

If you wish to descend to pendantry crush-depth, sure.  But for short-ToF trajectories (the topic), I can't imagine a case where you're deep enough into the atmosphere to capture (i.e., exit below escape speed), but you're willing to do subsequent aerobrakes using that deep periapse.

Why "subsequent aerobrakes?" The next pass is going to be direct entry. This isn't Mars Reconnaissance Orbiter. We're reentering, so the vacuum periapsis altitude should be well within the Martian atmosphere.

If you're that strapped for delta-v, then use a longer ToF, with a lower-energy transfer.

It's not that you're "strapped" for delta-v. That's the wrong mental model.

You want to use every available advantage. That's what SpaceX does, and it's the right thing to do.

Your low-ToF trajectory can be even shorter for the same fuel (or less fuel for the same ToF) if you use one-pass aerocapture instead of direct entry. Two-pass is almost never worth it, because that initial aerocapture pass is the limiting case.

[TheRadicalModerate]

I cleaned up my circular coplanar model as much as I could.  It's shared here.  It's still cryptic as hell, and I can't 100% guarantee its accuracy.

The two cases showed are Earth-to-Mars as faster as possible, with a direct EDL, and Mars-to-Earth. 

In the latter case, I really can't see anybody being allowed even to aerocapture, to say nothing of direct EDL, using a Ship that's sat on the martian surface.  Even if the crew were to transfer to a Cat III-compliant Ship in LMO, they're still potentially infected with the Space Plague; you don't want their only-partially-charred bodies falling into the ocean.

So I computed a propulsive capture case, using the same extremely optimistic mass estimates in the paper.  For a type 1 transfer, it's still less than 6 months to an ISS-like stable orbit, where the crew can sit out their quarantine.

I guess some day everybody will be comfy with the non-existence of the the Martian Space Plague, and you can do zippy transfers.  I wouldn't hold my breath, though.

PS:

FWIW, when I plugged in more reasonable vehicle parameters (155t dry, 60t crew, 1450t boiling prop, 367s avg. Isp, still 650m/s for landing, and max periapse speed of 7500m/s), I get 125 days ToF, with 2340m/s of delta-v for propulsive braking. 

4.2 months.  That's still pretty good.

[TheRadicalModerate]

You want to use every available advantage. That's what SpaceX does, and it's the right thing to do.

Your low-ToF trajectory can be even shorter for the same fuel (or less fuel for the same ToF) if you use one-pass aerocapture instead of direct entry. Two-pass is almost never worth it, because that initial aerocapture pass is the limiting case.

No, you don't.  Two cases:

1) You're carrying cargo, in which case:  who cares about ToF?

2) You're a crewed mission.  But there's no way you're exiting from an aerocapture with any idea what your orbital parameters are.  If it were just a question of apoapse, it might be reasonable to consider a one-orbit entry.  But the aerodynamic forces on the vehicle during capture are going to change your orbital plane (both inclination and RAAN), rotate your apse line, produce an uncertain apoapse, and even change the periapse a bit. 

Nobody in their right mind would do a one-orbit entry.  At the very least, you'd have to have a contingency to stabilize the orbit if you can't compute your parameters and clean them up before the entry.  And if you have the prop for the contingency, why not just use it?

I think it'd be easier to do a direct EDL than a one-orbit aerocapture+EDL.  At least then you can use terrain to navigate.

[Twark_Main]

You want to use every available advantage. That's what SpaceX does, and it's the right thing to do.

Your low-ToF trajectory can be even shorter for the same fuel (or less fuel for the same ToF) if you use one-pass aerocapture instead of direct entry. Two-pass is almost never worth it, because that initial aerocapture pass is the limiting case.

No, you don't.  Two cases:

1) You're carrying cargo, in which case:  who cares about ToF?

For cargo missions you're using the one-pass aerocapture to maximize payload mass, not minimize ToF.

2) You're a crewed mission.  But there's no way you're exiting from an aerocapture with any idea what your orbital parameters are.  If it were just a question of apoapse, it might be reasonable to consider a one-orbit entry.  But the aerodynamic forces on the vehicle during capture are going to change your orbital plane (both inclination and RAAN), rotate your apse line, produce an uncertain apoapse, and even change the periapse a bit. Nobody in their right mind would do a one-orbit entry.

Those JPL control theory folks sure are amazing, aren't they? 

  At the very least, you'd have to have a contingency to stabilize the orbit if you can't compute your parameters and clean them up before the entry.

"Compute your parameters" is effectively instant and real-time with modern IMUs and Sun/star trackers.

"Clean them up before entry" is a single burn at apoapsis, if necessary.  A handful of meters per second, I'd expect. The required burn can be computed in milliseconds on a smartwatch.

So no, you really don't need such a contingency.

  And if you have the prop for the contingency, why not just use it?

A) because then you have less contingency propellant margin for landing later.

B) because you're unnecessarily adding orbits, increasing schedule costs and operational complexity.

C) if you can save prop, why not save it?   

I think it'd be easier to do a direct EDL than a one-orbit aerocapture+EDL.  At least then you can use terrain to navigate.

The only time you can use TRN at the very end, after all the major aerodynamic maneuvers are done and you're close to the landing site.  It's for fine-tuning at the end.  If the open-loop GNC wasn't able to get Starship near the landing site (through the plasma of reentry), the TRN wouldn't matter.

If you're biased toward direct entry it's only because it's more familiar, not because it's technically any easier. All the same coupled control dynamics that you worry about during aerocapture....  you also need to solve those problems for direct entry. 

[Twark_Main]

Two-pass aerobraking is also the plan of record, last time we heard an update on the question.

https://www.twitter.com/elonmusk/status/1176566245925085184

For sure more than one pass coming back to Earth. To Mars could maybe work single pass, but two passes probably wise.

[TheRadicalModerate]

For cargo missions you're using the one-pass aerocapture to maximize payload mass, not minimize ToF.

If you have a low arrival v∞, there's nothing to be gained by two-pass.  Just go straight in and have done with it.  And if you're worried about straight-in having nav problems, aerocapture into an orbit with a low apoapse, so raising to a safe periapse doesn't cost you very much.  (55 x 300 to 200 x 300 costs 36m/s.)

"Compute your parameters" is effectively instant and real-time with modern IMUs and Sun/star trackers.

Around Mars?  After slamming things around during aerocapture?  With little or no PNT support?

"Clean them up before entry" is a single burn at apoapsis, if necessary.  A handful of meters per second, I'd expect. The required burn can be computed in milliseconds on a smartwatch.

It's only an apoapse burn if the intersection of your current plane and the target plane is at apoapse.  That only happens for an inclination change if apoapse is also on one of the (Mars-relative) nodes, and for a RAAN change if apoapse is over the poles.  Neither of those is likely to be true.�

As for the apse line rotation (changed argument of periapse), that's least efficiently done at apoapse, most efficiently at periapse.

A) because then you have less contingency propellant margin for landing later.

Contingency prop is additive.  You budget for worst-case.  That's a worst-case "oops we need to raise periapse and figure this out" in addition to "oops, we're starting the flip-and-burn higher, and/or spending more time hovering looking for a good spot".

B) because you're unnecessarily adding orbits, increasing schedule costs and operational complexity.

Then go straight in.

C) if you can save prop, why not save it?

You're not saving prop if you have to budget it for contingencies.  It just means that you're landing heavier.


The heart of our disagreement is:

1) How much the intended post-aerocapture orbital parameters get torqued around by the vagaries of the aero environment.

2) How hard it is to do the observations to compute trajectory corrections with adequate precision in half a post-capture orbit.

3) Whether you can do all of those corrections with a single apoapse burn.

Convince me that the answer to these are "not very much", "easy", and "an apoapse burn is good enough", and I'll cry "uncle".

_______
�I'm trying to decide if it's possible to engineer your capture so that apoapse is normal to your desired orbital plane.  It doesn't seem like a natural consequence of capture, but maybe there are ways of putting a little english on your initial aerocapture corridor to get the apoapse closer to normal to the target plane.  Of course, "putting a little english" on your capture sounds like an excellent way to have larger nav residuals when you pop out.

[sdsds]

On the topic of these specific opportunities in the 2030's I'm wondering if they're created by times when the inclinations of the planetary orbits are aligned. I suppose the other possibility has to do with the eccentricity of the Mars orbit, but that seems less likely.

To get a sense of it I compared the window in 2026 with the one in 2033, looking only at the departure vinf requirements. For a given vinf limit the shortest duration transits differ by almost a factor of 2!


Departure window: 26-10-08 - 26-12-31
Arrival window: 27-06-30 - 28-02-29
Departure vinf Limit 3500.0
Shortest duration transit:
Departs Earth 26-11-11
Arrives Mars 27-07-08
Transit duration 238.82 days

Departure window: 33-02-23 - 33-06-02
Arrival window: 33-08-12 - 34-03-29
Departure vinf Limit 3500.0
Shortest duration transit:
Departs Earth 33-04-12
Arrives Mars 33-08-23
Transit duration 132.44 days

[Robotbeat]

so relative q_dot on Earth is 13.31 and relative q_dot on Mars is 4.76, or 2.8x less heating on Mars

You can probably go higher than 2G (what the 12km/s Earth entry says).  I'd think they'd be OK at 3G.  And I'm surprised that qdot doesn't get your first.

Your math looks OK, but I didn't grok the fullness. (Seems I'm having a Heinlein cliche day today...)  I had a slightly different plan in mind for determining an equivalent altitude to generate the needed lift.  I'll post it when it's done.

Let's go by intuition.  At the same deceleration, it takes the same time to go from 11km/sec to 10km/sec as it does from 8km/sec to 7km/sec

The former requires shedding for a 150t vehicle 9 - 7.5 = 1.5TJ.   The latter requires 4.8 - 3.7 = 1.1TJ.

so intuitively it makes sense there's less heat when slowing down the same amount at a lower velocity.

Thus it's limited by G-loading.  For reference

Shuttle: 3G (on launch)
Falcon-9/Dragon: 4.5G (launch, reentry is less)
Starship: 3G (on launch)

so somewhere in the 3-3.5 range is likely the limit.

Nah, higher g loading is fine. Starship and Super Heavy experience high gee loading during reentry and/or landing or near the end of burns. Humans can withstand high gee loading. These limits are no lethal limits, but limits for pilot consciousness (thus are somewhat conservative). Humans can withstand like 8 gees in the right orientation for over 30 seconds (the limit of the graph). 5-6 gees for minutes is doable, and multiple pass entry is also feasible (although the first pass is still a limiting factor, of course).

“Intuition” is just pessimism in this case. 11-12km/s periapsis speed is feasible, maybe higher depending on duration and countermeasures.

[Robotbeat]

If you're certain enough of your nav and can't afford to scrub off the velocity all at once (eg because you want to get as much performance out of the hardware as possible, or reduce risk as much as possible), then you can do a aerocapture with no orbit raising and lowering burns.

If you wish to descend to pendantry crush-depth, sure.  But for short-ToF trajectories (the topic), I can't imagine a case where you're deep enough into the atmosphere to capture (i.e., exit below escape speed), but you're willing to do subsequent aerobrakes using that deep periapse.  You're pretty much guaranteed to enter on the next periapse.

If you're that strapped for delta-v, then use a longer ToF, with a lower-energy transfer.

This is a bad argument. You�re always strapped for delta-v. You can�t calculate the limit of something by insisting on some arbitrary conservatism. The point of this thread to look at fast time of flight, not to design a conservative architecture.

Calculate the limit given your /actual/ constraints. THEN decide whether or not it�s worth it. That�s the only sensible way. No point fudging constraints halfway in as that just muddies the analysis.

[Vultur]

Nah, higher g loading is fine. Starship and Super Heavy experience high gee loading during reentry and/or landing or near the end of burns. Humans can withstand high gee loading. These limits are no lethal limits, but limits for pilot consciousness (thus are somewhat conservative). Humans can withstand like 8 gees in the right orientation for over 30 seconds (the limit of the graph). 5-6 gees for minutes is doable, and multiple pass entry is also feasible (although the first pass is still a limiting factor, of course).

That's closer to what I would expect. (wasn't Apollo's peak something like 10 g?)

If the limits are set by blackout, not structural damage, would deconditioning from zero g on the Earth-Mars cruise affect them at all?

(For that matter, if the flying is totally automatic, does blackout even matter?)

So while we probably can't expect Apollo era test pilot level gs, I'd be really surprised if 5 g was a problem at all.

[TheRadicalModerate]

This is a bad argument. You�re always strapped for delta-v. You can�t calculate the limit of something by insisting on some arbitrary conservatism. The point of this thread to look at fast time of flight, not to design a conservative architecture.

Calculate the limit given your /actual/ constraints. THEN decide whether or not it�s worth it. That�s the only sensible way. No point fudging constraints halfway in as that just muddies the analysis.

It's perfectly reasonable to circumscribe the use of fast ToF to missions that actually need fast ToF.  That pretty much restricts it to human missions.  Human missions simply require more safeguards.  One of those safeguards should be that, post-aerocapture, you need enough spare delta-v to make the vehicle safe in Mars orbit.  The bare minimum is to lift its periapse to a point where it won't reenter if correction maneuvers take longer than one orbit.

Two options:

1) At the first apoapse, your nav is good enough, and the errors in orbital parameters are small enough, that you can do a single burn to put the vehicle into the entry corridor.

2) If you're having trouble nailing down your parameters, or if they're off enough that a single burn can't manage the correction, then you need to raise your periapse and reserve enough delta-v to get the crew onto the surface.

For early missions, that second restriction requires that you trade ToF risks (radiation, micro-g, and plain ol' bad stuff that happens in deep space) against entry risks (e.g., a very bad corridor, or landing so far away from your pre-positioned supplies that your mission is compromised, possibly with the crew dying).  For later missions, when there are assets on the ground that can rescue you, maybe you can afford a narrower delta-v margin.

[InterestedEngineer]

This is a bad argument. You�re always strapped for delta-v. You can�t calculate the limit of something by insisting on some arbitrary conservatism. The point of this thread to look at fast time of flight, not to design a conservative architecture.

Calculate the limit given your /actual/ constraints. THEN decide whether or not it�s worth it. That�s the only sensible way. No point fudging constraints halfway in as that just muddies the analysis.

It's perfectly reasonable to circumscribe the use of fast ToF to missions that actually need fast ToF.  That pretty much restricts it to human missions.  Human missions simply require more safeguards.  One of those safeguards should be that, post-aerocapture, you need enough spare delta-v to make the vehicle safe in Mars orbit.  The bare minimum is to lift its periapse to a point where it won't reenter if correction maneuvers take longer than one orbit.

Two options:

1) At the first apoapse, your nav is good enough, and the errors in orbital parameters are small enough, that you can do a single burn to put the vehicle into the entry corridor.

2) If you're having trouble nailing down your parameters, or if they're off enough that a single burn can't manage the correction, then you need to raise your periapse and reserve enough delta-v to get the crew onto the surface.

For early missions, that second restriction requires that you trade ToF risks (radiation, micro-g, and plain ol' bad stuff that happens in deep space) against entry risks (e.g., a very bad corridor, or landing so far away from your pre-positioned supplies that your mission is compromised, possibly with the crew dying).  For later missions, when there are assets on the ground that can rescue you, maybe you can afford a narrower delta-v margin.

On later missions fallback to orbit and get rescued  from the Mars surface is a viable option once ISRU is set up.

[TheRadicalModerate]

On later missions fallback to orbit and get rescued  from the Mars surface is a viable option once ISRU is set up.

Yes.  But that lets you eliminate the orbital correction delta-v, not the periapse-raising delta-v.  On early, pre-ISRU missions, you need both if you're going to aerocapture.

I don't know how to quantify the error for either straight-in EDL or aerocapture.  I also don't know which method is likely to generate more error.  My intuition is that straight-in EDL creates more error early in the entry, but Starship may be able to correct that aerodynamically when terrain-matching finally locks in.  On the other hand, aerocapture is never going to get a chance to terrain-match, and there's not much correction you can do on the way out of the atmosphere.  So:

if (TRN can correct <3-to-4-sigma direct entry/descent errors�) {
   straight-in EDL;
   deltaVreserve = landing only;
} else if (no rescue available) {
   if (apogee burn can correct <3-to-4-sigma aerocapture errors) {
      aerocapture;
      corridor correct at first apoapse;
      EDL on next periapse;
      deltaVreserve = correctionFor3to4sigmaErrors + landing;
   } else {  // apogee burn not reliable enough
      raise periapse;
      do the set of burns necessary to clean up the corridor;
      EDL when ready;
      deltaVreserve = periapseRaise + correctionFor2to3sigma + landing;
} else {  // rescue available
   if (error < 2-to-3-sigma) {
      correct at apoapse;
      EDL on next periapse;
   } else {
      periapse raise;
      wait for rescue;
   }
   deltaVreserve = max(periapseRaise, correctionFor2to3sigma + landing);
}

________
�Feel free to choose your own error tolerances.  IMO, a 99.7-to-99.99% chance of not dying is adequate for the no-rescue cases.  For the rescue cases, you pick your error tolerance by the risk that you'll have to spend expensive prop retrieving a crew from orbit.  A <5% chance of spending the prop seems about right.