Tug-Assisted Arrivals and Departures

Bear in mind that I am no expert in orbital mechanics,  and I have no computer codes to analyze 3-body problems.  But I do understand the basics of 2-body problems,  especially elliptical orbits,  fairly well.  There are simple formulas for those.  That is the basis for the discussion topic here.

It is one thing to build and fuel a large craft in low Earth orbit.  It is quite another to propel it from there onto an interplanetary trajectory.  The velocity requirement is to reach a speed somewhat over escape,  from only circular orbit speed. 

The math says that escape speed is larger than circular orbit speed by a factor of the square root of 2,  or about 1.414.  For Earth,  that is about 11 km/s for escape, and about 8 km/s for circular orbit,  with the velocity requirement being the difference,  at about 3 km/s.  To depart, we actually need a bit more than that 3 km/s difference,  because we actually need to exceed escape speed.

By using a space tug and an extended elliptical orbit about the Earth,  that velocity requirement on the departing spacecraft can be substantially reduced.  The space tug is only reusable if it ends up remaining in that extended ellipse,  from which it can then return to low circular orbit.

Geometrically,  the situation is symmetrical,  so that this concept also works for arrivals from interplanetary trajectories.  But the sequence of events that must happen is not symmetrical,  so the arrival trajectory plan cannot be the exact mirror reverse of the departure trajectory plan. 

The example here is for Earth,  using low Earth orbit as the basis,  as this is the most easily reached orbit for launches from the surface.  But the same arguments and math apply to departures and arrivals at any planetary body!  Only the numbers are different. 

Let us start with the arrival scenario depicted as sequential sketches in Figure 1.  The arriving craft is coming in on a hyperbolic path with respect to the Earth,  with its perigee specifically located at low Earth circular orbit altitude,  and a speed at perigee somewhat larger than Earth escape speed at that same altitude. 

As the arriving craft reaches its hyperbolic perigee,  it must impulsively make a modest speed reduction (delta-vee,  or dV) to slow to a speed just under Earth escape speed at that altitude.  That puts it onto an extended elliptical orbit about the Earth,  instead of continuing on into deep space. 

The space tug that is going to retrieve this craft from that extended elliptical orbit is not already on that ellipse,  and in fact cannot be on that ellipse!  It must be somewhere on the low circular orbit with the short period of about 90 minutes.  The extended ellipse has a much longer period near 4 (or even 5) days! 

Because the timing of the craft’s arrival into that extended ellipse,  relative to where the tug is located on that low circular orbit,  is not something that can be controlled,  the tug could be “anywhere” around that circular orbit!  It will pass the ellipse perigee point multiple times,  while the arriving craft makes one circuit about the extended ellipse. 

There will be one tug circuit about the circular orbit where it and the arriving craft are both very near each other at the ellipse perigee,  at the same time!  That is where the tug must fire its propulsion to accelerate impulsively to ellipse perigee speed,  thus matching both position and velocity with the arriving craft.  The closer the orbit period ratio is to an integer,  the closer together this rendezvousing pair of vehicles will be,  and the lower the required rendezvous dV budget.

Actual rendezvous and docking take a finite interval that is not trivial!  The two can dock,  but by the time that is accomplished,  they will no longer be anywhere near the ellipse perigee point!  The docked pair must complete another circuit about the ellipse.  When they reach ellipse perigee the second time,  the tug can decelerate the docked pair into low circular orbit,  precisely because the perigee altitude is preserved by making burns there,  and not anywhere else along the orbit. 

From there,  normal rendezvous procedures can be used to reach any desired orbital station or facility.

Figure 1 – The Arrival Scenario

The departure scenario sequence of sketches is given in Figure 2.   The difference in the event sequence is that the departing craft and the tug are docked together when this scenario starts!  They must only wait in circular orbit until the geometry lines up with the intended departure path,  and then the tug fires to bring the docked pair to the perigee speed of the extended ellipse. 

They undock as that burn terminates,  and the departing craft immediately makes its modest burn to reach the intended departure speed.  Meanwhile,  the tug just coasts one circuit about the ellipse.  When it reaches perigee,  it can decelerate back into low circular orbit. 

From there,  standard rendezvous procedures can return the tug to any desired orbital station or facility.  Starting out docked together is precisely what provides the proper timing of the departure events sequence,  that is inherently lacking during the arrival sequence!  Undocking and moving away a short distance,  for departure burn safety,  is something that only takes several seconds,  not the several minutes to an hour or so,  for close-in rendezvous and docking. 

Figure 2 – The Departure Scenario

For the sake of argument,  presume the following data:

Vcirc = 7.8 km/s

Vesc = 11.0 km/s

Vper = 10.9 km/s

Vdep = 11.5 km/s = Varr

Those values produce the following departure results:

 

Laden tug dV = Vper – Vcirc = 3.1 km/s

Craft departure dV = Vdep – Vper = 0.6 km/s (unassisted this is 3.7 km/s)

Unladen tug back to circular dV = Vper – Vcirc = 3.1 km/s

They produce similar results values for the arrival scenario,  reflecting the geometric symmetry:

Craft arrival dV = Varr – Vper = 0.6 km/s (unassisted this is 3.7 km/s)

Unladen tug onto ellipse dV = Vper – Vcirc = 3.1 km/s

Laden tug back onto circular dV = Vper – Vcirc = 3.1 km/s

To these figures one should add some dV budgets for rendezvous and docking for the tug,  likely near 0.2 km/s for each such maneuver.  For departure,  there is likely only one such maneuver,  conducted unladen,  as the tug returns to the appropriate facility in low orbit.  For the arrival scenario,  there are likely two such maneuvers:  one unladen to rendezvous and dock with the craft in the extended ellipse,  the other laden to rendezvous (and dock) the docked pair with the appropriate facility in low orbit.  This reflects the decided asymmetry of the events sequences and circumstances,  for arrival versus departure.

For the departure scenario,  the tug sees these dV requirements in the listed order:

Laden onto ellipse                        dV = 3.1 km/s  (this is the total,  and it is done first!)

Unladen back to circular              dV = 3.1 km/s

Unladen rendezvous and dock     dV = 0.2 km/s

Total unladen                                dV = 3.3 km/s (second)

For the arrival scenario,  the tug sees these dV requirements in the listed order:

Unladen onto ellipse                    dV = 3.1 km/s

Unladen rendezvous and dock     dV = 0.2 km/s

Total unladen                                dV = 3.3 km/s (first)

Laden back onto circular              dV = 3.1 km/s

Laden rendezvous and dock         dV = 0.2 km/s

Total laden                                    dV = 3.3 km/s (second)

Either way,  the interplanetary craft sees the same departure and arrival dV requirements:  some 0.6 km/s for both of these scenarios.  The weight statements for these cannot be the same,  so you cannot simply sum the dV’s,  as neither scenario (as described) includes operations,  any staging,  or any refueling,  at the destination.  All of those are set by the overall mission design.

As for the tug,  the laden vs unladen weight statements are drastically different,  so you cannot sum the laden and unladen total dV’s for one simple rocket equation calculation.  Those must be two separate but linked rocket equation sizing calculations.   And the order in which the events occur controls the linkage between the calculations!  That linkage is via the weight statements.

The asymmetry of the events sequence also shows up in how many times the craft and the tug must each go around the ellipse. 

For the arrival sequence,  the craft will go around the ellipse either 0 (unlikely) or 1 time,  before the tug can enter the ellipse with it.  Then the docked pair go around the ellipse a second time,  for either 1 (unlikely) or 2 (likely) total ellipse circuits on arrival for the craft,  and just 1 for the tug.

In contrast,  for the departure sequence,  the craft never goes around the ellipse at all,  and the tug must go around once. 

What if the departure/arrival speed requirement is higher?

A higher departure/arrival speed requirement than the nominal 11.5 km/s discussed above,  just means the difference between those arrival/departure speeds from 11.5 km/s,  simply adds directly to the interplanetary craft dV requirement.  There is no change to the tug dV requirements,  because the actual departure/arrival speed is not part of its dV requirement calculations.  Those only figure into the interplanetary craft dV requirements. 

What would affect both is electing a different extended ellipse from the 10.9 km/s perigee speed used for this discussion.  For that reason,  it is recommended that for any given mission to be designed,  first you pick a low circular orbit and get its speed and period.  You don’t really need escape speed at that altitude,  except as a check value (arrival/departure must be higher than that).

Then pick an extended ellipse such that its perigee is at the low circular altitude,  and its period is an integer multiple of the circular period.  Then get its perigee and apogee speeds.  I would recommend apogee altitudes almost out to the moon,  in order to get perigee speeds up as close as you can,  to escape at perigee altitude.  That is the way to reduce (as far as is possible) the dV requirement on the interplanetary craft. 

Analyze separately what your near-Earth departure/arrival speed requirement is,  for the interplanetary mission that you want to fly.  The formulas for the dV’s to be figured,  are given in the text right after Figure 2 above. 

Final Remarks

The topic here has been propulsive arrivals and departures,  assisted by a space tug.  For arrivals only,  there is also the possibility of the craft aerobraking in a pass down in the atmosphere,  such that it is on an extended ellipse as it leaves the atmosphere.  However,  this is not without propulsive burn requirements on the part of the arriving craft,  so it is no “freebie”. 

First,  at the ellipse apogee,  the craft will have to make a small burn posigrade to lift the ellipse perigee up out of the atmosphere and yet further to circular orbit altitude.  This is to avoid an unintended entry on the next perigee pass. 

Second,  the craft will have to make some sort of modest burn on the next raised perigee pass,  to get the “right” apogee,  such that the ellipse period is an integer multiple of low circular orbit period. 

Third,  bear in mind that peak heating starts before peak deceleration gees in any sort of entry,  and the gees required here are significant,  meaning the pass has to go deep in the atmosphere.  In turn,  that means the peak heating on this type of a deceleration pass will be of similar magnitude to that of a direct entry!  And that means the vehicle must be fairly compact,  have no parallel-mounted nacelles or other structures,  and must be protected by what amounts to a fully-capable direct entry heat shield.  Those are very restrictive design requirements!

Once these orbital adjustments are made by the arriving craft,  then the tug rendezvous-and-assist back to circular can proceed,  exactly as described above.  (There is no such aerobraking thing for departure,  though.)

For more details about aerobraking deceleration and elliptic capture,  please see my article “Elliptic Capture”  on this site,  dated 1 October 2024.

Update 12-8-2024:

There’s no real difference between the results for the presumed data used above in this article,  and more exact data obtained from analyzing the elliptical orbits problem,  in this case automated with the “orbit basics.xlsx” spreadsheet that I created for 2-body ellipse problems. 

Figure A is an image of a portion of the spreadsheet results,  showing both low circular and a particular extended ellipse.  Figure B is a not-to-scale sketch of those orbital results,  explicitly showing the important velocity data.  Figure C has a table of computed delta-velocity (dV) data from these results,  for an arbitrary set of departure speeds.  All figures are at the end of this update. 

The first lesson here is that presumed data in the article give almost exactly the same dV to get back and forth between the circular and extended ellipse orbits:  3.103 versus 3.1 km/s.  Therefore the above article’s results are actually quite accurate. 

The second lesson here is that it is not very hard to determine an extended ellipse whose period is an integer multiple of the period of the low circular orbit.  Iterative apogee distance inputs are easy with the spreadsheet.  One can make this as accurate as one desires.  To 4 or 5 significant figures,  that period ratio as an approximation to an integer,  should be more than accurate enough to make rendezvous much easier.   Clearly,  there are other similar solutions at 144:1,  146:1,  and so forth.  Take your pick,  just get the period ratio as close to an integer as you can.

The third lesson here is dramatically pointed out by the third figure:  the dV between circular and elliptic is always constant,  regardless of the hyperbolic departure velocity needed by the interplanetary craft.  That is because neither the circular nor the elliptical orbit are changing,  only the required hyperbolic departure speed.  The dV to be supplied by the craft is low if the required departure speed is lower.  If that departure speed is higher,  that craft dV then gets larger.  The difference in departure speeds simply adds to the craft’s dV requirement,  not the tug’s. 

All that really means is that tug assist is more valuable for min energy Hohmann travel,  and a bit less valuable for higher-energy interplanetary trajectories.   But,  if you try to obtain more of the total dV from the tug,  you almost immediately push it beyond escape speed,  where it is lost in space instead of returning via the ellipse to be reusable!  This fourth important lesson shows up,  in the small difference between ellipse perigee speed and local escape speed at that altitude.  For these data as illustrated here,  that difference is only 0.1 km/s = 100 m/s!

It is only for purposes of lunar missions that the tug can supply essentially all of the departure speed requirement,  precisely because the required departure speed is just barely less than escape speed!  That puts the craft at essentially near-zero speed at that ellipse apogee,  very near the distance of the moon’s orbit.  The moon essentially “runs over” the craft from behind at its orbital speed,  which is very nearly 1 km/s.  The gravitational interaction from there is a 3-body problem (Earth,  moon,  and craft),  which in Apollo’s case led to a “figure-8” trajectory into a retrograde low lunar orbit,  with the circular entry burn occurring behind the moon as viewed from Earth.

3-body problems cannot be done pencil-and-paper,  or with pencil-and-paper calculations automated in a spreadsheet.  They are done only with finite-difference computer programs.   That 3-body figure-8 trajectory was essentially the only real computer analysis done during the Apollo program.  The rest was mostly slide rule (or desktop calculator) work.  Pencil-and-paper stuff!

Figure A – Two Results Excerpts From the Spreadsheet,  for Circular and Extended Ellipse

Figure B – Sketch Showing the Spreadsheet-Calculated Orbits and the Relevant Velocity Data

Figure C – Computed Delta-Velocity (dV) Data

Trump Again?

There is a joke circulating in Germany after former President Trump won our election.  See the first figure.  I find it rather telling,  myself. 

We elected the convicted felon instead of the former prosecutor.  We elected the adjudged sexual predator.  We elected the 6-time bankruptcy filer infamous for stiffing vendors,  to manage our national economy?  We elected the violator of our classified document laws,  to be commander-in-chief,  when we quite evidently  cannot trust him with classified materials,  or he would not have been indicted for it. 

We re-elected the only president we have ever had in all our national history,  who refused to peacefully transition power at the end of his first presidency,  instead trying to overturn it by every means available,  up to and including inciting an insurrection,  on Jan. 6,  2021.  

That is very evident stupidity on our part as a nation,  and that is the source of the joke in the figure! 

All of this has happened because far-right media sources now far outnumber the so-called "mainstream media" sources,  and those far-right sources are rife with disinformation and misinformation,  including propaganda from the Russians and other hostile nations.  These lies from those far-right sources are all that way-too-many-of-us ever encounter anymore!  And also quite evidently,  as a population overall,  we lack the critical thinking skills to know when we are being lied-to by these sources. 

Extremism is the real enemy here.  Far-right,  far-left,  religious,  all are pure evil!  I don’t see very many far-left extremists in the US anymore,  but I do see an alarmingly-growing number of far-right extremists.  The political spectrum is not the straight line everyone assumes.  It is,  in fact,  a circle,  with democracy on one side,  and dictatorship on the other,  and two different paths leading to the dictatorship side.

Both types of political extremism lead to exactly the same end:  a military-supported dictatorship,  as illustrated in the second figure.  Religious extremism can ally with either path.  It does not matter what “they” say,  it only matters what they do!  We've seen this for centuries now. 

A very serious problem here is a total lack of critical thinking ability on the part of a majority of the voting public.  They simply cannot tell when they are being lied to by their favorite sources!  Which is virtually all the time. 

That lack is the result of two generations (!!!) of dumbing-down public education with a low-ball standardized test,  and then tying school funding to its outcome,  which exerts enormous pressure to teach only to the test,  not the full curriculum.  Critical thinking is just not on that test,  as we have already seen. 

As a result,  the gene pool needs more than just a little chlorine now!

The election is over.  Trump won,  in the electoral college and in the popular vote!  Let me predict what is going to happen to you all,  as his second term unfolds.  It will not be what he and his team told you.  Not by a long shot!  But it will take significant time to unfold.  Why?  It just takes a long time for the dead dinosaur to fall over.

Mass deportations of undocumented aliens: 

Trump swears he wants to deport about 11 million undocumented aliens from this country.  He will certainly try to do it!  And if Congress backs him,  he will do it!  The more deportations,  the bigger the effects will be.  Just be aware that there is a time lag between action and effect.

Bear in mind that these people to be deported are mainly the harvesters of our food supply,  and the backbone of our construction industry.  By and large,  statistically,  they are actually more law-abiding than the majority of American citizens,  despite the lies you have been told about them,  in the right-wing media.  Yeah,  there’s exceptions,  just not very many.  Not very many at all.

These deportations will cripple the agricultural and construction sectors of our economy,  simply for lack of available labor.  Food and housing prices will rise drastically,  first because of a lack of supply,  then because the producers will have to drastically raise the wages they pay these workers,  in order to get American citizens to take these jobs. 

The result will be (1) economic depression from the supply-chain disruptions,  and (2) rampantly-high inflation,  because those costs will be passed on to the public in drastically-higher prices.  This will ripple all-across the economy.  It is inevitable.   It will happen!

Depression and inflation simultaneously:  we have not seen this disaster since the late 1970’s!

And a majority of you voted for this!

Tariffs on foreign imports,  largely from China,  but also possibly Mexico:

The majority of things that American consumers buy,  come from these two sources.  They come from there,  because those products are generally not produced within the US anymore.  We can argue about why that happened,  but it is a simple fact-of-life today!  Deal with it!

A tariff is a tax upon imported goods.  The importer has to pay that tax,  which increases his cost of doing business.  He will pass that added cost on to you,  the consumer,  as a price increase big enough to cover it,  if not even higher (which some term “greedflation”).  It is inevitable.  We’ve seen this passing-on of increased costs before!

Mr. Trump is talking about enormous tariffs,  anywhere from 10-or-20% to 100%.  He will attempt this!  That means enormous price increases for most of the things you buy!  And that means both supply chain disruptions,  leading to economic depression,  and large price increases,  leading to massive inflation.  Period!

Again,  this tariff policy will add greatly to the simultaneous disaster of depression and inflation caused by the mass deportations!  Our economy stands no chance!

 A majority of you voted for this!

 A climate change disaster is coming:

Almost to a man,  Trump and his political supporters and financial backers are anthropogenic climate change deniers.  Trump himself usually calls climate change “a hoax”.  That is far-right extremist dis/mis-information,  which is actually where he came by that belief.  Anthropogenic climate change is quite real,  and it is already here,  now.  We’ve been seeing it in action,  the last several years.  You are entitled to your own opinions about this,  but you are not entitled to your own “facts”!  Facts come from science,  not far-right media sources.

Trump will kill all the climate change-mitigating efforts of Biden,  and that will push the world over the hump of inevitable total disaster,  because American leadership on this issue is,  and always was,  critical!   Now that will stop.  No other very-powerful country has “bellied up to the bar” as much as we have,  on this.

The extreme weather events will get worse over the next very few years,  and within your lifetimes,  you will see a sudden sea level rise in the 3-6 meter (10-20 feet) range,  which is a total disaster,  not just for the US,  but for all of humanity!  Most of our critical and most valuable assets are within 1 meter (3 feet) of current sea level,  all around the world. 

Something like half the world’s population lives within 1 meter (3 feet) of current sea level!  Imagine the “immigration disaster” as these 4 billions go on the march across international borders looking for new places to live!  Illegal immigrants?  You ain’t seen nothin’ yet!  This will start wars!

But the majority of you voted for this,  too!

Pandemic health disasters are coming:

It seems rather likely that Trump will call upon Robert F. Kennedy,  Jr.,  to head the department of Health and Human Services.  RFK,  Jr.,  is a vaccine denier,  despite the science and the track record,  which actually means there is something mentally wrong with that man!  You can expect decreased availability of things like Covid and flu vaccines.  More people will sicken and die from these otherwise-preventable or reducible diseases.  You can also expect zero attention to fending-off the next pandemic!  Why?  Because that will require more vaccines!

We already have a serious vaccination problem in the US.  Rates of whooping cough and measles are on the rise,  despite there being very-effective vaccines for both.  We have allowed too many exceptions to the required-vaccine rules for public schools,  pure and simple!  RFK,  Jr.,  would likely make that much worse!   He says he won’t deny you vaccines,  but he won’t promote them.

There are many other possible pandemic threats out there.  So,  who is going to pre-emptively try to counter them?  Not vaccine-denier RFK,  Jr!  Something somewhere between the 1918 flu disaster,  and the 14^th century Black Death disaster,  is coming!  You will see it,  likely in Trump’s term as the 47^th president!

A majority of you voted for this!

You just elected your first dictator-for-life,  ending our democracy experiment:

You just elected a man who is quite old,  and already showing signs of age-related cognitive impairment,  but not yet as bad as Biden did,  during their 2024 debate.  Ignoring the risks of cognitive impairment,  Trump (if he lives that long) will not relinquish control at the end of his term after the 2028 election,  for the transition of Jan. 20,  2029! 

We’ve already seen this after the 2020 election,  regarding the Jan. 6,  2021 insurrection,  to prevent the Jan. 20,  2021 transition.  And note that he promised exactly that same behavior after the 2016 election,  if he lost!  So why would 2028/2029 be any different?

Maybe he will still be somewhat-functional at the end of his term as 47^th president,  and maybe not!  But if not,  there are plenty of Trump-wannabees to take his place as dictator.  None of them will willingly turn over power to the next elected president,  if we even have a next election at all! 

Look at what Trump did appointing federal judges and nominating candidates for the Supreme court.  Those candidates came from lists generated by far-right institutions,  which more-or-less guaranteed that they would do Trump’s bidding,  instead of following the law and the established rules.  That is right out of Adolf Hitler’s playbook for becoming the dictator of Germany in 1934 after his election to the Chancellorship in 1933. 

Example:  Trump appointee Aileen Cannon in Florida,  who gave Trump’s lawyers everything they asked for,  and all the delays they asked for,  up to and including trying to dismiss the federal classified documents case entirely,  which on the face of it,  was a slam-dunk conviction!  Back in the 70’s-to-90’s time frame,  if I had done with classified documents what Trump did at Mar A Lago,  I would still be jail today!

Now he has an immunity ruling from the Supreme Court that he and Mitch McConnell packed,  for anything he does “officially” as President.  Anything can be claimed to be “official”.  In effect,  he can no longer be held accountable for anything!  No matter how egregious the act!

Trump will pack all the important offices and institutions with underlings who will violate the law to do his bidding instead.  He will start with the Justice Department,  thus actually implementing the weaponization of it,   that he has long falsely accused Democrats of doing.  It won’t end there,  it extends up to and including sending the Army to capture all who oppose him.  Does that remind you of Germany circa 1935-1940?

Update 12-1-2024:  his cabinet selections have been not only loyalists who would violate the law for him,  but also incompetents and crackpots who would totally disrupt the institutions they were selected to lead.  And by using recess appointments,  the Senate has no say in this!  Disrupting the institutions makes them dysfunctional,  and Trump is going to point at a dysfunctional government to justify overthrowing it to install himself as dictator.  

You the majority voted for this,  too!

Ending the Ukraine-Russia war:

Trump promised to end this war “on day 1” of his presidency.  How?   Essentially by handing the Ukraine over to Putin.  No more support to Ukraine,  Ukraine cannot be a NATO member for some 20 years,  and no territory invaded and held by Russia,  will ever be anything but Russian territory.  That’s a lost war for Ukraine!  And a loss for all of us who supported Ukraine against Putin!

Trump wants to take the US out of NATO,  our only effective defense against Soviet Russia,  and now Putin’s Russia,  since its founding.  He sucked-up to our adversaries,  insulted our allies,  and threatened to renege on the NATO treaty!  Those are matters of the public record!  Yes,  that misbehavior got some more spending on defense from some of our allies,  but this is very most definitely NOT the way to go about doing that!  We need our allies!  Now more than ever!

Trump is already well-known to be an ardent admirer of Putin.  That makes him a puppet of Putin,  and thereby a traitor to US interests!  We saw this in his first term as president:  at the Helsinki conference,  where he publicly preferred Putin’s lies,  to the determinations of his own government’s various intelligence agencies.   You had apparently elected a traitor in 2016!  And that treasonous behavior hasn’t changed since.

What will happen when Trump hands Ukraine to Putin?  The far-right sources didn’t tell you that,  did they?  But I will!  It emboldens Putin to try to invade and reconquer the other former Soviet Republics,  most of which are now NATO allies.  Failing American involvement (because of Trump very likely reneging on the NATO treaty,  he has a history of threatening that),  that starts World War 3 in Europe!  It also emboldens Xi in China to try to invade and conquer Taiwan,  starting World War 3 in the Pacific.  Xi is just waiting to see Putin succeed,  before he embarks on his conquests.

Doesn’t matter whether World War 3 actually starts in Europe or the Pacific,  it will eventually go nuclear!  With utterly devastating loss and destruction in the US,  and throughout much of the world!   A disaster for the US and all the rest of humanity!

The majority of you voted for this!

What about Taiwan?

If Trump hands Ukraine to Putin,  Xi will invade Taiwan.  Period!  Most of your electronics are made in Taiwan.  That means both no more electronics for you,  and World War 3 in the Pacific!  Period,  end of issue.  And it will eventually go nuclear!

The majority of you voted for this!

Final remarks:

A totally-depressed economy with massive inflation,  chronic expensive weather disasters culminating in truly massive sea level rise within your lifetime,  pandemic health disasters coming,  a dictator you cannot get rid of,  and World War 3 going nuclear on us without any allies. 

The majority of you voted for all of this,  although you obviously thought he would bring prosperity and strength instead!  That’s NOT what he will bring you!  You were lied-to!

I hope the majority of you that voted for this,  are prepared to live with the consequences of your vote,  which are in turn the consequences of not knowing you have been lied-to by far-right extremists. 

Getting To Low Earth Orbit and Back

There are two pictures and a lot of notations in the figure.  Near center is a plot of altitude versus velocity,  similar in format to a standard flight envelope presentation,  except that the values extend to low circular Earth orbit.  Top right is a diagram of Earth with low circular orbit at 300 km shown,  plus a transfer ellipse that grazes the surface at its perigee,  and grazes low circular at its apogee. 

Typical non-lifting vertical launch pretty much reaches the vicinity of the transfer orbit at ~90 km altitudes at low drag loss,  and accelerates onto it exo-atmospherically at no drag, by about 200 km altitude,  give or take.  From there,  the vehicle loses a little speed coasting to apogee at circular orbit altitude,  where a small burn speeds it back up to circularize.  

Typical entries start with a small deorbit burn onto the transfer orbit,  where significant entry forces begin at the “entry interface” altitude of 140 km.  From there,  peak heating precedes the peak deceleration,  which finally ends at the end-of-hypersonics point near Mach 3 speed and 35-40 km altitude,  as indicated on the altitude-speed plot.  This was figured for an Apollo capsule.  Be aware that the “circularize” and “deorbit” points need not be co-located around the circular orbit. 

Also shown is a winged lifting spaceplane ascent trajectory to orbit.  This trajectory is limited above by too little lift with a practical wing area size,  and by heating too intense to endure below.  It is essentially entry flown in reverse!  The point reached on this trajectory by the fastest of the X-15 rocket plane flights is also shown on the altitude-speed plot.   If your vehicle takes off horizontally,  it will inherently have to use this entry-in-reverse ascent trajectory,  incurring devastatingly-huge drag losses.

Vertically-launched non-lifting vehicles endure only very modest ascent heating,  with windblast forces being just as important for payload protection.  They must only endure high heating during entry,  where orbital-class speeds still exist at much lower altitudes.  In contrast,  the winged lifting ascent vehicle must endure entry-class heating (and drag) on that ascent,  and on the descent.   Its heat shielding must endure two,  not just one,  entry-level heating episode per flight,  which means it will “wear out” twice as fast!

This is why I strongly recommend that winged spaceplane designs be vertically launched on non-lifting trajectories!  

Why Vote For He Who Will Hurt You?

I found this on LinkedIn.  It’s too good not to re-post here.  While it is pointless trying to change the minds of Trump-cult believers,  perhaps there are non-Trump-cult Republicans,  and independents like me,  who might be willing to listen.

I would only add one thing that was left out of the image.  This is a man so hungry for power (and trying to stay out of jail) that he would incite an insurrection in an attempt to overthrow his own government,  in order to become a dictator-for-life.  He would do this by using martial law “to quell the violence” as the excuse.  He will do that again,  or whatever else he thinks is needed,  to become that dictator-for-life (and stay out of jail),  if given the chance!

Please do NOT vote for this person!  Do please vote,  just NOT for him!  We had enough chaos the first time around!

 

Drugged Spiders?

My wife found this somewhere on Facebook.  It was too funny not to repost here. 

While intellectually I know it is likely that different species will respond to drugs in different ways,  it was still startling to see caffeine apparently disrupt web-spinning,  while speed and marijuana apparently do not! 

If this is real research being done somewhere,  it is a contender for the Ig Nobel!

Starship/Superheavy Flight Test 5, 13 October 2024

Note:  a version of this article appeared as a board-of-contributors column in the Waco "Tribune-Herald" for Tuesday,  15 October,  2024.

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I found out after the fact that the test took place this morning.  I watched the SpaceX videos to find out what happened.  While not perfect,  the test was a resounding success! 

The launch was normal with all 33 Raptors working in the Superheavy booster stage.  Hot staging was successful,  and they seemed to keep control of the propellant ullage problem by running 3 booster engines all during the staging event and the flip-around.  The Starship upper stage pulled away on all 6 of its Raptor engines successfully.  Staging took place at approximately 67 km altitude and 5200 km/hr (1.44 km/s) speed (which is actually a bit less speed than I expected to see).

The booster successfully flew back to the South Texas “Starbase” facility,  and successfully made the landing burns (initially 13 engines,  finally 3 engines) and the tower catch,  which was utterly amazing to see!   I did see the methane plume from one vent burning with air along one side of the stage near its base.  That vented material continued to burn for some time after the landing.  (They might consider adding a water spray on the tower to put such fires out.)

The Starship upper stage successfully made the same kind of almost-an-orbit suborbital trajectory,  to come down in the ocean on the other side of the world.  There is no need for a deorbit burn on this trajectory:  entry is automatic.  The video was astonishingly good.  I saw no visible plasma effects at the nominal entry interface altitude 140 km.  Speed was somewhere around 27,000 km/hr (7.5 km/s) at this point,  although I did not recover the speed data on the screen.

I saw a visible plasma glow under the tail and portside aft flap,  starting at about 102 km altitude and at a speed of about 26,727 km/hr (7.43 km/s).  The announcer said the flaps were in control of vehicle attitude at about 85 km altitude and 26,720 km/hr (7.42 km/s).  I started to see the speed readout begin dropping at a noticeable rate (indicating significant deceleration beginning) at about 75 km altitude and 26,350 km/hr (7.32 km/s).  The vehicle is generating lift at about 60 degrees angle of attack,  which shallows the descent angle and makes the entry process longer in time. 

When the announcer said peak heating occurred,  the ship was at about 70 km altitude,  and about 25,500 km/hr (7.08 km/s) speed.  This always occurs before the “max dynamic pressure” (or max deceleration gees) point.  I never heard the announcer say where max dynamic pressure occurred.  But I saw one of the flaps develop a hinge line burn-through!  I’m not sure which one,  there were 4 views of 4 flaps,  the other 3 were unlabeled as to which they were.  That was at roughly 45 km altitude and 9500 km/hr (2.64 km/s),  probably substantially after the max dynamic pressure point.  There is still very significant heating going on,  just not the maximum amount. 

According to the announcer,  the ship was down to about Mach 2,  which I read off the screen as about 25 km altitude and 1400 km/hr (0.39 km/s) speed.  He indicated the ship was in the subsonic “belly-flop”,  for which I read the screen as 3 km altitude and 400 km/hr (0.11 km/s) speed. 

The ship fired up its 3 sea level Raptors successfully,  and flipped tail first rather quickly,  at very low altitude (apparently per plan),  and touched down on the ocean in the proper attitude (nose high).  It hit the target zone,  and a camera on one of the target zone buoys recorded a huge steam cloud obscuring everything,  then a fiery explosion.  Apparently the ship broke up and exploded when it tipped over onto the water.  There was burning cylindrical wreckage visible,  sticking up out of the water at about a 45 degree angle.  The last recorded speed,  which I took to be speed at touchdown,  was 8 km/hr  (2.2 m/s).

All in all,  this was an astonishingly successful test flight.  Kudos to SpaceX,  they did good,  really good!  And,  they are doing things no one has done before,  and accomplishing them faster than anyone has a right to expect.  Well done!

The heat shielding at the flap hinge lines obviously still needs some improvement (see figure).  I do believe it is time to try landing and recovering the Starship on land,  and it is time to try doing Raptor restart burns in space.  Solve those issues,  and they are ready to attempt propellant transfer tests “for real”.

Update 10-15-2024:  Here is the simplest notion I could come up with,  for a “fix” to stop the hinge line burn-through problems.   It’s not a reusable part,  you would install these on the 4 flaps before every launch.  But these are not large items;  they would not “break the bank” on launch costs.  My materials selections are just a start point.  But the final product might be very similar to my sketch.

Elliptic Capture

This concept applies to either arrivals or departures from a planetary body.  Arrival and departure would take place at the periapsis of an extended elliptic orbit about the planet,  where the orbit speed is closest to any required arrival or departure spacecraft speed,  all measured with respect to the planet.  The min and max radii of the ellipse determine both its shape and its speed distribution.

Figure 1 shows everything you need to compute from min and max distance any of the elliptic orbit parameters,  given a mass and radius for the central body,  and a value for the universal gravitation constant.  Figure 2 shows a numerical example computed for a nominal 4-day extended ellipse about the Earth,  with a perigee altitude of 300 km,  to match “typical” low circular Earth orbit conditions.

From low circular orbit,  the ideal dV required to get onto the co-planar ellipse from circular orbit would be the ellipse perigee speed minus low circular orbit speed.  Any interplanetary trajectory has a “near-the-Earth” speed requirement that is always beyond escape speed,  sometimes significantly.  To get onto that interplanetary trajectory from the extended ellipse,  the ideal dV is trajectory speed minus perigee speed,  a smaller number.  To get onto that same trajectory directly from low circular orbit,  the ideal dV would be near-Earth trajectory speed minus circular orbit speed,  which is a much larger number!  Same applies to arrivals,  just reversed in direction.

To get a perigee speed that is close to escape at perigee altitude,  the ellipse has to be quite extended.  Its apogee distance will generally be well outside the geosynchronous distance,  and it will usually fall outside the outer Van Allen radiation belt as well.  But such an extended ellipse will transit the two major Van Allen belts twice each passage,  both outbound,  and both inbound.  (Note that the geosynchronous distance actually does fall within the outer Van Allen belt.)

Figure 1 – All the “How-To” for Elliptic Capture Orbits Anywhere

Figure 2 – An Elliptic Capture Orbit of 4 Day Period About the Earth

These dV values are ideal in the sense that they are astronomically-derived values.  Depending upon whether the propulsion is “impulsive” or not,  these may need to factored-up higher for the mass ratio-effective values necessary to use the rocket equation for sizing stages or vehicles.  This allows only for gravitational losses,  since there are no drag losses outside of the atmosphere.  If the propulsion is “impulsive”,  a factor f = 1 may be used.  For electric propulsion as we currently know it,  use a factor f between 1.5 and 2.  I prefer the more conservative 2,  some others recommend only 1.5.

The value I use for the universal gravitation constant is G = 6.6732 x 10^-11 N-m²/kg².   Values for planetary body masses M and radii are given in the table just below.  The orbit equations work in N, kg,  m,  and sec units of measure.  However,  it is customary to show distances in km not m,  and speeds in km/s not m/s.  The values for G and planet M “go together”,  in the sense that it is their combined effect that determines orbit characteristics.  Do not mix values from different sources!

Figuring interplanetary speed requirements is out-of-scope here.  Suffice it to say that differences V_far between body and spacecraft with respect to the sun must be corrected for 3-body attraction as distances close,  which is then the V_near needed at departure.  V_near² = V_far² + V_esc²,  escape figured at periapsis,  not the surface.  The magnitudes are accurate,  but there is no direction information!

More Detail

Note that elliptic capture (or departure) takes place at the extended elliptic orbit’s periapsis,  where speed is the highest and closest to arrival and departure speed requirements.  It does not take place at the ellipse’s apoapsis,  where speeds with respect to the planet are lowest,  and very far indeed from interplanetary arrival or departure speeds (as measured with respect to the planet).

Note also that for the extended ellipse,  the periapsis speed is very close to the escape speed at that altitude.  That means there is a large dV required to get onto the ellipse from circular orbit,  very nearly the difference between escape speed and circular orbit speed (usually near 30% of escape).  This also applies going back to circular from the ellipse,  just reversed in direction.  To do this,  the burns must take place at periapsis,  not apoapsis.  That is part of the fundamentals of making changes to orbits: a burn changing the speed at one end,  changes the distance at the other end.

Now,  there is one additional nuance of using an extended elliptical capture orbit,  and that would be to put its periapsis altitude down in the atmosphere,  somewhere between the entry interface altitude (140 km for Earth) and the surface (0 km altitude).  The idea would be to use an aerobraking periapsis pass to decelerate from interplanetary arrival speed (near the planet) to the calculated periapsis speed for the ellipse penetrating the atmosphere.  Instead of departing hyperbolically,  the vehicle then follows an extended ellipse out of the atmosphere,  without making any burn at all.  See Figure 3. 

If nothing else is done,  the vehicle will inevitably enter the atmosphere,  upon returning to periapsis passage,  which is still within the atmosphere.  If instead,  the orbit needs to be modified to move that periapsis above the atmosphere,  that is done with an apoapsis burn (of rather modest magnitude).  But the move to a low circular orbit will still require a periapsis burn of rather large magnitude (roughly 30% of escape),  no matter what.  See Figure 4.

This one aerobraking pass into an extended ellipse that gets modified into a stable orbit with a small apoapsis burn,  is an attractive capture method,  excepting the difficulty of reaching this orbit from either the surface or low orbit,  because the dV to reach it terminates very nearly in escape speed,  not just low orbit speed!  That difference is always inherently on the order of 30% of escape at the periapsis altitude.  If the vehicle so capturing must also contain the propellant to change to a low orbit,  this attractiveness entirely evaporates!  It is actually “cheaper” by the value of the stabilizing apoapsis burn,  to decelerate directly into low orbit from the interplanetary trajectory,  always outside the atmosphere (and thereby eliminating the need for a heat shield).

One way around this dilemma is as follows:  after the initial hard aerobraking pass (which always requires a deep penetration,  or you will NOT get the deceleration!!!),  you adjust periapsis with a small apoapsis burn,  such that the periapsis altitude just barely falls below the entry interface altitude.  That way,  over repeated passes,  the drag deceleration at periapsis reduces apoapsis altitude on each pass,  ultimately toward the desired final circular orbit value.  Then one small burn at that final desired apoapsis altitude pulls your periapsis up out of the atmosphere,  for a stable low circular orbit.  See Figure 5.

Implicit in this process is the requirement to decelerate hard on the first aerobrake pass,  deep in the atmosphere.  This is imposed by a required deceleration dV on the order of a nontrivial fraction of escape,  or else you will not capture at all!  The subsequent apoapsis-lowering decelerations can be much smaller,  not nearly so deep in the atmosphere.  Gentler is more such orbital passes,  over a longer period of time,  though.  It’s a tradeoff.

The hard braking required on that first pass deep in the atmosphere implies that the vehicle must have a very significant heat shield!  You do not get such deceleration amounts unless you go deep in the atmosphere:  there is no “shallow-skimming” that gets you any significant deceleration!  And if you get deceleration,  you WILL get heating!  The peak heating pulse precedes the peak deceleration pulse in all entries. 

Further,  if the vehicle uses multiple shallow passes to adjust apoapsis after the initial deep deceleration pass,  its heat shield must remain serviceable for multiple entries,  each a little less demanding than the preceding one.  The initial one occurs at near-escape speed at periapsis.  As each subsequent shallower pass decreases the apoapsis,  periapsis speed decreases toward circular orbit speed,  which is still quite the demanding entry in terms of heating (at Earth). 

Finally,  in Earth’s atmosphere,  which has repeatable and predictable density vs altitude at entry altitudes,  this multi-pass aerobraking elliptic capture process has much merit. 

But on Mars,  where the high-altitude densities vary through factors of plus-or-minus two (or more),  rather unpredictably,  this aerobraking deceleration process has far less merit!  As you leave the atmosphere on the first pass,  if your speed is still too high,  you will have to burn to decelerate,  lest you not capture at all,  becoming quite literally “lost in space”!  (Mars entry interface is 135 km, Earth’s is 140 km.)

If you have to be prepared to do that,  you might as well avoid the uncertainty and risk,  and just decelerate with a burn directly into some orbit,  all outside the atmosphere.   And not need any heat shield!

Figure 3 – Aerobraking Elliptic Capture With No Burn,  Resulting in a Second-Pass Entry

Figure 4 – Aerobraking Elliptic Capture,  With A Burn To Raise Periapsis Out Of the Atmosphere

Figure 5 – Aerobraking Elliptic Capture With A Burn To Allow Subsequent Braking Passes

Yet More Detail

The aerobraking capture notion (into an extended capture ellipse) is conceptually illustrated in Figure 6.  The simple 2-D Cartesian entry spreadsheet model that I have,  cannot do this analysis,  although a typical entry plot is shown in that figure for a simple direct entry off Hohmann at Mars,  with a big heavy object,  which did use the simple spreadsheet analysis.  The point of including it was to show that peak heating is seen before significant deceleration gees are seen!  And that will always be true,  in any entry! 

In addition,  at the figure’s bottom,  a couple of sketches are provided to conceptually show what an actual aerobraking capture event must entail.  All the dV to capture into the extended ellipse must be obtained in the first pass,  by definition!  Or else it is not capture at all!

The entering object has a significant dV requirement in order to capture,  which must be produced by aerobraking drag,  by definition in this scenario.  To accomplish that requires that the entering object experience significant deceleration gees,  although perhaps not actually the peak possible value in a straight entry.  To obtain those significant levels of deceleration in only the 1 pass,  it must inherently dive rather deep into the atmosphere,  to somewhere near (or even deeper than) where peak convective heating will occur.  (If at Earth or Venus where speeds exceed 10 km/s at entry interface,  there will also be even-larger amounts of plasma radiation heating.) 

If the required deceleration dV is not achieved in the first pass,  the object is literally lost in space,  likely exiting at a speed still above escape,  unless it can quickly burn to make up the difference.   Bear in mind that the extended-ellipse periapsis speed is only very slightly below escape speed at that entry interface altitude,  while the hyperbolic approach speed off Hohmann transfer will be significantly above escape speed at that same altitude.  For faster transfers,  the approach speeds are,  in point of fact,  well above escape,  easily by as much as 50-60% of escape!

Figure 6 – Summary of the Aerobraking Capture Process Into an Extended Ellipse

Conclusions

1.      (1) Elliptic capture makes sense at Earth where high-altitude densities are reliably predictable.  The “right” process is that in Figure 5,  where one deep pass captures into the ellipse,  with an apogee-raising of the perigee to a higher altitude,  but still in the atmosphere,  where the apogee altitude can be reduced by drag deceleration at perigee in multiple circuits. 

2.     (2)  Elliptic capture does not make sense at Mars,  where high-altitude densities can vary up or down by a factor of 2 or more,  erratically and unpredictably,  in terms of current known science.  If you must be prepared to burn to make up an unpredictably-deficient first pass deceleration,  you might as well just burn directly into orbit,  all outside the atmosphere,  entirely eliminating the need for any heat shield.   The dV is about the same either way.  

3.      (3)  There is no “shallow skimming” of the upper atmosphere to decelerate in one pass into elliptic capture,  without the need for a full entry-capability heat shield.  You either decelerate significantly for capture (and suffer heating) during the initial pass,  or you escape into “lost in space” status,  if you cannot burn to make up the deceleration deficit.  The very significant heating occurs before you ever see any significant deceleration gees,  and you must see significant deceleration gees,  in order to capture at all,  per Figure 6.

4.     (4)  Further:  to use repeated shallow passes to reduce elliptic capture apogee per Figure 5,  your full entry-capability heat shield must be capable of surviving repeated heating episodes,  although only the first pass is the worst.  Materials embrittled upon cooling after the first (deep) pass will fall apart under the influence of pressure forces and re-heating effects,  even during shallow subsequent passes.

Other Final Comments

1.      (1)  Entries off the interplanetary trajectories at Mars (from Earth) take place somewhere in the 5 to 8 km/s range,  depending upon the speed of the interplanetary trajectory.  Only convective heating is significant in this speed range,  which varies roughly proportional to speed at entry interface cubed.  The plasma sheath is more-or-less transparent to infrared,  so that refractory heat shields that re-radiate to cool are feasible,  just as they are at Earth from low Earth orbit,  at about 8 km/s at entry interface (this is not true of entry from extended ellipses about the Earth).

2.    (2)   Entries at Earth and Venus off of interplanetary trajectories take place at speeds in the 12-17 km/s range,  for which plasma radiation heating dominates over convective by far,  varying as some very high exponent equal to or exceeding 6,  of speed at entry interface.  Under these conditions,  the plasma sheath is not at all transparent to infrared re-radiation,  so that only ablatives are feasible,  according to all known technologies.

3.     (3)   The new heat shield concepts based around carbon fabrics on spars (resembling umbrellas),  or around carbon or other materials extended as inflatables,  are NOT reusable!  Per the designs and the testing,  they are only good for one heat exposure!  There is shrinkage,  cracking,  and embrittlement,  in all of those materials,  after only one heating exposure.  Re-heating on a subsequent exposure means a re-exposure to the wind forces,  whereupon the embrittled or shrinkage-cracked materials will fall apart!