Sunday, January 17, 2016

Fact checking Neil deGrasse Tyson

Tyson is well known for fact checking movies, comics and other pop culture stuff. Here's giving Tyson a taste of his own medicine.

17 GMOs


Some of the above might be called pedantic nitpicks. Much like Tyson's pedantic nitpick when he calls out the stars in the movie Titanic. However some are serious errors and I've bolded these.

"Bush and star names" is an attack on an individual and the story is false. "Idiot doctors" is an attack on doctors and the American Medical Association. This unfounded attack is based on Tyson's ignorance on how a prognosis is delivered.

Items 1 through 4 were all parts of Tyson's keynote address at the TAM6 meeting. TAM was an annual conference for skeptics. It is revealing the self proclaimed skeptics accepted Tyson's falsehoods without question.

Ghazali's supposed demonization of math and the supposed Christian belief in a flat earth are part of Tyson's argument that religious belief is a destructive force that hinders progress.  As is Tyson's argument that Newton's belief in the God of The Gaps stopped him dead in his tracks. Tyson is free to argue religion is bad but his arguments should be based on fact.

Why did I bold Tyson's trailer for The Martian? If you peruse my blog you will see I'm a space enthusiast. And there are different camps within space enthusiasts. I happen to believe the moon and near earth asteroids will play important roles in opening a new frontier. Infrastructure in the earth-moon neighborhood would make access to the rest of the solar system much less difficult. Maybe Zubrin and various flavors of Mars Firsters have a better plan. But it is fair for me to point out it's physically impossible for Hermes to depart Low Earth Orbit (LEO) and arrive in Mars orbit 124 days later. Had the Hermes departed from EML2, the 124 day trip Tyson describes would be physically possible.

I'm sometimes asked "Why are you tearing Tyson down?" That's not what I'm trying to do. Tyson's work as a science evangelist is important and I want him to succeed. I want Tyson to step up his game.

Tyson on "idiot doctors"


The first half of the video Tyson argues surviving cancer doesn't demonstrate divine intervention. I'm fine with that.

But the second half of the video is a clueless rant against idiot doctors, the American Medical Association and Pre-Med students.

So a patient lives longer than predicted. Does this make the doctor an idiot? No. Typically a doctor will give his patient statistics for people in a similar condition. If someone lives longer than the norm, it demonstrates there are statistical outliers on a bell curve. It is..... astonishing. Astonishing that Tyson and the physics 101 prof are unfamiliar with entry level statistics.

Also Tyson as well as the physics prof seem to believe someone who's failed freshman physics would go on to med school. There are idiot physicists, I assure you!

Well known skeptic Dr. Novella called Tyson out on this (scroll to Those Darn Physicists). Novella noted this was part of the keynote speech at TAM6, a 2008 conference for skeptics. Dr. Novella thought it was an excellent lecture except for the idiot doctor part. Which goes to show he wasn't paying close attention to the rest of the lecture.

President Bush and Star Names

Tyson tells us President Bush attempted to "distinguish we from they" in the wake of the 9-11 attack. This routine was also included in the TAM6 keynote address.

Stands to reason right? We all know a Republican would seize this emotionally charged moment to stir up hatred against Arabs.

However Bush's actual 9-11 speech called Islam the religion of peace. Bush was calling for inclusion and tolerance. Exactly the opposite of the xenophobic demagogue Tyson falsely portrays.

In fact Bush and his administration have repeatedly condemned anti-Muslim rhetoric. Colin Powell was one of the first to bring Corporal Kareem Kahn's sacrifice to public attention:


Tyson's shallow stereotype may apply to some Republicans, but not all.

Tyson eventually admitted his story was false and apologized to President Bush. However Tyson qualifies his apology with these words:

"Of course very little changes in that particular talk. I will still mention Islamic Extremists flying planes into buildings in the 21st century. I will still contrast it with the Golden Age of Islam a millennium earlier..."
Well, the rest of that particular talk is just as wrong Tyson's Bush and Star Names fantasy.

Ghazali "Math is the work of the devil"

The Bush quote confabulation segues into a non existent Hamid Al-Ghazali quote. Hamid Al Ghazali was a muslim cleric that supposedly ended the Islamic Golden Age. According to Tyson, Ghazali wrote that math was the work of the devil. Tyson  would make that claim in other talks besides the TAM6 keynote speech. Tyson claims Islamic progress stopped and hasn't recovered since.

Ghazali would praise the disciplines of science and mathematics saying they are necessary for a prosperous society. So I very much doubt that Ghazali ever demonized math. When challenged Tyson replied:
"As for Al Ghazali, a more accurate representation of his views is that the manipulation of numbers was an earthly rather than a divine pursuit. And it was divine thoughts and conduct that were widely promoted -- to the exclusion of earthly conduct. Earthly conduct became associated with being anti-God, which I characterized as the devil. In later speeches (over the past year or so) I leave it as a simple split between earthly and divine pursuits, realizing that I was misleading some people by mentioning the devil at all."
This quote is from Tyson's comment below. In other words he admits there was no Ghazali text containing the assertion that math is the work of the devil.

Did Islamic innovation end with Ghazali? No. There were many Islamic scientists and mathematicians who came later. Abu al-Hasan was born three centuries after Ghazali died. Hasan was the father of symbolic algebra.

The Golden Age of Islam ended more in the 1600s when the mideast ceased to be a trading hub where diverse cultures would meet and exchange ideas.

Tyson claims the once innovative civilization would surely have rebounded if not for Ghazali. He notes that the 1.3 billion Muslims alive today don't earn that many Nobel science prizes. Well, neither do the 1.3 billion people living in China. Nor the 1.3 billion people living in India. And these civilizations enjoyed periods of innovation. In fact our zero and numbering system comes from India, not the Arabs as Tyson falsely claims. Is Neil going to blame the Chinese lack of Nobel science prizes on Ghazali?

Newton Invented Calculus On A Dare

About an hour into his TAM6 lecture, Tyson portrays Newton as a super human saying Newton invented calculus on a dare. Tyson frequently makes this claim and usually says it took Newton a month or two to establish this branch of mathematics.

 Well, no.



Two thousand years before Newton Eudoxus was slicing stuff into small bits to get more accurate approximations of volume and area. Cavalieri was doing this prior to Newton. These methods were well known when Descartes and Fermat invented analytic geometry (also known as graph paper with an x and y axis). With this invention y=x2 became a parabola. x2 + y2 = 1 became a circle with radius one. Descartes’ way of looking at things enabled us to scrutinize conic sections and other curves with symbolic algebra.

After Descartes and Fermat invented analytic geometry, it was only a matter of time before someone used Eudoxus like methods to get good approximations of the slope of a curve or the area under a curve. Which was done by Fermat among others. There is also Cavalieri's Quadrature Formula.
.
Fermat was the father of calculus. After Fermat the discoveries of Newton were inevitable as evidenced that Leibniz made them at the same time. Rick Stryker paints a more accurate picture -- The development of calculus was the collaborative effort of many. And it didn't take two months.

After thinking he had established Newton’s super powers Tyson flatly asserts Newton could have knocked out perturbation theory in an afternoon. “You know this!” Tyson shouts to his enthusiastic audience. Well, no. I don’t. And neither does Tyson or his credulous audience.

Euler took a crack at perturbation theory and n-body mechanics. As did Lagrange. Both these men were giants in their own right but did not make satisfactory models. 100 years after Newton, Laplace built on the work of Euler, Lagrange and Newton. To say Newton could have done it in an afternoon is disrespecting Laplace, Euler and Lagrange. It is also profoundly ignorant.

In Tyson’s alternate history Newton would have easily done Laplace’s n-body work had he not been stopped by his belief in the “God of The Gaps”. Tyson states this as a flat out fact. But an alternate history is not a testable hypothesis. We can’t rewind history and see what happens with different parameters.

Here’s another alternate history: An agnostic Newton would have been a normal young man who spent his spare time in taverns chasing women. No splitting of light, no laws of motion, and no contributions to calculus. His accomplishments would have been zip, zero, nada. Like Tyson’s alternate history this is nothing more than idle speculation.

More Transcendentals than Irrationals

In an interview with Joe Rogan, Tyson asserts there are more transcendental numbers than irrationals. He also tells Joe there are five cardinalities when it comes to infinite sets.

Was this a fluke? Maybe Neil just mispoke. But Tyson gives a similarly confused account in an interview with Dazed and Confused Magazine:
You know how numbers, you can count them forever? Well how about fractions? The infinity of fractions is bigger than the infinity of numbers; and then there are transcendental numbers, like Pi. There are more transcendental numbers than pure irrational numbers, and there are more irrational numbers than counting numbers. And more fractions than all of them. 
It's appropriate the above rambling passage comes from Dazed and Confused Magazine. Tyson's assertions earned him a mention in the badmathematics subreddit. The Rational Skepticism blog also chastised Tyson for this misinformation.

Five Centuries Regressed

Is the earth flat or round? This silly argument between Tyson and rapper B.o.B. generated a great deal of publicity for B.o.B., Tyson, and Tyson's nephew.

Part of the exchange: "@bobati Duude — to be clear: Being five centuries regressed in your reasoning doesn't mean we all can't still like your music."

Supposedly folks during the dark ages thought the earth was flat. Sadly Tyson is perpetuating this myth.

Tyson's misperception of the dark ages is a common error. Well summarized in "The Chart":

"The Chart" What Tim O'Neill calls


In the August 1991 issue of History Today Jeffrey Russel effectively argues people knew the earth was round during and before the time of Columbus. In his comment reply (below Russel's article) Tyson perpetuates the myth that knowledge of a spherical earth was lost in the "Dark Ages". Historian Tim O'Neill explains where this myth comes from. O'Neill also documents prominent scholars from that period that knew the earth was spherical.

The above links as well as more interesting reading can be found in this reddit badhistory thread on Tyson's battle with B.o.B.

A Rainbow Forms Only Broadside
To Your Line Of Sight

What does he mean by "line of sight"? A line of sight could be any line passing through the viewer's iris and hitting the retina. There are a multitude of such lines. If the rainbow is broadside to one line of sight, it is at an oblique angle to another line of sight.

I'm guessing Neil means rainbows can only form directly in front of the viewer. And he says as much  in this video:
It can only be a rainbow that is exactly face on to you. You've never seen a rainbow that was like at an oblique angle.
Which is rubbish, of course. On rainy days it common to see rainbows in the afternoon in the western sky. A viewer can turn and face southwest and the rainbow still remains in the western sky at an oblique angle to his or her view.

A rainbow forms perpendicular to the line extending from the sun through the viewer's head. The center of the rainbow lies at the shadow.

The "line of sight" can be any line from an obect passing through the viewer's pupil to the retinae.

Lines of sight from the edge of the rainbow to the viewers eye intersect the rainbow plane at 48º. Not perpendicular.

Again, there is one line through the viewer's pupil that is perpendicular to the plane. The line that passes through the sun as well as the viewer's head. Also lying on this line is the shadow of the viewer's head. The shadow of the head occupies the rainbow's center. I'll call this line the center line.



Now the viewer turns his head to the right. The rainbow remains perpendicular to the center line. However now the center line lies outside of the viewer's cone of vision. In this case there are zero lines of sight perpendicular to the plane.

The rainbow does remain perpendicular to the line passing through the sun, the viewer's head and the shadow of the viewer's head. To reach the Pot of Gold, the viewer would have to detach himself from his shadow and walk to the rainbow's end. Clearly impossible. But calling this line "line of sight" is a sloppy, inaccurate label.

Blind As A Bat

This common misconception is addressed in  Christie Wilcox's Discover article Actually, Bats See Just Fine, Neil.


Tyson's trailer for The Martian

Hermes' impossible trajectory


Above is a link to Neil deGrasse Tyson's trailer for The Martian. At 1:15 of the vid, Tyson has the space ship Hermes departing from Low Earth Orbit (LEO). 124 days later he has Hermes arriving at Mars orbit (2:17 of the video).

Hermes is propelled with low thrust ion engines. In the book when Hermes is about to rendezvous with Watney's Mars Ascent Vehicle (MAV), Lewis says Hermes can do up to 2 mm/s2. This acceleration is also given online:



Two millimeters per second squared would require an extremely good alpha. But it's possible future power sources will deliver more watts per kilogram. So 2 mm/s2 is only medium implausible. I'll let this slide.

Problem is, low thrust ion engines really suck at climbing in and out of planetary gravity wells. From low earth orbit, it would take Hermes about 40 days to spiral out of earth's gravity well and about 20 days to spiral from the edge of Mars' gravity well to low Mars orbit. Two months spent climbing in and out of gravity wells destroys Andy Weirs' 124 day trajectory.

Given 2 mm/s2, the trajectory Tyson describes is flat out impossible.

A slow ride through the Van Allen belts.

At 1:50 of Tyson's video he talks about the danger of solar flares and how astronauts are vulnerable to radiation. Well, departing from LEO means a month long spiral through the Van Allen Belts. Not only does the long spiral wreck Weir's 124 day trajectory, it also cooks the astronauts.

Tyson enjoys some notoriety for fact checking fantasies like Star Wars or The Good Dinosaur. This leaves me scratching my head. Many of the shows he fact checks make no pretense at being scientifically accurate. However The Martian was an effort at scientifically plausible hard science fiction and thus is fair game. Same goes for Tyson's trailer.

A physically impossible trajectory along with cooking the astronauts? Tyson's effort at hard science fiction isn't any better than Gravity or Interstellar.


Neil's Five Points of Lagrange Essay

The Five Points of Lagrange was a Neil deGrasse Tyson article published in the April, 2002 issue of Natural History Magazine. A few excerpts:

Gravity falls exponentially with distance


Popular usage has made "exponential" a general term for dramatic change. But a physicist should know the more specific mathematical meaning of the this word. Gravity falls with inverse square of distance, not exponentially.

Arthur C. Clarke was first to calculate altitude of geosynchronous orbits


Wrong. Clarke's contribution was suggesting communication satellites be placed in geosynchronous orbit (GSO). A fantastic idea with tremendous impact. But Clarke wasn't the first to calculate the altitude of GSOs.

Herman Potočnik calculated the altitude of GSO in 1928.  It's possible this altitude was calculated even earlier. Newton might have done it.

Unhackable Systems


The solution is so simple, just make unhackable systems. Oh my gosh, why didn't the cyber security folks ever think of that?

Twitchy published some good responses.



The Coriolis Force in Naval Battles

The Coriolis Force was a Tyson article published in the March 1995 issue of Natural History. In the article Neil has this to say about the 1914 Falklands battle:
But in 1914, from the annals of embarrassing military moments, there was a World War I naval battle between the English and the Germans near the Falklands Islands off Argentina (52 degrees south latitude). The English battle cruisers Invincible and Inflexible engaged the German war ships Gneisenau and Scharnhorst at a range of nearly ten miles. Among other gunnery problems encountered, the English forgot to reverse the direction of their Coriolis correction. Their tables had been calculated for northern hemisphere projectiles, so they missed their targets by even more than if no correction had been applied. They ultimately won the battle against the Germans with about sixty direct hits, but it was not before over a thousand missile shells had fallen in the ocean.
However the role of Coriolis correction in this battle is a an urban legend.

Coriolis Force in Football

Tyson likes to say the Coriolis force would deflect a 50 yard field goal half an inch to the right.


He repeats this fairly often. More recently for the Houston stadium. He seems unaware different  latitudes feel different Coriolis accelerations.

Coriolis force felt by a football would depend on the velocity and direction of the football as well as the latitude of stadium.

Coriolis acceleration = -2 Ω X v

Metlife is about at latitude 40.8 degrees. Metlife tilts about 11º from the north. I will go with the horizontal speed of the ball of 23 meters/second.

We can choose our coordinates so the x axis runs west to east, the y axis runs south to north and the z axis is the local vertical going up...

Ω = (0, 5.52e-5, 4.76e-5) 1/sec
v = (4.39, 22.58, 0) meters/sec
a = -2 Ω v = (.0021, -0004, .0005) meters/sec2,

Deflection from uniform acceleration is 1/2 a t2,
where t is time of flight. For a ball with a 23 meter/sec horizontal speed, it takes a little less than 2 seconds to traverse 50 yards.

1/2 a t2 = (.0043, =.0008, .00096) meters = (.167, -.032, .037) inches.

Of that displacement, the component displacement to the right is .17 inches. Tyson's half inch is off by a factor of three.

Field goal kickers don't have the level of precision where 1/6 of an inch vs 1/2 an inch makes much difference. However I wouldn't want Dr. Tyson to be calculating Coriolis in situations where it's important, like naval battles.

2001 Space Odyssey station rotates too fast



In an interview with Dan Le Batard, Tyson tells Batard:

… by the way I calculated the rotation rate of their space station which gives you artificial gravity on the outer rim. And it turns out it's rotating three times too fast. So if you weigh 150 pounds you'd weight 450 pounds on that space station (hee hee).
Tyson is wrong on several counts.

2001 A Space Odyssey's Space Station V has a radius of about 150 meters and a spin rate of about 1 revolution per minute. The spin gravity comes out to about one sixth of earth's gravity. A 150 pound man would weigh about 25 pounds on this station. This is close to the gravity on the moon's surface.

Also weight scales with the square of spin rate. So tripling spin rate would increase weight by a factor of nine.

Brick Helicopters


Helicopter blades will continue rotating after engine failure. Descending through the air at an angle can spin up the blades. Leveling off just before reaching the ground makes for a soft landing.

The process is described and demonstrated at this Getting Smarter Every Day Video.

GMO = artificial selection

In this video Tyson defends genetic modification by claiming it's not different from the artificial selection humans have been practicing for millennia.

Which is wrong. Genetic modification as practiced by Monsanto is splicing DNA from one species onto the DNA of another species. Artificial selection encourages traits that already exist in a population's gene pool. Here is a primer: Genetic Modification Explained.

Are GMOs beneficial? Or are they harmful? I don't know. I'm not taking a position pro or con. I'm pointing out Tyson's argument conflates two different techniques.

Before NASA nobody thought about miniaturizing electronics

In an interview with Fareed Zakaria, Tyson said:
The urge to miniaturize electronics did not exist before the space program. I mean our grandparents had radios that was furniture in the living room. Nobody at the time was saying Gee, I want to carry that in my pocket. Which is a non-thought. 
Well, the TR-1 hit the market in November of 1954 and NASA was formed in 1958

The TR-1 hit the market 4 years before NASA was formed

Here is the Wikipedia article on the history of transistors.

Are there more Tyson bloopers?

I don't have the time and energy to maintain a complete list of Tyson's bloopers. If you want to call attention to a noteworthy mistake, feel free to comment. For example, one of the commenters below (Phil Wilson) talks about Deflategate. The folks at The Federalist are also enthusiastic Tyson fact checkers.

Some comments I won't bother publishing. I don't have strong feelings what label we give to Pluto but I'm more or less in Mike Brown's camp. I'm fine with calling the earth an oblate spheroid. Also I have no use for racist comments.

Sometimes good comments get thrown away along with mountains of spam. Editing for clarity and brevity will make it more likely that I read and use a comment.

Thursday, January 7, 2016

Deimos Tether

This is a fourth in a series of blog posts looking at various tethers using Chris Wolfe's model.

50 kilometer Deimos tether - minimum length to remain aloft.

Mars-Deimos L1 and L2 are about 14 kilometers from Deimos' surface. Another 26.5 kilometer length extended past these points would balance. Extending the tether 50 kilometers either way along with a counterweight would provide enough tension for the elevators to stay aloft.

Safety
 Factor 
Zylon
Taper
Ratio
Tether to
Payload
 Mass Ratio 
1
1.000003
.000007
2
1.000006
.000015
3
1.000009
.000022

Even with a safety factor of three, needed Zylon mass is tiny. Less than a quarter kilogram of tether could handle a 10 tonne payload.

Benefits

There is no net acceleration at L1 and L2, so docking at ports at these locations would be like docking with the I.S.S.

This first step could serve as a scaffolding additional tether infrastructure could be added onto.


2942 kilometer lower Deimos tether - ZRVTO to Phobos tether


Given an ~1000 upper Phobos tether and a ~3000 lower Deimos tether, it is possible to move payloads between the two moons with almost no reaction mass. The tether points connected by the ellipse match the transfer ellipse's velocities. See my Upper Phobos Tether post.




Safety
 Factor 
Zylon
Taper
Ratio
Tether to
Payload
 Mass Ratio 
1
1.01
.04
2
1.03
.06
3
1.04
.09

So even with a safety factor of 3, the elevator's Zylon mass is modest. 1 tonne of Zylon can handle 11 tonnes of payload.

The red transfer orbit pictured above is called a ZRVTO - Zero Relative Velocity Transfer Orbit. At either end of the transfer orbit, relative velocity with the tether at rendezvous point is zero. ZRVTO is a term coined by Marshall Eubanks.

The notion of a ZRVTO between Deimos and Phobos tethers is not new. Above is a diagram from an article by JPL engineer Paul Penzo. Page 70 of the 1997 publication Tethers In Space Handbook. I believe Penzo came up with this idea in 1984.

Penzo's 940 and 2960 km lengths aren't that far from my 937 and 2942 numbers. It is reassuring that an aerospace engineer's numbers are close to my own.

Benefits

The idea of ion driven interplanetary vehicles excites me. The Dawn probe has demonstrated ion rockets are long lived and amenable to re-use. An ion rocket's fantastic ISP means a lot more mass fraction can be devoted to the dry mass structure and payload.

However ion rockets have pathetic thrust. They suck at climbing in and out of planetary gravity wells.

Here Mark Adler talks about ion rocket trajectories:

The fictitious Hermes from Andy Weir's The Martian can do 2 mm/sec2 acceleration. That would take an implausibly high alpha, But perhaps possible so I will go with that number.

At Deimos' distance from Mars, gravitational acceleration is about  80 mm/s^2. The Hermes' acceleration over Mars gravitational acceleration at that orbit is about 1/40. A small fraction but a lot larger than the 10^-3 fraction Adler mentions.

Deimos moves about 1.35 km/s about Mars. With an impulsive chemical burn, it would take about .56 km/s to achieve escape. But with a 2 mm/s^2 acceleration, it would take about 5 days and and .8 km/s to achieve escape.

To spiral down to low Mars Orbit, it'd take Hermes more than 17 days and 3 km/s. So the Deimos rendezvous saves about two weeks and more than 2 km/s delta V.

Once in heliocentric orbit, it is the sun's gravitational acceleration that we put in the denominator. Here is a chart of gravitational acceleration at various distances from the sun:


If the rocket's acceleration is a significant fraction of central body's acceleration, we can model burns as impulsive. The trajectory would be more like an ellipse than a spiral. At earth's distance from the sun., Hermes 2 mm/s^2 acceleration would be about a third the sun's gravity. At Mars, it's about four fifths. In the asteroid belt, Hermes acceleration exceeds acceleration from sun's gravity.

Ion rockets may not be great for climbing in and out of planetary gravity wells. But they're fine for changing heliocentric orbits, especially in the asteroid belt and beyond.

Saturday, January 2, 2016

Upper Phobos Tether

This is third in a series of posts that rely on Wolfe's model of tethers from tide locked moons. As with the Lower Phobos Tether post, I will look at possible stages of this tether examining tether to payload mass as well as benefits each stage confers.

7 kilometer upper Phobos tether - tether doesn't collapse but remains extended

I used Wolfe's spreadsheet to find location of tether top where tether length Phobos side of L2 balances the length extending beyond L2. This occurs 6.6 kilometers from the tether anchor. Having the tether extend 7 kilometers is sufficient to maintain tension.





Safety
 Factor 
Zylon
Taper
Ratio
Tether to
Payload
 Mass Ratio 
1
1.01
.04
2
1.03
.06
3
1.04
.09


Benefits
Docking with a facility at the L1 or L2 regions is easier than landing on Phobos. In the words of Paul451: "Instead of a tricky rocket landing at miniscule gravity on a loosely consolidated dusty surface, you just dock with the L1-hub of the ribbon (same as docking with ISS), transfer the payload to the elevator car and gently lower it to the surface. Reverse trip to bring fuel from Phobos to your ship (Assuming ISRU fuel is available on Phobos.)"

Also this small tether can serve as scaffolding on which to add longer tether lengths.

937 kilometer upper Phobos tether - transfer to Deimos tether

Given tethers from two coplanar moons tidelocked to the same central body, it is possible to travel between the two moons using nearly zero reaction mass.

Above I attempt to show how peri-aerion and apo-aerion of elliptical transfer orbit matches velocity of the tether points this ellipse connects. Tether Vs are red, transfer ellipse'sVs are blue.


Above I try to explain the math for finding the tether lengths from Deimos and Phobos.

Trip time between the two tethers is about 8 hours.



Safety
 Factor 
Zylon
Taper
Ratio
Tether to
Payload
 Mass Ratio 
1
1.02
.035
2
1.04
.070
3
1.05
.107

With a safety factor of three, one tonne of Zylon could accommodate about 9 tonnes of payload.

I look at the Deimos tether here.

The notion of a ZRVTO between Deimos and Phobos tethers is not new. Above is a diagram from an article by JPL engineer Paul Penzo. Page 70 of the 1997 publication Tethers In Space Handbook. Penzo came up with this idea in 1984 (I believe).

Penzo's 940 and 2960 km lengths aren't that far from my 937 and 2942 numbers. It is reassuring that an aerospace engineer's numbers are close to my own.

Benefits

Easy travel between Deimos and Phobos is a benefit in itself. 

But this would be a huge help to ion driven Mars Transfer Vehicles.

I like the notion of reusable ion driven MTVs. Ion engines have have great ISP thus allowing a more substantial payload mass ratio. However they have pathetic thrust. Andy Weir's fictional Hermes spacecraft can accelerate at 2 millimeters/sec^2. Which actually is very robust ion thrust. However ithis is only medium implausible. Low thrust means little or no planetary Oberth benefit. Plus a lo-o-o-ng time to climb in and out of planetary gravity wells.



300 km above Mars surface in low Mars orbit, gravitational acceleration is about 3 meters/sec^2. For a 300 km altitude low earth orbit, gravitational acceleration is about 9 meters/sec^2. 2 mm/s^2 acceleration is less than 10^-3 of the gravitational acceleration at initial orbit velocity in both these case. However I will be kind and go with Adler's .856 * initial orbit velocity.

At 2 millimeters/s^2 it would take Hermes 38 days to spiral out of earth's gravity well from low earth orbit and 17 days to spiral out of Mars gravity well. Most of the slow spiral out of earth's gravity would be through the intense radiation of the Van Allen belts.

I was very disappointed when Neil deGrasse Tyson's trailer had Hermes departing from low earth orbit and arriving in Mars' orbit 124 days later.

Besides adding 10 km/s to the delta V budget, climbing in and out of gravity wells would add about two months to Hermes' trip time. Tyson's video describes an impossible trajectory.  I wish he'd fact check himself with the same enthusiasm he applies to others.

It would be much better for Hermes to travel between the edges of each gravity well. At least as close as practical to the edge. In earth's neighborhood, Hermes could park at EML2 between trips. In Mars' neighborhood, parking at Deimos would save a lot of time and delta V. From Deimos, astronauts and payloads can transfer to Phobos and then to Mars surface. In this scenario, Hermes' 124 day trip from earth to Mars is plausible.

2345 kilometer upper Phobos tether - Mars escape

If anchor in a circular orbit, escape velocity can be achieved if tether top is at a distance 2^(1/3) anchor's orbital radius. I try to demonstrate that here. Phobos is in a nearly circular orbit. To achieve escape, the tether would need to be 2435 kilometers long.




Safety
 Factor 
Zylon
Taper
Ratio
Tether to
Payload
 Mass Ratio 
1
1.11
.204
2
1.22
.436
3
1.35
.700

A 7 tonne Zylon tether could deal with a 10 tonne payload, even with a safety factor of three.

Benefits:

Achieve mars escape.

6155 km kilometer upper Phobos tether - To a 1 A.U. heliocentric orbit

A tether this long can fling payloads to a 1 A.U. heliocentric orbit, in other words an earth transfer orbit.

Safety
 Factor 
Zylon
Taper
Ratio
Tether to
Payload
 Mass Ratio 
1
1.80
1.57
2
3.24
4.77
3
5.82
11.16

With a safety factor of three, an 11.2 tonne elevator could lift a one tonne payload. Not great, but it'd be worthwhile if we were tossing lots of payloads earthward.

Benefits

Catch/throw payloads to/from earth. Phobos is about 24º from Mars orbital plane. Mars orbit is about 1.5º from the ecliptic. So there may be some plane change expense.

7980 kilometer upper Phobos tether - to a 2.77 A.U. heliocentric orbit.

Safety
 Factor 
Zylon
Taper
Ratio
Tether to
Payload
 Mass Ratio 
1
2.5
3.1
2
6.4
12.5
3
16.2
39.5

With a safety factor of three, it would take a 40 tonne Zylon tether to handle a 1 tonne payload. We would need to be tossing many payloads for this to be worthwhile.

Benefits:

2.77 A.U. is the semi major axis of Ceres. A tether this long could catch/throw payload to/from Ceres. But this doesn't take into account plane change because of Ceres inclination.

Even with plane change expense, this tether could be very helpful for traveling to and from The Main Belt.

This could also throw payloads into a faster than Hohmann transfer orbit towards earth.