Contact, the Movie.

Contact, the Movie.

I did say once I saw Contact again I would do a write up on it and I saw part of it this morning so here it is partially from the last hour or so this morning and from memory. Oh still the s is broken so it will lower case s all the way.

The opening credits start with a view of the Earth from orbit and you hear music form and tv programs from the late 90s and then you pull back to the various planets in the solar system and the you hear different audio. This represents how distance and time are related the further away you are from an object the longer it takes the signal to get there and thus the information will bee that far out of date. Then it pulls back to a point where the sun is just a dot with a thin shell of dust around it representing the heliopause, the heliopause is a region where the sun solar wind pushes back the particles from the galaxy at a distance of about 128 au. Then it it pulls back to a nebula probably the Eagle nebula because it contains what appears to be the pillars of creation a star forming region. Then you notice the noise from Earth drops off, the Dec.8 1941 FDR speech the day after the bombing of Pearl Harbour in Hawai’i, then the final bit was a bit of German from the 1936 Olympics in Berlin. Then it pulls back through the spiral arm of the galaxy and then past the local group and then an elliptical galaxy and then the local supercluster of galaxies and then just a stream of galaxies.

Now to the main part of the story and that is the signal. The signal i first heard by Ellie with her headset plugged into the Very Large Array in New Mexico. This is really not done they normally just look at screens and most times they just have a program that keeps an eye on any signal to see if there are signals coming in. In the book and the movie they have sETI researchers being the only ones using these big arrays and hogging them from other research. It is usually completely the other way around until the Allen Array was built just for sETI by a wealthy tech executive, but usually research into from planets to nebula’s to galaxies are being studied with the sETI searches going on in the background. After the signal is detected she calls into the office of the array where to other scientists are taking car of other business and then they rush into recording the oncoming signal and measuring the signal and realizing that the signal comes in bursts of prime numbers. Prime numbers are numbers that only evenly divide when they are being divided by itself and one, like 2,3,5,7 etc. Nothing in nature creates signals that come in prime numbers, anything rotating will repeat in regular intervals, jets will produce a study that might vary but will be probably irregular, or you will get sudden bursts of signals. Also they move one of the dishes away from where the rest of them a pointing, this is to make sure the signal is not coming from a local source and actually coming form where they think the signal is coming from. Also they talk about local military bases and the shuttle to make sure they are not just picking up some errant noise from them In the signal they thought they were receiving was just a way of the ET’s of getting the humans attention with information hidden underneath, like the a copy of the first broadcast they received. Which was from the 1936 Olympics games with a speech from probably the worst human being that ever lived, the aliens probably didn’t know about his politics it took 26 years to get to Vega and back and since the book was wriiten in 88 the total trip was 52 years. And yet underneath that was another layer of information which was a design for a machine that would generate a wormhole.

There are several main differences between the book and the movie. In both Ellie’s father dies but in the book Dr. Drumlin actually married Ellie’s mother becoming Ellie’s stepfather. Also in the movie there is only one spot in the machine and in the book there was six spots but the movie needed some extra drama so they made a bit of competition. Also there was only one machine made .

The movie touches on some of the consequences of what would happen if such claims would happen. Mostly of how people would react from the people who welcome the aliens to ones that would think the aliens are demons or a hoax. Once Ellie goes through the wormhole and it appears that she was gone only 5 minutes but from her perspective she was gone for 18 hours, and the clip recording device also recorded 18 hours of static. She is put in front of Congressional hearing where the former NsA head goes on about how it was all generated by Hayden a rich business man who funded a lot research into the project. The underlying idea was Hayden made it all up for attention. This all reminds me of what happened Galileo during his trials, some the early arguments were probably how can we know you just made up the sketches, or put something in front of telescope to make it look like the moons of Jupiter were going around Jupiter or there were phases of Venus like the moon, there is a huge difference all you had to do was to make your own telescope and look, you did not have to build a wormhole machine. One thing the movie does well is the friendship between Ellie and Pastor Joss, although they are coming from different approaches on scientific and the other religious there is a romantic relationship and tolerance which is lacking nowadays. With some people you just have to mention vaccines or there is a horrible disease going around and they go into a conspiracy. Also in the clip above there a scene where Ellie had to go around to get financing before Hayden stepped in, scientists do have to a lot just to get financing, like taking a lot of time to write proposals to committees to get funding or time at a facility.

Calculus War(preview)

Calculus Wars

Before discussing the battle of who should get credit for who came up with calculus we probably should discuss what is calculus. Calculus has to main branches on is differential calculus and the other is integral. Differential calculus is used to find the rate of change in a system because it is based of finding the slope of the tangent line to a curve.

Let say that a particle changes it speed a rate of a=x²

The formula to find the derivative of an equation of the above function is given by:

f'(x)=lim(h->0)((f(x+h)-f(x))/h), h is a small increase in the distance in the x direction and f'(x) is the notation for a derivative or dx/dy is used.

Now you place the a=x² into the formula you get

f'(x)=lim(h->0)((x+h)²-x²/h

f'(x)=lim(h->0)(x²+2xh+h²-x²)/h

Now you can see the x squared terms cancel each other out and the division of h cancels the h’s in the 2xh term and of the h’s in the h squared and putting the 0 in the last h left you get 2x.

There is more general expression to find the derivative is:

f(x)=xⁿ

f'(x)=nx^n-1

It is a bit more complicated than that for some functions but it is important tool for finding how fast something is moving or growing like my favourite exam question how fast is mold growing a block of cheese(yes that was an actual question on an exam. )

Now the second type of calculus and that is integral calculus. Integral calculus is finding the area under a curve. This is done by dividing the area under the curve into smaller rectangles so the area of rectangle is really small and there is no area that is not left over. An integral generally looks like:

∫F(x)=(1/(n+1))xⁿ⁺¹+C, where F(x)=xⁿ

The ∫ is just a fancy s because you are summing a lot of thing together, also to get a definite answer you need to have an upper and lower values but if you don’t you need to add the C. Thi can be useful to find area and if you rotate around an axis you can get a volume. But also work is defined by W=Fd where d is the distance and if divide the distance into small increments and integrate you can find work done. Also there is a relation between the integral and the derivative and that is:

F(x)=d/dx∫F(x)dx

More from the Flat Earth

Preamble/Disclosure

Here is another Flat Earther MultiTomTom, I find some these topics on other debunking websites and youtube channels and find other issue that they do not cover or I go to the original source an watch a number of their videos. This is the case here unfortunately some his stuff goes into religious grounds I want to discuss a few things before I get started, like I am just trying to point out the difference between their claims and science, there are plenty of people who are religious and trust the science of evolution, their is a somewhat famous situation between a Prof. Lenski and a lawyer schafly who wanted to disprove Lenskis’ research in the study of evolution of the bacteria e.coli, Lenski was actually in church attending a wedding during a day schalfy group was attacking him. Also that flat earthers are just doing this as a creative exercise a members of the Flat Earth s society an organization which has been around for some time. But some of them are looking for attention,some are trying to prove that they are smarter than everyone else and know some hidden truth that the rest of us sheeple don’t get and there are other reason for them arguing for the flat earth. These conspiracy theories do have a cycle at one time the moon landing was being argued, then it was anti-vax, then flat earth and now covid-19, and of course all the theories of Lee Harvey Oswald didn’t shoot JFK. Why go thru debunking these claims if most people know that they are false one reason is to prevent others going down that road, and I have heard people on a call on show trying to prove the flat earth several times. There is nothing wrong in asking questions, this i why Carl sagan said children are smarter than adults because they ask questions that adults are not ask. Another warning this guy uses some curse words in hi videos.

In the first video here he trie to convince us that the sun and stars are different kind of objects and that the sun is not as hot as it is and is a lot closer then it is. First how do we know that stars and the sun are basically the same type of objects we use their spectrum. They all have a large very hot source of light and heat in their cores and as the light leaves the the gases adsorb the energy that the light has and leaves dark bands in the spectrum corresponding to the wavelength or energy that it takes to excite the electron out of its orbit, given by the equation E=hv, where h is the plancks constant and v is the frequency of the light. Now if you point this new device called a telescope it ha only been around for about four hundred years at a star and pass it thru a prism or let the light hit a diffraction grating and you will see a spectrum kind of like the suns He also goes into how temperature in the upper atmosphere is higher than lower layers, these particles have more energy and therefore a higher temperature.

In this second video he starts with a picture of a beach and he says the evidence for a non-rotating Earth because the water is not being flung int space. If you have a spinning object there will be a force called the centrifugal force which will cause this but this does not take into account gravity, one thing a lot of flat earther don’t understand is gravity and how mass effects it. Gravity id giving by the equation by F=GM₁M₂/r², for this argument it does not matter which mass is the Earth but the value does it i 5.84 exp24 kg, which easily counteracts the centrifugal force. Another argument that some flat earthers use that there is a vacuum in space and you need something to hold the atmosphere in so you can not have an atmosphere that goes into a vacuum, without a dome or similar device. Gravity actually work on every molecule and atom and keeps the atmosphere around the Earth but the distance from the center affects the strength of attraction and also the mass of the molecules, like O₂
has a stronger attraction to the Earth then H₂ which is much lighter and that is why isn’t much H₂ jut floating in the atmosphere.

Now in the last video for now, he tries to debunk the radius of the Earth by the showing a picture taken by another flat Earther of two oil rig on jut over 6 miles away and the other over 9 miles away. Not going to worry about the calculation but they don’t seem to take into account refraction, the Earths atmosphere will bend light and this changes in different conditions like humidity and temperature. I think three video is enough at one time he ha more and maybe more later.

Oortn’t be nice

Our star probably have a cloud of debris leftover from the creation of the solar some 4.5 billion years ago called Oort clouds after Jan Oort, this cloud extends from about 1000 AU to 10,000 AUs. This was probably formed when there was a lot debris left orbiting around the sun with protoplanets and if this debris come close enough to the protoplanets their orbits will change and can be thrown to the out edge of the solar system but these new orbits will be highly elliptical at first but since these systems are formed in the galaxy the galaxy’s gravitational potential will circularize the orbits. One way to think of it is a banked racetrack, If you don’t have enough energy or speed you fall into the center, as you gain speed you go up the bank and if you have enough speed you can go off the track, but in this system the racetrack is embedded inside of another racetrack. Actually again it is more like a racetrack embedded in a racetrack that i embedded in another. As the debris or asteroid approaches a planet the gravitational attraction between the two increases and the speed increases and if asteroid gain enough speed it will be thrown out into the solar system and finds it own orbit or if has enough speed it will leave the sytem but if it doesn’t it will keep orbiting around its sun. Over time the interaction between the influence on the asteroid by the galaxys’ gravity will make the orbit more and more into a circle, and this happens to many objects at the same time. It is likely that other stars have Oort clouds of their own that have evolve over time. This study looks at star that are within that are within 16 pc of the sun and rewind them back about a billion years to where they where in the galactic potential. This was done because a you go near the center the galaxys’ gravity become stronger so the amount of energy needed for the asteroid needs to be less and the distance from the star is less as well. Most stars in this study formed at least 3 to 4 planets within 100 AU of the center of the disk. After 100 million years after the simulation began only 2 percent of the small bodies remained in the system, and after a billion years only 0.3 percent are left. Forty percent of the planets are ejected by the first 200 million years and after a billion years 71.6 percent are ejected. The pace between stars could be full of planet and small bodies that be useful if someday we do venture out there, they might have water, hydrogen, carbon,oxygen, sulfur, hydrogen,nitrogen, and phosphorus or also known as CHONPs which are the key ingredients for life on Earth.

2011.08257.pdf (arxiv.org)

Oortn’t be nice (preview)

Our star probably have a cloud of debris leftover from the creation of the solar some 4.5 billion years ago called Oort clouds after Jan Oort. This was probably formed when there was a lot debris left orbiting around the sun with protoplanets and if this debris come close enough to the protoplanets their orbits will change and can be thrown to the out edge of the solar system but these new orbits will be highly elliptical at first but since these systems are formed in the galaxy the galaxy’s gravitational potential will circularize the orbits. One way to think of it is a banked racetrack, If you don’t have enough energy or speed you fall into the center, as you gain speed you go up the bank and if you have enough speed you can go off the track, but in this system the racetrack is embedded inside of another racetrack. Actually again it is more like a racetrack embedded in a racetrack that i embedded in another. As the debris or asteroid approaches a planet the gravitational attraction between the two increases and the speed increases and if asteroid gain enough speed it will be thrown out into the solar system and finds it own orbit or if has enough speed it will leave the sytem but if it doesn’t it will keep orbiting around its sun. Over time the interaction between the influence on the asteroid by the galaxys’ gravity will make the orbit more and more into a circle, and this happens to many objects at the same time.

The Pluto Files or The rise and fall of Plutos planetary standing or how Neil Degrasse Tyson got on every child in America hitlist.

sorry for no capital s I am having trouble with the s key.

Before he was talking about the stars, before he was travelling the Cosmos in the ship of the imagination, before he was correcting James Cameroon use of constellations in Titanic or before he was on the Daily show he was hired as director of the Hayden Planetarium and at the beginning of his tenure he oversaw the redesign of the Planetarium which costs 230 million dollars to do. In the s scheme there were two displays comparing the two classes of planets in the solar system theTerrestrial planets (Mercury, Venus, Earth and Mars) and the Jovian planets (Jupiter, saturn, Uranus and Neptune). But there was no Pluto when the display was opened on February 19, 2000 but really wasn’t noticed for nearly a year when a reporter heard a kid asking their parent where Pluto was and an article came out on Jan 22 2001. How did this happen?

For thousands of years there were several objects that did not move like the distant or what they thought were the fixed stars. These were known as the planets by the Greeks from their word for wanderer, these were Mercury, Venus, the Moon, Mars, the sun, Jupiter, and saturn. These were found by looking up at the sky with the unaided eye. Then came the telescope and some individuals started to point them at the sky and after a time the disease called aperture sickness, this is a desire for bigger and bigger telescope to get better and better resolution. One of the first people to take up astronomy professionally was William Herschel who was also a composer. In 1781 on March 13 he discovered Uranus, he wanted to call it George after the king at the time but the international astronomy crowd didn’t think was appropriate so an it was named after a Greek god. In 1845 John Couch Adams asked to check if there was a planet where he calculated but was denied but at the same time in France Urbain Jean Joseph LeVerrier calculated the coordinates and sent to the Berlin observatory where Johann Gottfried Galle discovered Neptune on september 23 1846 within half degree to where was predicted to be. But there still seemed to be something effecting the orbits of Neptune and Uranus. This planet was dubbed Planet X for unknown. One of the people who took the hunt of Planet X was Percival Lowell who was a member of wealthy family in Massachusetts, who got into looking for evidence of Martians on Mars and also looking for Planet X but died in 1916 before he could find it. Then came Clyde Tombaugh to look for the mysterious object. And on January 23 and 29 of 1930 he saw an object around Delta Geminorum the eighth brightest star in the constellation of Gemini. He did using a new device for the time called a blink comparator which you put at least two photos of the region you are looking at and quickly switches them back and forth quickly and if there is an object that change position then it is a planet , an asteroid, or a comet. When people started to search for they thought the planet should be around 18 time the mass of Earth based off how much Neptune was off the orbit they predicted. The total new planet was eventually determined to be about 1 percent that of the Earth. This was determined by measuring how much it moved over a period of time, for orbits a long as Plutos you can only measure a small part of the orbit. To determine the angular velocity of the an object you use a formula like :

dθ/dt=-ωsin(ωt)+ωcosωt

The speed was determined by measuring how long it took to pass in front of a star. And for the longest time Pluto was out there all be itself until its largest moon Charon was found in 1978. And in 2005 the moons Nix and Hydra were found and eventually a fifth moon styx. All orbiting the iceball that is 70 percent rock and 30 percent ice, but since rock is much denser it only take ups 45 percent of the volume at a surface temperature of a -365 F some 40 times the distance from Earth. But the neighborhood was already getting crowded, first Pluto crosses the orbit of Neptune for 20 years of the 248 year orbit. But in 1992 Dave Jewitt and his grad student Jane Luu using a 2.2 meter telescope in Hawaii found 1992 QB1 and then more and more objects were found. Like the 20000 Varuna which i about 900 km, in 2002 50000 Quaoer about 1300 km in diameter(I have board game IQ 2000 which is a kids trivia game made in the 80s with the final destination is Quaoer). And then came sedna at 1500 km, when it was first found Mike Brown the discoverer wanted to name it Xena (I guess someone like the warrior Princess). About this time the International Astronomical Union which is an international group of about 10,000 astronomers which started in 1919 got involved in the definition of what a planet was. Eventually after trying for a couple of years they made a committee of five astronomers, a journalists and a historian. The committee was considering two criteria for planethood, they must be large enough to overcome resistance from it becoming a sphere and they must orbit around a star and not another planet. This was taking place at a conference and out on the conference floor there was another criteria and it was that it had clear its orbit which was the death nail for Pluto planethood, it was voted on and the new definition of a planet was:

A “planet” is a celestial body that(a) is in orbit around the sun,(b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape (c) it clear its neighborhood.

Now Pluto is considered the leader of a new class of objects called Plutoids in the Kuiper Belt that has new objects found all the time. Pluto is still an interesting object especially since the New Horizons pace probe flew by on July 14 2015, where they found ammonia on the surface suggesting water underneath the mostly ice mantle. It ha mountains made from ice cyrovolcanoes that instead of lava coming out of it has water and has 45 kilometer long dunes that are over the spuntik Planitia a large region that looks part of a heart over a large part of its surface. The surface of Pluto and Charon both have no impact craters which means of there are impacts there i a liquid ready to fill in crater. Does it really matter if it is called a planet, a minor planet or a Plutoid, not really it will till orbit around sun like it always no matter what is called. There weren’t any rally death threats but a lot kid did write him about the change, some kids actually debated the issue, and the grown ups at the time did not storm the planetarium to make him change the display. It was mostly an issue in the states where the discoverer was from, his ashes actually to Pluto.

Liquid water ocean under Pluto ice? | Space | EarthSky
Ammonia on Pluto’s surface points to liquid water underground | Astronomy.com
Home – Neil deGrasse Tyson (haydenplanetarium.org)

Part 6

As they approached the carrier/probe hybrid vessel they veered over to the port side and docked with one of the probes. The airlock cycled and the doors opened. On the other side a thin but in shape middle aged man with a goatee and old fashioned glasses on and a bald head. “ Hi, I am commander John Hrab of escort carrier 841, welcome aboard, well this is probe 842. Flight officers Smith and Urusa, and specialist Tom and Jerry LaChance will be manning this vessel so you can leave your gear here but come with the rest of the tour.”

They went down a long thin corridor and then into the main body of the carrier. There was a long corridor that ran along the length of vessel with quarters for the fighter pilots, so the left their gear in their chambers. In the the center of the ship was the observation deck in the front, in the the middle was the control and command room with the engine room at the rear, the top deck had an observation lounge with a retractable metal covering, and the far side was another corridor and more quarters. And there was probe 842 on the other side. “Please go back to your chambers and at o1730 we will start to brief you all in the observation lounge and then have a meal.”

When they were all assembled in the lounge/conference room the metal covering wa over the glass ceiling. “At 0 hundred hours two freighter and the destroyer Pandora will be rendervousing with us here and then we will be going to hyperspace to journey to a nearby brown dwarf. Already there is already an asteroid/ice mining operation. The freighters will be picking up the already mined materials and the staff their and leave the next round of staff. Even in the thirty to one hyperspace zone it will take us several months to get there and we will drill the new crews, so none of you will go into hibernation, yet.” Everyone in the room seemed to understand what this was convoy duty. Next came the meal, nothing really fancy but it was fresh food the commander informed everyone fresh food non freeze dried, non powdered, non frozen food was rare. At the end of the meal the commander asked a young lieutenant he called Ian but no one caught the last name to get the dessert, it was a watermelon filled with lemon sorbet with mashed bits of watermelon mixed in. It was just about 1800 hours until everyone went back to their ships.

Back on board the 842 the crew started talking to one another. Urusa was from the New Haven moon colony in the Union in sector that most of the planet were taken form the New England area, the LaChance brothers were from a mostly warm water world called California and they came from the island of San Francisco. All four seemed to like growing some of their own food and started to think about how to grow something with artificial light in the cargo hold. After a while they settled in their bunks until about 40 minutes before the rendervous. They got the power plant to produce more energy and started to communicate with the command center. They started their main engine, even connected to the large vessel they needed their engine going as well. Also their hyperdrive was always on because it supplied the gravitons needed for the artificial gravity. Well more like aligned the gravitons in a field that kept the crew from floating around in the space.

About 5 minutes before they were suppose to arrive the Pandora and three freighters came into real space. Over ther intercom came a signal, “Guess we are early is everybody ready to go, we are.” Then Commander Hrab, “Yes. Get the hyperdrives online, probes switch navigation control over to command.” Then several moments later all craft disappeared in a shrimmer.

Are These the Planets You Are Looking For?

In science there are of course new ways of looking for evidence for what you are looking for. That is true if not specially so for SETI. There are two different technological searches and a biological searches to talk about. One is looking for Dyson Spheres and other mega structures orbiting other stars in the search of life because it would take life to build such an object. But it might not be a direct observation but if there was seen a series of regular space emissions specially if the pattern is something that can not be made in nature like 1 dot, 3 dots, 5 dots, 7 dots and so on up the prime number series. Another way of looking for life is looking at chirality of the molecules on a planet. The chirality is the basically is that molecules can have a mirror image one another and usually referred as it handiness, this will also affect the light reflected. Now light has several different ways it can be polarized, it can either be polarized along the x or y direction or it can be polarized along the axis the wave is moving around it can either be clockwise or right handed, or counter clockwise or left handed. When light is reflected off an planet some of the light will interact with organic molecules and this will change the polarization of the light. When organisms make molecules they are made with the same chirality because they are basically factories on the level. So if if the is polarization of the light coming from a plane is in own direction there is more of a chance that there is life on the planet. Another one is looking thru the TESS’s input catalogue of possible worlds which numbers around 2120 possible worlds that need to confirmed with 66 confirmed. The 100 m Greenbank Telescope in Virgina was used to look at 28 stars with 6 observations at 5 min exposure times and then run thru TurboSeti a program looking at doppler shifts in the data in four different bands, L-band 1.10-190 Ghx, S band 1.80-2.80 Ghz, C band 4.00-7.80 Ghz, X-band 7.80-11.20 Ghz with the strongest signal being in the l and X-bands. These are on going projects in the SETI world of science so there were no real results but the results should be interesting.

2101.11137.pdf (arxiv.org)

Ejected

This paper studies what happens if a star has a Jupiter sized object orbiting around a star and a second star comes close to it. This is studied in the environment of a open star cluster where stars are formed so the likely hood of such encounters would be increased. Also from 50-75 percent of FGK type stars are in binary pairs with some in triple configurations or more. In this study the final configurations comes in 7 different variations, one the planet is ejected from its host star and is adrift without a new host, second the planet is ejected by its host and is captured by another star, another possibility is the planet collides with another object, the two stars could become a wide binary pair and with the planet orbiting around one of them could an S capture, the stars could become close binaries and the planet orbits the pair could a P type capture or the planet could be put into an unstable orbit around a star.

The authors start with a cluster large enough to have 100s or 1000s of stars in it, this being larger than most still generate the same number of stars as a number of smaller clusters. This density allows for multiple encounters over several 100s of Myr. The main criteria on what a planet will do is determined the masses of the planet (m_J),the mass of the sun (m_s), the mass of the each of the binary stars (m₁,m₂), m_SJ is the mass of the star and planet, and m_bin is the mass of the binary pair. All this is used to determine the critical velocity of the on coming star,v_crit=(G(m_SJ+m_bin)/m_SJm_bin)*((m_sm_J)/a_SJ)+m_b1m_b2/a_bin), where a_SJ is the semi-major axis of the Star-Planet, a_bin is the semi major axis of the binary pair, and G is the gravitational constant. Another factor that is needed to considered and is dependent on the critical velocity is the cross section area of the interaction between the stars, withibn this area is when the gravity between to the stars can affect the planet. The cross sectional area is given by σ_x=πb_max (N_x/N ) where b_max is the maximum semi-minor axis that could be effective and N is the number of passes and N_x is the number of times that x happens. Also, b_max is given by (Cv_crit/v_inf+D), were v _inf is the velocity of the object coming from far off, C and D constants determined empirically.

There were thousands of runs done with different values like for the total mass of the binaries of 0.2, 1,5 and 25 solar masses, semi major axis of the binary of 0,0.2,5, 125 and 3125 Aus. For orbits of less than 12 days or less the eccentricity was set 0 because the orbits would self circularize over time. And stars with an eccentricity of 0.6 AU we considered to be poorly constrained. It was found that cross section for ejection is 1.7 *10⁵ au ² for a system. Out of every planet that is ejected there are 10 that stay with their host star, 0.1 collide with a star, 0.1 are captured by other stars.

paper

Just testing around

,v_crit=(G(m_SJ+m_bin)/m_SJm_bin)*((m_sm)/a_SJ)+m_b1m_b2/a_bin)