Orbital tethers as momentum capacitors Carmack to Musk: What about rotovators? Carmack's game set on Phobos Zero Relative Velocity Transfer Orbit (ZRVTO) between Phobos and Deimos tethers ZRVTO mass savings ZRVTO equations End of life sats to use as a momentum bank anchors Propellant mass as cost driver Re-entry propellent imported by tethers The Heteroclinic Zone Phobos help with Mars EDL Park…
Science historian Thony Christie (also known as @rmathematicus ) had a number of essays on the Scientopia website. Scientopia bit the dust and I thought the essays were lost. But Bryan Kelly showed me they still exist on the Wayback Machine. This essay by Christie is one I often refer to. I copied and pasted it from the Wayback machine with Thony Christie's permission. Edit June 12, 2023:…
Kerbal Space Program The Kerbal Space Program has demonstrated video games can be a very effective teaching tool. It used to be very frustrating trying to talk about orbital mechanics. Use a word like "perigee" and eyes would glaze over as the audience tunes out. But now there are many KSP players who are comfortable with terms like The Oberth Benefit, Bi Elliptic Transfers and other what use to…
Back in December 29, 2016 Bridenstine made a blog post "Why The Moon Matters". Bridenstine was representative of Oklahoma at the time. Sadly the post was taken down when Bridenstine left his post as representative and became NASA administrator. But I recently found the post using the Wayback Machine . Bridenstine's reasons were pretty the same arguments made by lunar scientist Paul Spudis (RIP). I…
Now Available at our online store Hopefully it will soon be available on Amazon as a Kindle book. I am not happy with this coloring book. Pages should be opaque enough that images on the other side don't show through. I had failed to specify heavier weight paper when printing this book. So I am cutting the price of this book from $5.00 to $2.00. I will print a version with better quality paper…
On June 30 in 1908 the Tunguska object took out a good chunk of forest in Siberia. In February of 2016 the United Nations approved a resolution stating 30 June International Asteroid Day to observe each year at the international level the anniversary of the Tunguska impact over Siberia, Russian Federation, on 30 June 1908 and to raise public awareness about the asteroid impact hazard A good time…
Sections of this long post: 1) Space Cadets 2) Space Meow Boys 3) Tom Murphy 4) James Nicoll 5) Charlie Stross 6) Opening A New Frontier Is Doable Space Cadets We are confined to a small, fragile planet. Being limited to a finite body of resources mean logistic growth . And we're rapidly approaching the ceiling to our logistic growth. Opening a vast new frontier would allow growth for centuries or…
I've been invited to talk at a recreational math conference at Lake Tahoe April 28. I will talk about the family of conics associated with a space elevator or a vertical orbital tether. The presentation combines stuff from a number of my earlier blog posts. Here is the pdf I will use for this talk. A screenshot from the cover of the booklet. Pages 2 — 5 -- includes the visualizations I use to…
Mars Elevator With Conventional Materials Mars spins nearly the same rate as earth (about a 24.62 hour day). Mars has about 1/9 earth's mass. At 17,000 kilometers, altitude of Mars synchronous orbit is less than half the altitude of geosynchronous orbit (about 36,000 kilometers). These considerations have led some Mars enthusiasts to claim a Mars elevator made of conventional materials is…
Vectors Rotation Matrix Proportional Scaling Matrix Non Proportional Scaling Matrix Shear Matrix Reflect Matrix Determinant of a Matrix Lorentz Transform Matrix Vectors Vectors are a way to describe point locations with numbers. Vectors can be used to build simple shapes like a cube or just about any shape you can imagine. We do lots of stuff to these vectors with matrix multiplication . We can…
Gravity doesn't cancel at the Lagrange points "There are places in the Solar System where the forces of gravity balance out perfectly. Places we can use to position satellites, space telescopes and even colonies to establish our exploration of the Solar System. These are the Lagrange Points." From Fraser Cain's video on Lagrange points . A lot of pop sci Lagrange articles repeat and spread this…
Xenon The Noble Gas Xenon is one of heavier Noble Gases Screen capture from ChemicalElements.com The noble gases are the orange column on the right of the periodic table. These are chemically inert. Which means they're not corrosive. This makes them easier to store or use. Low Ionization Energy Per this graph is from Wikipedia , Xenon has a lower ionization energy than the lighter noble gases.…
A Family of Conic Sections Below is a general vertical space elevator. The conic sections are the paths payloads would follow if released from a point on the tether a distance r from body center. We choose our units so radius of the balance point is 1. Centrifugal acceleration matches gravity at the balance point and net acceleration is zero. For tether locations above the balance point,…
Double Tidal Locking Pluto and Charon are mutually tidally locked. That is, they both present the same face to the other planet all the time. They hover motionless in each other's sky. Pluto is in Charon synchronous orbit and Charon is in Pluto synchronous orbit. What is more, the orbit is very nearly circular . From Stern et al's 2015 paper : (Thank you to Dr. Kirby Runyon for pointing me to this…
Three Orbital Tethers This post revisits Orbital Momentum As A Commodity . But now I will examine these tethers using Wolfe's spreadsheet . I envision 3 equatorial tethers to move stuff back and forth between LEO and the lunar neighborhood: The location of these vertical tethers avoids zones of orbital debris : The orange regions, LEO, MEO and GEO, have high satellite and/or debris density. Thus…
Kim Holder has been urging me to do this blog post. Her comments in various forums have been helpful in thinking about this. Vertical Lunar Tether In A Polar Orbit This sky hook is a gravity gradient stabilized vertical tether. It's in a polar orbit so it will pass over the poles as well as the lower lunar latitudes. Unlike an equatorial orbit, there are only two occasions during a lunar orbit…
Hilda Asteroids - Red , Sun Jupiter Trojans - Blue , Main Belt - Green The above image was made from screen captures of Scott Manley's beautiful animation Asteroids In Resonance With Jupiter. Jupiter is the dot off to the left, the sun is the yellow dot in the middle. Within the Main Belt can be seen Mercury, Venus, Earth and Mars. I colored the different asteroid populations so we can tell them…
There are proposals for rotovators to catch payloads in low earth orbit and then throw them to higher orbits. It occurs to me that rotovators used for throwing comm sats to GTO could also help the upper stage re-enter earth's atmosphere at a lower velocity. 1) Rotovator catches upper stage and payload in LEO. 2) Rotovator throws payload to higher orbit. 3) Rotovator drops upper stage into a…
This is the fifth in a series of posts using Chris Wolfe's spreadsheet to look at various elevators. 274,000 km Lunar Tether This is based on the Ladder PDF written by Liftport founder Michael Laine and Marshall Eubanks. Eubanks and Laine suggest the use of Zylon or M5. This is why I've been using Zylon through out these tether posts. These gentlemen have invested a lot of time and effort…
Malthusian growth model The Malthusian growth model sees population growth as exponential. P(t) = P o e rt where P o = P(0) is the initial population size, r = population growth rate t = time Growth of microbe populations are often used to illustrate this. Let's say an amoeba will grow and divide into two amoeba after an day of absorbing nutrients. Day 1: 1 amoeba Day 2: 2 amoeba Day 3: 4 amoeba…
Here you will find information on Neil Tyson you won't find on his Wikipedia page. Carl Sagan's critics were wary of pop science. Would the need to entertain come before rigor and accuracy? And those fears have been realized with Neil Degrasse Tyson. So much of his pop science is wrong. The man is a source of misinformation. 1. Idiot doctors 2. George Bush and star names 3. Hamid al Ghazali: "Math…
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…
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…
A Phobos tether can be built in increments, it is useful in the early stages. So there's no pressing need to build a huge structure overnight. I will look at various stages of a Phobos tether, examining mass requirements and benefits each length confers. To model the tether I am using Wolfe's spreadsheet . I will use Zylon with a tensile strength at 5,800 megapascals and density of 1560 kilograms…
I plan to do a series of posts examining elevators and tethers. I will link to them as posts are completed: Lower Phobos Tether Upper Phobos Tether Deimos Tether Mars Elevator Liftport Lunar Elevator through EML1 Lunar Sky Hook Trans Cislunar Railroad LEO Rotovator Pluto Charon elevator They will be based on Chris Wolfe 's spreadsheet for modeling tethers. I'll try to explain how Wolfe's…