Stainless Steel Starship

Welders in a Texas swamp have built a starship. But don’t bet against SpaceX.

Starship is a prototype upper stage for a next-generation, fully reusable, two-stage-to-orbit launch vehicle designed to enable the human exploration of the solar system and the colonization of Mars. It’s made from stainless steel. (A little carbon converts iron to hard steel; a little chromium converts steel to corrosion-resistant stainless steel.) At cryogenic temperatures, grade 301 stainless steel has higher strength-to-weight and strength-to-cost ratios than carbon fiber reinforced polymer, and it has a higher melting temperature.

Starship will dissipate orbital energy by entering a planetary atmosphere like a sky diver, belly first, its fore and aft fins rapidly moving to control its descent prior to a tail-first rocket-powered landing. Strong electric motors powered by Tesla batteries will flap the fins.

Starship is powered by next-generation Raptor engines, the first full-flow staged combustion rocket engines to fly. In these efficient closed cycle engines, no propellant is wasted: all the oxidizer (and some fuel) power the oxidizer turbopump and all the fuel (and some oxidizer) power the fuel turbopump, which together pump gaseous oxidizer and fuel into the combustion chamber to combust and thrust. The oxidizer is liquid oxygen; the fuel is liquid methane, the primary component of natural gas, which can be manufactured from the martian (or terrestrial) atmosphere.

SpaceX Stainless Steel Starship Prototype

After the Moonwalk

Iconic is Neil Armstrong’s photograph of Buzz Aldrin during the first moon walk, with Armstrong reflected in Aldrin’s visor. Much less well-known is this pair of photographs taken just after the moon walk. To my eyes, Armstrong seems exhausted but happy; Aldrin seems satisfied … and over his shoulder, almost casually, is a window, and outside the window is the lunar horizon, with its stunning airless black sky at day! Fifty years later, I still imagine A & A trying to catch a few zzzs … in hammocks … in their home … on the moon.

Neil Armstrong and Buzz Aldrin in the LEM after the first moonwalk, Monday, July 21, 1969

“Contact Light”

Our TV is broken, so Aunt Nora invites us to her apartment. (Aunt Nora isn’t really our aunt, but she introduced our parents to each other, so that’s what we call her.) My brother Jim and I lie on the floor close to the TV, while the adults sit on the couch. We watch NBC not CBS, so we miss Cronkite’s commentary. The late afternoon video is a simple animation; the famous 16-mm film — only later synchronized with the audio — would return to Earth with the astronauts 4 days later.

The tension is palpable. The cartoon lander reaches the surface at the expected time, but Aldrin’s monotone readouts continue. Absence of video heightens the audio. Mission control radios “60 seconds” of fuel remaining. Then “30 seconds”. I hold my breath. At last, Aldrin reports “Contact light” — we have touched the moon — followed by Armstrong’s famous, “Houston … Tranquility Base here, the Eagle has landed”. Of the landing site, my mother observes, “They’ve already named it”.

No one wants to cook, so we go to McDonald’s for dinner. As we drive, I see a small shop with photos of the three astronauts in its window. The streets are still. The world seems stopped.

10:56:15 PM EDT, Sunday, July 20, 1969

As Collins orbits the moon solo, Armstrong and Aldrin forgo a scheduled sleep period, moving forward the moonwalk. Finally video — live from the surface of the moon —  shows a LEM landing leg, first inverted but quickly rectified. Armstrong describes the surface as “almost like a powder”. Again I hold my breath, a lump in my throat. “Okay. I’m going to step off the LEM now … that’s one small step for [a] man, one giant leap for mankind.” I don’t hear the indefinite article, but I immediately grasp the meaning. Armstrong reads the plaque, “We came in peace for all mankind”. Aldrin practices locomotion, which “would get rather tiring”. The president phones. We leave Aunt Nora’s as the astronauts prepare to return to the LEM.

The next morning I sit on my living room floor reading two newspapers: The New York Times, with its simple banner headline “Men Walk on Moon” — which still brings me tears of joy, triumph, and wonder as I write this 50 years later — and the local newspaper, with its astonished “Now Do You Believe!”.

My Monday morning newspapers, July 21, 1969

Wooster Epicycles

A vector is the sum of its components, a mechanical vibration is a combination of its normal mode motions, a quantum state is a superposition of its eigenstates, and any “nice” function is a Fourier sum of real or complex sinusoids, $e^{i \varphi} = \cos \varphi + i \sin \varphi$.

The animation below traces the Wooster W in epicycles of 100 circles-moving-on-circles in the complex plane. Algebraically, the trace is a complex discrete Fourier series $\sum c_n e^{i n \omega t} =\sum r_n e^{i (n\omega t + \theta_n)}$, where $r_n$ are the circle radii, $\theta_n$ are carefully chosen phase shifts, $\omega$ is the fundamental angular frequency, and $t$ is time.

Using Fourier analysis, any reasonable path can traversed by a moon orbiting a moon orbiting a moon orbiting … a planet orbiting a star

Redefining SI

Today the SI (Système international d’unités) base units are redefined. The following are now exact. Memorize these numbers!

Cs-133 transition frequency constant $Δν_{\text{Cs}} = 9\,192\,631\,770~\text{s}^{−1}$ defines the second.

Then light speed constant $c = 299\,792\,458~\text{m}\cdot\text{s}^{−1}$ defines the meter.

Then Planck’s constant $h = 6.626\,070\,15\times 10^{−34}~\text{kg}\cdot\text{m}^{2}\cdot\text{s}^{−1}$ defines the kilogram.

Then electron charge constant $e = 1.602\,176\,634\times 10^{−19}~\text{A}\cdot{\text{s}}$ defines the Ampere.

Then Boltzmann’s constant $k = 1.380\,649\times 10^{−23}~\text{kg}\cdot\text{m}^{2}\cdot\text{K}^{−1}⋅\text{s}^{−2}$ defines the Kelvin.

And Avogadro’s constant $N_{\text{A}} = 6.022\,140\,76\times 10^{23}~\text{mol}^{−1}$ defines the mole.

And luminous efficacy constant $K_{\text{cd}} = 683~\text{cd}\cdot\text{sr}\cdot\text{s}^{3}\cdot\text{kg}^{−1}\cdot\text{m}^{−2}$ defines the candela.

(Where “sr” is the steradian or square radian, the 3D analogue of the 2D radian.) Discussion continues about the mole and the candela, including whether they should even be base units. The new definitions break the relationship between the C-12 mass, the dalton, the kilogram, and Avogadro’s constant, and the candela is arguably a photo-biological quantity.

I wish my phone number were 919-263-1770.

I set the alarm for 8:55 AM. Brutal, but I wanted to watch live the National Science Foundation Event Horizon Telescope news conference. I was expecting the first image of a black hole, and the EHT team did not disappoint. But the black hole was not the Milky Way’s Sgr A*, but M87*, a thousand times further but a thousand times larger (billions rather than millions of solar masses).

For Astronomy Table lunch at Kitt’s Soup & Bread, I quickly created the graphic below to illustrate various radii of a mass $M$ Schwarzschild black hole, a good approximation to this rotating Kerr black hole. The event horizon with reduced circumference $R_s = 2 G M / c^2$ is the point of no return, the causal disconnection from which even light can’t escape. The innermost stable circular orbit at $3R_s$ marks the inner edge of the accretion disk. Massless particles like photons can orbit even closer, at the $1.5R_s$ photon sphere, where you can see your back by looking straight ahead! The ring of light (mainly 1.3 mm synchrotron radiation) in the EHT photo comes from photons with impact parameter $\sim 2.6R_s$ that just graze the photon sphere and can orbit multiple times before spiraling in or out.

Schwarzschild (“black shield”) black hole with event horizon, unstable photon sphere, grazing photon sphere, and innermost stable circular orbit

The Longest Day

December 22 is the longest day of the year, despite being near the northern hemisphere’s shortest daylight.

Earth’s sidereal day is the time to rotate 360° with respect to distant stars, about 23 hours and 56 minutes, and its solar day is the time between successive noons, about 24 hours. Earth’s obliquity (tilt) and revolution (orbit) require an extra rotation (spin) of about 4 minutes to go from noon to noon. Because Earth is coincidentally at perihelion (nearest sun and moving fastest) during the December solstice (maximum tilt toward sun), these effects combine to produce the longest solar day, about 24 hours and 30 seconds. (Clocks average this variation by recording mean solar time.)

In a discrete two-step approximation, the diagram illustrates the difference between solar and sidereal days for planets with 3 different tilts. From the first row to the second, the planets orbit the sun as they spin 360° (in the sense of the green right-handed arrow). From the second row to the third, the planets spin through extra angles (in the sense of the yellow right-handed arrow), so that the marked longitudinal planes again includes the sun. Tilted planets must spin further, taking extra time, to extend a sidereal day to a solar day.

Planet (yellow) orbits sun (green) near perihelion through solar and sidereal days (rows) for 3 planetary tilts (columns). Longitudinal square rotates 360° for a sidereal day and >360° for a solar day.

March Meeting — Guest Blog by Carlos Owusu-Ansah ’21

Carlos in action at his poster, with Andrew Blaikie ’13 and Daniel Blaikie ’19.

I thought the March APS meeting was fantastic. It felt great to present our research findings to people who cared about what Dr. Lindner and I were working on at the College. I attended fun talks about astronomical phenomena and learned many cool things about the evolution of our solar system.

It is easy to think that physicists are an elite squad and that their subject matter is esoteric, but being so close and interacting with them made me realize that they are just like us and that learning about physical phenomena is really great fun. I am really happy to have been given this opportunity.

March Meeting — Guest Blog by Katie Shideler ’21

Having never been to a physics conference, or even to the city of Boston, attending the annual American Physical Society’s March Meeting was all around a new and incredible experience. Being able to present my research to physicists from across the globe was nerve-racking but very insightful to get opinions of others who are far removed from the research I’m doing, so they brought in new perspectives I hadn’t thought of before.

Ready to start the poster session

My poster was set up next to a man who conducted similar research to me, so it was fascinating to see what he did differently with his system and how that changed the course of the experiment. Talking with him and exchanging ideas was one of my favorite parts of the conference.

Deep in conversation with an interested attendee

I also had the opportunity to sit in on numerous fascinating talks various researchers were giving. My favorite talk I went to talked about improving the design of the wheels on Mars Rovers, because NASA has been having problems with the Rovers getting stuck in the sand. This researcher and his team designed a new body for the Rover with new axes of rotation for the wheels to allow the Rover to keep moving and get itself out of the sand. It was pretty sweet to see clips of this thing moving through the sand. I also found this talk about nanorobots powered by lasers extremely interesting which seem to have the potential to make improvements in the medical fields.

Anyway, there were so many cool talks to go to I found it difficult to choose which ones to go watch. In addition to the awesome physics that was taking place, the city of Boston was extremely cool to explore and find local place to grab a coffee or a bite to eat. All in all, the March Meeting I would say was a success.

Wooster in Boston

As mentioned earlier, I’m at the APS March Meeting in Boston this week.  There’s so much to say about all the talks that I’ve been to, etc, but in this post I’m just going to tell you about all the amazing Wooster connections!

First off, of course, we have five students here this year from the REU program last summer, and Dr. Leary and I are both here.  It’s fun to bring students to the meeting so that they can see how huge and diverse the larger world of physics is.  One of the great things that usually happens at the Meeting is that Wooster alumni come by to see our student posters.

Andrew asks Carlos to fill him in on the latest progress in this work studying gravitational interactions for non-spherical objects

Tuesday morning I went to see Andrew Blaikie ’13 give a cool talk about graphene trampolines to be used as broadband bolometers.  Andrew is just about finished with his Ph.D. at Oregon.  He did a nice job with his talk, since he’s an old hand at the March Meeting by now.  Devoted readers of the blog will remember that we featured Andrew last year in the blog posts about the March Meeting in LA.  Andrew did the slash-slash project with Dr. Lindner for his Senior IS, so he came by the posters today to quiz Carlos Owusu-Ansah about his results with the latest incarnation of that research.

Melinda listens to Daniel explain light sensitive BZ waves.

Walking around, I also bumped into Melinda Varga, who was at Wooster last year doing a post-doc with Erzsébet Regan that blends physics and biology.  She is still doing the postdoc but now is physically based at Harvard Medical Center.  She came to the poster session to ask our students about their work!

Hannah!

I then also coincidentally sat down right next to Hannah Peltz Smalley!  Hannah was a Wellesley student who did the Wooster REU in 2017, and she is now a grad student at RPI.

Walking down the hallway to a session, I saw Nick Harmon ’04!  We chatted for a while to catch up.  He and his family recently moved to Indiana, where he started a position at the University of Evansville.

Amy Lytle investigates beautiful knit work at Elisabetta Matsumoto’s talk.

On Wednesday morning, there was session on Fabrics, Knits, and Knots that started with an invited talk by Elisabetta Matsumoto.  Many of you know that I am a knitter, so this was a cool “worlds collide” moment for me.  Afterward, I was up at the front looking at the demonstration pieces that Elisabetta had brought, and Amy Lytle ’01 tapped my elbow to say hi!  She graduated before I came to Wooster, but we’ve met many times by now.

Wednesday night, we had our group dinner, along with Popi Palchoudhuri ’16. She works here in Boston at E Ink, the maker of the ePaper technology that is in Amazon’s Kindle devices.  Popi is famous in beadpile history, both because she did the beadpile project as a first year summer student and again for IS, and also because of the quality of her lab notebook skills!

Maggie Donnelly, Wooster History ’11 and academic publisher for physics

Finally, I was walking around the exhibit hall one last time this afternoon.  I passed by the Institute of Physics booth, not planning to stop originally, but paused to ask a question about one of their display items.  The person I was talking to looked at my badge and said “College of Wooster!!”  It turns out that she was Maggie Donnelly ’11, a history major!  She was heavily involved in journalism at the College, took an editing job at an astrophysics journal once she left Wooster, and now loves being involved with academic publishing! One of her projects is the new Quantum Science and Technology journal by IOP, which you can see featured in the poster right beside her.  We talked for a while about the excellence of Wooster and what a wonderful community it is.  It was great to meet her.