I awoke early this Christmas morning to watch the successful launch of the James Webb Space Telescope. I remember the genesis of the telescope a quarter of a century ago when it was called the Next Generation Space Telescope. (The telescope’s name is controversial, and I would have preferred an astronomer’s name.) Its development has been prolonged and difficult, as the graphs below attest, but like its predecessor, the Hubble Space Telescope, I am confident of its revolutionary importance — if the upcoming weeks of deployment and months of commissioning succeed.

Development of the unprecedented Webb telescope has been long and challenging

Hubble is a warm visible light telescope, with some near infrared and ultraviolet capability, in a low 540-kilometer Earth orbit. Webb will be a cold infrared telescope, with some red and orange capability, in a halo orbit about the second Earth-Sun Lagrange point 1.5 million kilometers anti-sunward from Earth.

($L_2$ is an unstable equilibrium point: in an inertial reference frame, solar and terrestrial gravity combine to pull a mass into a solar orbit with a larger radius but the same period as Earth’s, so the mass appears to hover almost a million miles above Earth’s center; in a frame rotating with Earth about Sun, the combined gravitational force inward balances the centrifugal pseudo-force outward.)

Webb is optimized to study the early universe. Light from the first galaxies is both fainter due to distance and redder due to the expansion of the universe, so a larger, colder, more remote telescope is desirable. By contrast, Hubble is warm enough that its own infrared emission blinds it to this light.

During Webb’s long gestation, exoplanet science dramatically bloomed. Exoplanets are easier to detect in infrared light where the contrast between the glow of a star and its exoplanets is less. Consequently, the study of exoplanets and their atmosphere will be another Webb focus.

First though, Webb must survive six months of terror as it unfolds its giant sunshield and segmented mirror through hundreds of single points of failure.

## Burning Plasma

In August I received an urgent email from my brother with the title “Fusion”. The National Ignition Facility (NIF) had created a burning plasma — a star on Earth — a major milestone on the long road to controlled nuclear fusion.

A plasma is an ionized gas, but in this context “burning” does not mean chemically combining with oxygen. Rather it refers to the nuclear reaction

$${}^2_1 \mathrm{H}^{+} + {}^3_1 \mathrm{H}^{+} \rightarrow {}^4_2 \mathrm{He}^{++} + {}^1_0 \mathrm{n} + 18~\text{MeV},$$

where hydrogen isotopes deuterium and tritium combine to form helium. Nuclear reactions produce millions of times the energy of chemical reactions, but they are hard to initiate as hydrogen ions repel one another electromagnetically unless they are close enough to allow the short-ranged nuclear force to convert mass energy into kinetic energy.

NIF uses the world’s most powerful laser, capable (briefly) of almost 1000 times the power output of the United States’ electrical grid. The ultraviolet laser pulse heats a small gold cavity or hohlraum, which converts the incident radiation into x-rays, which causes an enclosed deuterium-tritium pellet to implode, which increases the pellet’s temperature and density to initiate fusion.

After missing its 2012 ignition goal, and steadfastly fine-tuning the experimental design since then, the August shot generated much more energy than was delivered to the pellet (but slightly less energy than was delivered to the hohlraum). NIF director Mark Herrmann reported that, “Everyone has a spring in their step”. To me, controlled nuclear fusion, like humans on Mars, has always seemed 20 years away; with progress at NIF (and elsewhere), today it seems closer.

## Part Science, Part Art, Part Luck

Launched just last month, Lucy will be the first spacecraft to visit Jupiter’s trojan asteroids, rocky swarms that orbit about 60 degrees ahead and behind Jupiter in its orbit. Hal Levison, Lucy’s Principal Investigator, has described Lucy’s complicated trajectory, which includes an Earth gravity-assist and visits to both trojan swarms, as “part science, part art, and part luck”.

Named after the Lucy fossil that elucidates hominid history, Lucy will illuminate solar system history as the trojans are thought to be pristine remnants of planetary formation. The Lucy fossil itself was named after The Beatles‘ song “Lucy in the Sky with Diamonds” and, indeed, Lucy’s thermal emission spectrometer includes a large diamond beam splitter. During its 12-year primary mission, Lucy will visit seven trojans, including a near-twin binary pair, and one tiny main-belt asteroid named after Donald Johanson, the discover of the Lucy fossil.

Lucy’s trajectory involves an Earth (green) flyby and visits to the trojan asteroids leading and lagging Jupiter (brown) in its orbit. (NASA)

## 4D Unknot

In four dimensions, you can’t tie your shoelaces — because 4D knots don’t work. Any 1D curve in 4D space can be continuously deformed to the unit circle, which is an unknot.

The looping animation below demonstrates how to undo a trefoil knot in 4D, where rainbow colors code the 4th dimension. The animation pauses when curve segments appear to intersect, but the segments’ different colors reveal their separation in the fourth dimension.

2D is too small to allow complicated neural circuits, and 4D is too large to enable knots; perhaps unsurprisingly, we find ourselves in a 3D world.

Unknotting a trefoil knot in 4D, where rainbow colors code the 4th dimension

Posted in Mathematics | 1 Comment

## Punch it, SpaceX

She’s not looking up at the sky; she’s looking down at it.

I am excitedly following the Inspiration4 spaceflight and its diverse all-private crew of Jared Isaacman, Sian Proctor, Christopher Sembroski, and Hayley Arceneaux. Orbiting higher than any humans this millennium and carrying the largest window ever flown in space, their Crew Dragon Resilience is providing unprecedented and breathtaking views of Earth and stars.

The crew and their personal stories are inspiring, but in addition to advancing human spaceflight, Inspiration4 is raising money for St. Jude’s Children’s Research Hospital. The mission also highlights Space Exploration Technologies Corporation at the dawn of a second space age. As Jared radioed seconds before launch, “Punch it, SpaceX”.

Floating in Crew Dragon’s remarkable cupola and orbiting at a near-record altitude, Hayley Arceneaux describes her view of Earth for children of St. Jude, the children’s research hospital that saved her life and for which she now works. (@Inspiration4x/Twitter)

## Dandelin Spheres

In 1609, Johannes Kepler first described how planets orbit the sun in ellipses. Kepler understood an ellipse as both the locus of points whose distances from two foci sum to a constant and as the intersection of a cone and a plane. But how are these familiar definitions equivalent?

In 1822, Germinal Dandelin discovered a beautiful construction that proves this classic equivalence. The looping animation below pauses periodically to emphasize key aspects of the proof.

A plane intersects a cone in a black ellipse. The red and cyan spheres are tangent to the cone at the parallel circles and tangent to the plane at the ellipses’ focal points. The red lines are equal because they are tangent to the red sphere from the same point; same for the cyan lines. The sum of the cyan and red lines is both the sum of the distances of an ellipse point from the foci and the fixed distance along the cone between the red and cyan tangent circles.

Dandelin spheres illustrate why the intersection of a plane and a cone is the set of points the sum of whose distances from two fixed points is constant.

## Thinking of Teague

A sunflower from Teague’s memorial service

Yesterday, Dr Manz and I went to Lexington, Kentucky to attend the memorial service for Teague Curless.  It was good to gather with Teague’s friends and family so that we could talk about him and remember him, and share our aching hearts with each other.

Teague’s family incorporated a lot of physics into the memorial service, including a beautiful discussion of energy conservation, reminding us that the total energy in the universe has been fixed since its creation, although that energy changes forms. The energy that was Teague is now in different forms, but no less real.  They also read from a lovely commentary by Aaron Freeman about having a physicist speak at your funeral.  These lines really struck me:

You want a physicist to speak at your funeral. You want the physicist to talk to your grieving family about the conservation of energy, so they will understand that your energy has not died…. You want your mother to know that all your energy, every vibration, every BTU of heat, every wave of every particle that was her beloved child remains with her in this world…

[You want the physicist to tell your family]  that all the photons that ever bounced off your face, all the particles whose paths were interrupted by your smile, by the touch of your hair, hundreds of trillions of particles, have raced off like children, their ways forever changed by you.

I know it’s very hard for many of us this Monday, remembering that last Monday, Teague was getting settled on campus and preparing for his senior year.  Things can change so quickly.

For me, the best part of my job is the relationships that I develop with the students. It’s a privilege to get to know you all as you grow and change so much from your first year to your fourth, and to keep in touch as you go out from Wooster and change the world in big ways and small. Thank you for the hugs and calls and emails this week — I am so grateful for all the ways that our community draws together to support one another in tough times like these.

## For Teague

Sadly and unexpectedly Wooster physics senior Teague Curless ’22 died yesterday. I was fortunate to teach Teague some physics, especially in my Nonlinear Dynamics class last spring. Teague’s semester project beautifully illustrated chaos in a double pendulum — a pendulum swinging from another pendulum, like The Swinging Sticks® kinetic sculpture that silently rotates and librates beside me as I write.

Using Mathematica, Teague numerically integrated the relevant Lagrange equations to simulate the motion of the double pendulum. He then created a two-dimensional initial angles plot of the time for the pendulum to flip as a function of the sub-pendulums’ starting angles, a beautiful high-resolution fractal-like image. I think Teague would have enjoyed the extension below, where I animate the color palette.

Rotating hues code time for a double pendulum to flip for different initial angles; central angles are too small to cause flips. Based on Teague Curless’s final Nonlinear Dynamics project.

Posted in Physics, Students, Wooster | 1 Comment

## 21st Century Skyscraper

Recently at its Boca Chica launch site, SpaceX stacked a Starship on a Superheavy booster to briefly form history’s largest rocket, dwarfing the Apollo Saturn V. Both a fit-check and a statement, SpaceX released the photograph below in black & white, which evokes classic mid-20th century skyscraper construction. But this 21st-century skyscraper is designed to fly to Mars — and be fully reusable.

SpaceX has many challenges to overcome to achieve those goals, but watching them try is tremendously exciting. Not since Apollo has space exploration seen such urgency, boldness, and optimism.

Stacking the world’s largest rocket evokes classic skyscraper construction (Credit: SpaceX)

Posted in Space Exploration | 1 Comment