Finding Ceres - The GOAT of Mathematics

TL;DR

1. Asteroid planetary defense
2. Ant-Man's limit?
3. Finding Ceres - the GOAT of mathematics

Current events

If the term "planetary defense" sounds like epic science fiction, fear not! There's a real-life Planetary Defense Coordination Office at NASA that tracks dangerous Near Earth Objects, and this week NASA is convening the 2019 Planetary Defense Conference to simulate a hypothetical 2027 asteroid strike

So what could NASA actually do to prevent a catastrophic asteroid impact? If you're thinking of the movie Armageddon, where Bruce Willis goes to space and nukes an asteroid, you'll be sorely disappointed (just like my roommate. He hated the movie when I made him watch it). Until now, we literally had no contingency plan, but NASA's Double Asteroid Redirection Test (DART) will be the first ever planetary defense mission, to be launched on a SpaceX Falcon 9 in 2021. DART will intentionally crash into the Didymos binary asteroid so that astronomers can measure how well the kinetic energy is transferred. If successful, future kinetic impactors could be used to deflect a larger asteroid on a real collision course with Earth. Watch this video to learn more

 DART plans to crash into the smaller of the two Didymos asteroids (dubbed Didymoon), illustrated on the right

Today I learned

I just saw Avengers: Endgame (Great movie! Don't worry, no spoilers), and if you follow the MCU you'll know Ant-Man is always talking about the Quantum Realm. While Marvel dumps a lot of scientific babble, since Ant-Man can shrink to subatomic sizes I thought the concept of Planck length would be fun to discuss.

The value of the Planck length is $1.6 \cdot 10^{-35}$m, which is about $10^{-20}$ times smaller than the width of a proton. Why does this matter? Based on our calculations, it's thought of as the smallest possible size of a black hole, and at that scale both general relativity and quantum mechanics have influence. That's significant because the two theories are mutually incompatible and typically considered separately, but at the Planck scale they somehow need to be combined. It may also be the fundamental limit to which even the best particle accelerators can probe, so measurements of length smaller than the Planck scale are sometimes considered meaningless because they may be irretrievably hidden from our observation.

Confused? Don't worry, such is the nature of quantum physics! Check out both the Astronomical Returns primer on theoretical physics and this great Quora page on Planck length!

This week in space history

Sports fans love debating the GOATs (greatest of all time) of their respective sports - what about mathematicians? Carl Friedrich Gauss was born on April 30, 1777, and he's definitely on the short list of mathematical GOATs, with enormous contributions to various fields like complex numbers and non-Euclidean geometry. So I was curious, what about astronomy?

The dwarf planet Ceres was discovered in 1801 by Giuseppe Piazzi, but he only could observe it for 41 days before it passed behind the Sun and was lost. When Gauss heard of the problem, he starting trying to calculate where it would reappear so that astronomers could rediscover it. The problem was tricky - Gauss was trying to plot an entire ellipse based on a tiny arc known from the 41 days of observation. Yet with painstaking effort and a few mathematical tools like the Fourier transform and the method of least squares, Gauss came up with a prediction that proved accurate to half a degree, allowing Ceres to be relocated!

 Modern day image of Ceres, taken by the Dawn spacecraft as it orbited Ceres

Gauss' work in astronomy proved essential in the study of conic sections for orbital mechanics and the defining of the six orbital elements. Learn more here!

Refresher on orbital mechanics here

1 comment

1. pretty sure if you said GOAT to a mathmetician they'd have no idea what it meant lol