--- title: "Asteroids and Resonance" author: Jed Rembold date: January 28, 2025 slideNumber: true theme: tokyo-night-light highlightjs-theme: tokyo-night-light width: 1920 height: 1080 transition: slide --- ## Announcements :::{style='font-size:.9em'} - Homework 1 due on Friday night! - Example computational essay posted in Guide section - Export each essay to a standalone HTML file, then upload the HTML file - **Be communicating with your partners** - Also on Friday: Virtual Alumni Career Panel for the Knight Campus Graduate Internship Program (at UO) - Materials tracks (semiconductor, optics, polymers) at noon ([RSVP for Zoom info](https://forms.gle/coqxZoMrSN4t6Paq7)) - Bioinformatics Track at 3:15 ([RSVP for Zoom info](https://oregon.qualtrics.com/jfe/form/SV_3xeyNcG8HmNeyX4)) - Technically part of the larger Genomics in Action conference, which is free to attend if you want more than just an alumni session - Lynde Ritzow is the recruiter for these programs, and has a long and successful history of bringing WU students into these programs. Please let me know if you have interest and would like me to make an introduction. ::: ## Recap - Kepler's other laws - Orbiting objects go fast when near, and slow when far apart - Period and semi-major axis linked: $$ \frac{a^3_{AU}}{p^2_{yr}} = \left(M_1 + M_2\right)_\odot $$ - Distributions show bulk trends - Histograms - KDE plots ## Today's Plan - 2D Distributions - Brightness / Magnitudes - Asteroids - Belt - Resonance - Impending doom # Multivariate Distributions ## 2D Histograms and KDE Plots ::::::cols ::::col - Sometimes you have multiple variables that you want to visualize together as a distribution - There are 2D analogs of both histograms and KDE plots - One variable along each axis - Counts or density still determine color :::: ::::col ![](../images/distribution2d.png) :::: :::::: ## Multivariate Distribution Creation ::::::{.cols style='align-items: flex-start'} ::::col :::{.block name=Python} - Histogram in Matplotlib ```python plt.hist2d(xs, ys, bins=20) ``` - KDE plot easiest through Seaborn ```python sbn.kdeplot(x=xs, y=ys, fill=True) ``` ::: :::: ::::col :::{.block name=R} - Histogram through ggplot ```python ggplot(data=df, aes(x=xs, y=xs) ) + geom_bin_2d() ``` - KDE plot through ggplot ```R ggplot(data=df, aes(x=xs, y=xs) ) + geom_density_2d_filled() ``` ::: :::: :::::: # Understanding Brightness ## How Bright! - Apparent brightness is the intensity of radiation (or reflected radiation) from a celestial body - As measured by the observer, so generally from the Earth's surface - Measured in units of watts per meter squared ($W/m^2$) - For our Sun, this is about $ 1400\\ W/m^2$ - Clearly, the apparent brightness of other stars is going to be much, **much** less - It is frequently useful to thus use a different scale, where instead we talk about _apparent magnitude_ ## Apparent Magnitude - System introduced around 150 BC! - Hipparchus divided stars into six groups: - Brightest were "1st magnitude" - Faintest (that he could see) were "6th magnitude" - These days we are much more precise, but have defined things to still largely adhere to these same ideas - Measured on an inverted logarithmic scale - Brighter objects have small magnitudes, and __they can be negative__ - A factor of 100 in brightness corresponds to a difference of 5 in magnitude $$ m = -2.5\log\left(\frac{B_{obj}}{B_{Vega}}\right)$$ ## Making Magnitudes Intuitive - Smaller numbers mean brighter stars - Numbers can be negative - Smaller differences in magnitude correspond to larger differences in brightness \begin{tikzpicture}%%width=100% [xscale=.25, lbl/.style={rotate=90,right,font=\tiny\sf}] \shade[rounded corners, left color=white, right color=black!50!blue] (-30,0) rectangle +(60,1); \foreach \e in {-30,-20,...,30}{ \draw (\e,0) --+(0,-2mm) node[below, font=\sf] {\e}; } \draw[Cyan,latex-] (-26.8,1) --+(0,3mm) node[lbl] {Sun(-26.8)}; \draw[Cyan,latex-] (-12.5,1) --+(0,3mm) node[lbl] {Full Moon(-12.5)}; \draw[Cyan,latex-] (-4.4,1) --+(0,3mm) node[lbl] {Brightest Venus(-4.4)}; \draw[Cyan,latex-] (-1.5,1) --+(0,3mm) node[lbl] {Sirius(-1.5)}; \draw[Cyan,latex-] (0.0,1) --+(0,3mm) node[lbl] {Vega(0.0)}; \draw[Cyan,latex-] (2.5,1) --+(0,3mm) node[lbl] {Polaris(2.5)}; \draw[Cyan,latex-] (6,1) --+(0,3mm) node[lbl] {Naked Eye Limit(6)}; \draw[Cyan,latex-] (10,1) --+(0,3mm) node[lbl] {Binocular Limit(10)}; \draw[Cyan,latex-] (26,1) --+(0,3mm) node[lbl] {4-meter telescope Limit(26)}; \draw[Cyan,latex-] (30,1) --+(0,3mm) node[lbl] {10-meter Telescope Limit(30)}; \end{tikzpicture} ## Activity! (10min) :::incremental - The file [here](../demos/bright_stars_10k.csv) catalogs most of the stars with magnitude brighter than 6.5 in our night sky (about 10 thousand) - Visualize the distribution of right ascension vs visual magnitude with a standard scatter plot, a histogram, and a KDE plot. Can you see a two-lobed distribution? - This distribution is actually caused by looking along the disk of the Milky way. The center of the Milky was is at a RA of about 18hr. ::: # Asteroid Time ## Asteroids ::::::cols ::::col What are asteroids? - Small (relatively) chunks of rock - Maybe around a million are approximately 1 km across - Many millions more are smaller - Irregularly shaped - Tiny = hard to see! - "Primitive" :::: ::::col ![Rocky Names](../images/meteor_names.png){width=80%} :::: :::::: ## {data-background-iframe="https://www.asterank.com/3d/"} ## {data-background-iframe="https://eleanorlutz.com/mapping-18000-asteroids"} ## Why a Belt? :::incremental - Enough rocky material to form a body only about 3% the size of the Moon - Gravity never brought it all together, like it did for the other inner planets. Why? - **Jupiter** - Played the role of a big bully - Gravity broke apart any starting planetoids before they could really get going - Still affects narrow bands of the belt today through _orbital resonance_ ::: ## Orbital Resonance - When the orbits of multiple objects sync up with one being a multiple of the other, they are said to be in _resonance_ - Resonance greatly boosts the interaction between the two bodies, with the most obvious effects on the smaller body - Imagine pushing a child on a swing: - Pushing in rhythm with the natural swing motion works best - Could also push every other swing, or every 3rd swing, etc - Pushing every 1/3 swing, for instance, would be highly counterproductive ## Unstable Resonance ::::::{.cols style="align-items: center"} ::::col - Most often, resonances make orbits _unstable_ - The slow accumulation of boosts gives the smaller body more and more energy - Generally results in the smaller body being ejected from the orbit - This is the case with the Kirkwood gaps in the asteroid belt, and the Cassini division in the rings of Saturn :::: ::::col ![Saturn's Cassini Division](../images/cassini_div.png){width=100%} :::: :::::: ## Resonance Pictured - Mimas distance from Jupiter: 186,000 km ![](../images/saturn_ring_density.png){width=100%} ## Stable Resonance ::::::{.cols style='align-items: center'} ::::col - Resonance isn't always unstable though! - Two body resonances can be stable if the ratios / orbits are such that they prevent the objects from getting too close - Multiple orbits can influence each other to lock into a 4:2:1 resonance - The most common is in the first three Galilean moons of Jupiter :::: ::::col
:::: :::::: ## How long before we all die horribly?
## Ensuring Life :::incremental - Stated goal was to find 90% of asteroids 1 km or larger with near-Earth orbits - **How do we know when that goal is reached?** - Crater comparisons - Rediscovery analysis - Theoretical models ::: ## Latest Estimates ![](../images/neo_census.jpg){width=60%} ## Dissertation work ![](../images/standalone/Cumulative_flux_all.svg){width=70%}