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Blog Post #33. Sun Oct 11 11:12:03 2026. Apurva Balaji wrote:
When reading about the mass-losing stars, I thought about binary star systems and read a few Wikipedia articles about them which I thought were interesting. In the book, it mentions how mass is shed through stellar winds or supernova explosions, and these articles were talking about in close-orbiting binary star systems that tidal attraction of the gasses near the center of mass can pull gas from one star onto its partner. There was also a reference to a study in 2012 that said that 'more than 70% of massive stars exchange mass with another causing binary mergers for 1/3 of them'. That article can be referenced here:https://arxiv.org/abs/1207.6397
Blog Post #32. Thu Oct 8 13:43:56 2026. Erik Payton wrote:
I gotta say, the idea of the sun's mass decreasing had never crossed my mind. I know it makes sense, but it was super interesting to read about. I know that starless exoplanets exist, and I wonder if this is part of how they might have been made. If their stars got too small and they were ejected.
On the aerospace side, it makes me think about gravity tractors for asteroids. As the spacecraft uses fuel, its mass gets much smaller too! Anyways, those are all the thoughts I have.
Blog Post #31. Thu Oct 8 13:15:29 2026. Erik Payton wrote:
I have been lied to! (I really should have thought about this before; now it's kinda embarrassing.) As a child, I was always told that winter happened because the sun was farther from the Earth, and summer was closer to the Earth, so imagine the surprise when the textbook said that Earth's perihelion is in January! This means we are several million miles closer to the Sun in the coldest time of the year (for those northern hemisphere dwellers) than in the heat of the summer. I guess the tilt and non-direct solar illumination are much more important than the change in distance.
Blog Post #30. Thu Oct 8 10:46:06 2026. Sophia Matthews wrote:
The casual mention of the Romans and Greeks using a north star other than our own but not naming the star!?!? I read ahead to section 6.1.4.3 and the authors don’t name the star there either.
I found a blog post where someone claims the previous north star was Thuban in the constellation Draco. Wikipedia and space.com have this as well, so I’m inclined to believe it’s true. There is a whole list of north stars that have come before our own and there is a whole list of stars that will inevitably supersede Polaris. Whether humanity will still be around to navigate by future stars is another question. https://www.cloudynights.com/forums/topic/786598-how-long-has-western-civilization-or-northern-hemisphere-civs-had-the-north-star/ https://en.wikipedia.org/wiki/Thuban https://www.space.com/stargazing/has-polaris-always-been-the-north-star-how-earths-26-000-year-cycle-changes-the-pole-star
In each section I learn of another factor I must consider for mini-moon. In this section, Roche’s limit is introduced. It seems I need to place an asteroid in an orbit between the Roche limit and Hill sphere if I aim to keep it (which I do).
Blog Post #29. Thu Oct 8 10:44:19 2026. Sophia Matthews wrote:
My main takeaways from these sections are that resonances are crazy and the solar system as we know it feels like a fluke. Yugadeep’s coining of “the cosmic version of the butterfly effect” is apt.
The authors mention spiral density waves and give Saturn’s rings as an example. I didn’t really know how to interpret this or have any idea what it would look like. There’s a picture here: https://science.nasa.gov/resource/spiral-density-waves/. I also found a paper on the topic. The authors include a visualization of the density waves that is very interesting: https://www.sciencedirect.com/science/article/pii/S0019103520304012.
Blog Post #28. Sat Oct 3 16:19:45 2026. Apurva Balaji wrote:
The book had some evidence for tidal slowing of Earth's rotation which I just thought were interesting! I think it's so cool that from studying are corals we learnt that Earth had 400 days per year 350 million years ago because we had shorter days.
This forum post from the Geophysical Institute at the University of Alaska Fairbanks makes note of it: https://www.gi.alaska.edu/alaska-science-forum/when-days-were-shorter
They mention how present day nautilus shells show about thirty daily growth lines with the current lunar month being about 29.53 days. When looking at the fossil record they found that the first nautiloids (420 million years ago) had only nine growth lines and studies have been conducted that around this time the moon circled Earth once every nine days
Blog Post #27. Fri Oct 2 20:02:10 2026. Yugadeep Kanaparthy wrote:
Blog Post #26. Fri Oct 2 19:59:52 2026. Yugadeep Kanaparthy wrote:
In my research, I've come across quantities like tidal Q, Love number, etc. but never quite understood what they meant, so these sections were helpful in clarifying that.
I've also found it helpful to think of Q as a measure of how smooth (frictionless) a system is. In fact, that's how it's defined for oscillators (as the Quality factor of a system). A low Q indicates that significant energy is dissipated per cycle and that the system will rapidly damp out.
So, it makes sense, for example, that in the semi major axis evolution equation (eq. 2.44b), Q is in the denominator. Lower Q means tides are strong and push a moon out quicker (provided it orbits prograde and outside the synchronous orbit.)
Blog Post #25. Fri Oct 2 19:34:32 2026. Yugadeep Kanaparthy wrote:
In my research, I've come across quantities like tidal Q, Love number, etc. but never quite understood what they meant, so these sections were helpful.
One helpful way I've found to understand Q is thinking about it as a measure of how smooth (frictionless) a system is. This is essentially how it's defined for oscillators. A low Q indicates that significant energy is dissipated per cycle
One question I had while reading was how the book derived the tidal force (Eq. 2.39, 2.40) I've seen derivations of tidal force before
Blog Post #24. Mon Sep 28 21:59:51 2026. Yugadeep Kanaparthy wrote:
Keeping up with the theme in the last couple posts about resonances, chaos and stability, I became interested in more examples of chaotic behavior in the solar system. I found a short paper from 2009 that performed ~2500 five billion year simulations of the solar system. These were performed including all eight planets, the Moon, and general relativistic effects.
The only thing they varied between the simulations was Mercury's semi major axis, changing it ever so slightly, just within a few meters from the true value. In 1% (20) of the runs, Mercury's eccentricity was found to increase to greater than 0.9, owing to a perihelion resonance with Jupiter. In a few of these, Mercury actually collides with the Sun within ~4 Gyr. In one particular run, Mercury's high eccentricity somehow makes Mars approach within 800 km of Earth, which would result in the tidal disruption of Mars.
This is like the cosmic version of the butterfly effect, with tiny changes in the initial conditions leading to incredibly different results!
Blog Post #23. Mon Sep 28 20:32:00 2026. John Ajamian wrote:
When we talk about the formation of our solar system I wonder how much smaller perturbations matter. Like how different would a simuation look if we forgot to include the heat differential on an asteroid? This is very open ended, but I think small perturbations add up over long periods of time. I also think that these smaller forces must have been found by observing things and seeing that the measurements do not line up with the expected physics (much like the Uranus problem).
Blog Post #22. Sun Sep 27 11:09:03 2026. Apurva Balaji wrote:
The introduction of this paper had a good explanation: https://www.pnas.org/doi/full/10.1073/pnas.2118692119!
It mentions how Pluto avoids close encounters with Neptune due to two librations of its perihelion.
There is the longitude of its perihelion longitude about a center +- 90 degrees away from Neptune's ecliptic longitude and this is the one talked about in section 2.4. It is the libration of the critical resonant angle every 20000 years and ensures that when Pluto crosses Neptune's orbit its spatial location is more than 45 degrees in ecliptic longitude (an azimuthal libration). This one happens due to the mean motion resonance.
The other libration of its perihelion is a latitudinal libration since Pluto is at a plane higher than those of the other planets and is characterized by the libration of Pluto's argument of perihelion which has the effect of elevating Pluto's minimum distance when approaching Neptune and the other outer solar system planets to help with stability!
Blog Post #21. Fri Sep 25 15:12:27 2026. Erik Payton wrote:
Chaos and Planetary Stability...It is amazing how stable our solar system is, considering how chaotic the space it inhabits is. I had never heard of the Kirkwood gap before reading these sections. It is fascinating to me that the orbital resonances cause the objects with those SMAs to be depleted, while there are other resonances (thanks Wikipedia) that do not, such as Jupiter's 3:2 resonance or several of Neptune's resonances. Very cool that resonances can cause both stability and instability even when constructed in a similar manner.
The article does note that there are some very high-eccentricity asteroids in that area, and that they will likely escape in a few million years!
Blog Post #20. Fri Sep 25 13:38:07 2026. Erik Payton wrote:
A bit late to the party on this one, but there were two things that I found very unique about 2.2. There was a comment that L4 and L5 have been suggested as potential space station locations, and that piqued my interest! I had never heard of such a plan, so I dug a bit further...
Several google searches later, I stumbled onto a name...O'Neill Cylinder Space Stations. Sounds straight out of science fiction (amazing), and I found his original paper from 1974 (linked below) as well as some concept art (also linked). I love old science fiction space art, so I might just get a poster of one of them!
It is a fascinating topic and location for a space station. He estimated the population at 5-700 million people, and that is just an insane number. Well beyond our current capabilities, but a really compelling location for a station. If I ever invent a time machine and can check if it happens, I will be sure to come back and update this blog post :)
P.S. Sophie, I am pro-mini moon
https://nss.org/the-colonization-of-space-gerard-k-o-neill-physics-today-1974/ https://nss.org/o-neill-cylinder-space-settlement/
Blog Post #19. Wed Sep 23 20:22:37 2026. John Ajamian wrote:
(Related to reading) There is a interesting resonance perturbation that not a lot of people know about for 0 degree inclined geosynchronus orbits. The moon pulls on the satellite with the correct frequency such that it changes its orbit to ~15 degrees inclination over 25-50 years then settles back down to 0 degrees over the next 25-50 years. I just think this is a cool perturbation.
(Unrelated to reading) For CR3BP this has been on my mind and I can't figure it out. So in astrodynamics you learn about gravity assists, and these have the ability to increase/decrease inertial velocity. The natural question is then how do we get this free extra energy, and the answer is it is essentially "taken" from the planet but it is just basically 0. So hypothetically, you can fly a satellite and keep doing gravity assists in the right way until it escapes.
Okay, so now take the earth moon system and assume it is CR3BP. If I fly my satellite such that it keeps doing un-assisted flybys of the moon, its inertial velocity increases, but yet the Jacobi constant remains the same?!?! Even a single flyby, how does the CJ not change if I am technically "taking" energy from the moon? This is my question for next class, and it wasted at least one hour at my job trying to ask people and track down the answer lol.
Blog Post #18. Tue Sep 22 12:17:29 2026. Adrienne Rudolph wrote:
On the note of horseshoe orbits, I found a paper that investigates the lifetime of objects in horseshoe orbits. That lifetime apparently increases with decreasing mass - which I suppose makes sense. The paper states "the relative widths of the horseshoe and tadpole regions is also a function of the mass ratio". So the smallest particles on horseshoe orbits are likely to remain in such orbits for potentially the lifetime of the solar system without perturbing the planet or larger body's orbit.
Link to paper: https://www.sciencedirect.com/science/article/pii/0019103581901470
Blog Post #17. Sun Sep 20 10:53:12 2026. Apurva Balaji wrote:
I looked a bit more into it and though a couple news articles refer to it as a mini-moon, scientific articles talk about it as a quasi-satellite, which it is because by definition it's outside of Earth's hill sphere and orbits the Sun with an Earth-like orbit.
It's most likely gonna stick around as a quasi-satellite till the 2080s until transitions into a horseshoe orbit.
(Also if you google 2025 PN7 you'll get an animation of two moons!)
Blog Post #16. Sat Sep 19 13:25:44 2026. Adrienne Rudolph wrote:
Maybe its obvious to others and I've been oblivious to it for years, but I wanted to know exactly where that cone came from and why the heck it relates so perfectly to orbit types. Why doesn't a cylinder work? Why not a sphere? Rectangular prism? Why is a cone SO special.
So I started questioning which came first, the cone or the orbits. I began wondering, is there some invisible cone-like structure in the universe around objects with gravity that produce bent trajectories, or did we simply get lucky that there is a 3D geometrical feature that just so happens to mathematically explain all of the orbit types?
Then I went down a rabbit hole and told myself that if the physical orbits have math to describe them, then the math of a cone has to be physically represented SOMEWHERE in space-time. So then I thought, that means either there has to be a relationship between gravity and the structure of a cone, OR the structure of gravity just so happens to be shaped like a cone. This whole time when we look at conic sections in the book, the pointy end is up, but what if its actually supposed to be down? Think of the gravitational potential, it goes down about an object with mass right? Think of a black hole, how its gravitational potential is so steep as it goes towards the singularity.
I had a very long and deep conversation with chatgpt about this because I don't have months to read through tons of papers. And I think I came to the conclusion that gravity is a cone-like structure, at least mathematically. The more massive an object is, the more "cone-like" its potential is. I used to think of it as a sphere, but maybe its closer to a sphere for less massive objects, and is more "cone like" the more massive it is. What I have settled on is that the geometry of the gravitational field determines the geometry of the trajectories. And I suppose that's satisfying enough for now.
Blog Post #15. Fri Sep 18 19:17:51 2026. Adrienne Rudolph wrote:
Blog Post #14. Thu Sep 17 15:30:51 2026. Sophia Matthews wrote:
Two concepts that were new to me as of yesterday (learned about them at an AMOS talk) were the Hill Sphere and temporary satellites. Both were mentioned in this section!
One thought I had while reading this is: can we (Earth) gain a permanent moon? This question is inspired by the DART mission and temporary satellites. Can we use kinetic impactor(s) to knock an asteroid coming near the Earth into a stable orbit around the Earth?
Some criteria to consider when choosing an asteroid and orbit (this is not exhaustive): 1. Needs to approach the Earth at a reasonable distance, so that we can knock it into place. 2. Should be visible with the naked eye to gain support from the public. I don’t think we can get the world’s population on board unless we can see it. 3. Should choose an orbit that won’t interfere with the current moon. There is some relevant info on resonances in reference to moons in section 2.3.
I’m taking this time to poll the class: Are you interested in a second moon?
Blog Post #13. Wed Sep 16 16:34:03 2026. Sophia Matthews wrote:
Like many of you, this is not my first time learning Kepler’s laws and the orbital elements. Every time I learn Kepler’s laws I want more information of the equal area over equal time rule. Specifically, no one ever goes into the math of this rule (I assume this is because the swept area isn’t really important to the problems we’re solving or an intuitive way to solve related problems.)
I did a quick search of the math of the swept area over time. The rule is a result of the conservation of angular momentum. For small areas a triangle can be used to approximate area and therefore the change in area with respect to time is 1/2*r*r*d_theta/dt (1/2*b*h).
https://www.mit.edu/~ashrstnv/keplers-laws.html
Blog Post #12. Mon Sep 14 20:16:20 2026. John Ajamian wrote:
I also have never heard of (m1+m2)^2/(m1m2) > 27 for this stability to occur, so I may look into that for fun. The book cites Danby 1988, but maybe we'll see if Dr. Hamilton knows why tomorrow!
Blog Post #11. Fri Sep 11 14:00:21 2026. Yugadeep Kanaparthy wrote:
We mentioned in class how alternate sets of elements can be constructed that are just as valid as long as there are 6 of them. There was even a post from Apurva giving a couple examples that they learned in Aerospace courses. I thought I'd make a similar connection to another subfield of astronomy, High Energy Astrophysics, where I recently encountered yet another set of orbital elements!
This paper, which involved observing far away pulsars, used these elements for analysis: orbital period, projected semi-major axis, eccentricity, longitude (not mentioned of which, assuming pericenter), time of pericenter passage.
Notably, that's only 5 of a required 6 to completely describe an orbit. Turns out that the ascending node is typically unknown for these sorts of observations. The same problem is also encountered in exoplanet discoveries. This usually limits the observers' ability to estimate the mass of the star/planet.
Unlike the poor folks studying exoplanets, however, high energy astrophysicists are able to leverage the extreme gravity around compact objects like pulsars to measure some useful quantities. The paper talks about how these general relativistic effects allows them to measure what are known as post-Keplerian (PK) parameters. Knowing at least two PK parameters allows them to determine the mass of the star, which is otherwise degenerate with the inclination of the orbit.
So, overall it sounds like different fields in astronomy and aerospace use different sets of elements based on what's more convenient and what's actually measurable!
Blog Post #10. Tue Sep 8 19:57:43 2026. Apurva Balaji wrote:
One of the ones we had mentioned was the longitude of pericenter which is an interesting angle since it gets measured at a bent angle since its both using an angle related to the reference plane and one related to the orbital plane and as I was referencing an old astrodynamics course, I realized that it could be useful for defining an equatorial orbit where your orbital plane just lies on your reference plane. Similarly, with the argument of latitude I have had this defined as the angle from ascending node to your position vector (argument of periapsis + true anomaly) which makes sense when you have a circular orbit as there is no periapsis.
Blog Post #9. Tue Sep 8 17:02:52 2026. Adrienne Rudolph wrote:
Paper here: https://ntrs.nasa.gov/api/citations/20190001188/downloads/20190001188.pdf
Blog Post #8. Tue Sep 8 12:55:26 2026. Yugadeep Kanaparthy wrote:
As a consequence, something I spent a lot of time re-deriving was Equation 2.1. I knew that I had seen something similar before in a previous class but it looked different than the polar equation of an ellipse that I'm used to. To derive it, I was trying to substitute the polar coordinates of X and Y in the Cartesian equation for an ellipse, but I was simply not getting the stated equation.
After the lecture last Thursday and re-familiarizing myself with some conic section basics, I realized the mistake I was making was placing the origin at the center of the ellipse and not at one of the focii, which leads to a different (but still valid) equation.
So, while I may have spent way too much time trying to derive something basic, I still felt like I refreshed conic section concepts, which it looks like are important for some of the later lectures anyway!
FYI: If you're interested in the derivation, it's pretty straightforward. It involves the definition of eccentricity, the distance from any point on the ellipse to the directrix and distance from the point to the one of the focii.
Blog Post #7. Sun Sep 6 13:41:36 2026. Erik Payton wrote:
Blog Post #6. Thu Sep 3 13:02:12 2026. Sophia Matthews wrote:
In the very beginning of the section, the authors mention how unexplored the outer regions of the solar system are, specifically stating that “many bodies remain to be detected, possibly including some of planetary size.” The planet nine hypothesis has come up a few times in S3-Lab discussions. There was a search that covered a significant portion of the hypothesized location of the planet (detailed here: https://iopscience.iop.org/article/10.3847/1538-3881/ad24e9/meta). The authors state that the Vera Rubin Observatory will cover the remaining portions of the hypothesized locations. I’ve only considered planet nine from a remote sensing point of view and would be interested to know how the hypothesis is perceived in the astronomy community.
In section 1.1.3, comets are introduced. While it seems really obvious, I did not realize that comets shed mass. Upon reading this, I had the horrible thought, “oh no, do comets disappear?”. I read ahead to Chapter 10 (spoiler alert), and a comet can shed all of its near-surface ice, at which point it becomes an asteroid. I guess nothing in our universe truly disappears.
Section 1.1.3 also introduces the zodiacal cloud, which is interesting from an optical remote sensing perspective because it’s a source of light. There is a paper titled “The 1997 reference of diffuse night sky brightness”, that reports on the brightness of zodiacal light from various observations. In section 1.1.3, authors state that the cloud has been observed “collectively, but not yet individually”. In the article linked below, there are some details about observing zodiacal dust via interactions with Juno’s solar panels, which goes into some individual observations of dust at a high level. https://www.nasa.gov/missions/serendipitous-juno-spacecraft-detections-shatter-ideas-about-origin-of-zodiacal-light/
As an aside, the details on planets and their orbits reminded me of Apurva’s project for our astrodynamics class, which was all about the effects of rearranging the planets in the solar system. I believe she maintained the states of the planets but swapped masses then analyzed what happened.
My final thought concerns the quote from The Republic at the very beginning of the section: “It amuses me to see how afraid you are, lest the common herd of people should accuse you of recommending useless studies”. I won’t go into how this quote feels antithetical to the realities of academia but I do love the authors’ subtle refute (whether intentional or not) of the idea of astronomy as a useless subject with sustained comparison of everything in our solar system, other than the sun, as debris.
Blog Post #5. Thu Sep 3 12:39:08 2026. Erik Payton wrote:
I looked more into Planet X, and NASA had some interesting material on it. Namely, Pluto and its moon Charon would not have the mass to be causing the observed perturbations. They predict that a Planet X would have a mass 5-10 times that of Earth, and an orbit 20-30 times farther than Neptune. The search remains ongoing, with some mentioning that Rubin might have the potential to help detect it!
Links: https://www.history.com/this-day-in-history/february-18/pluto-discovered https://science.nasa.gov/solar-system/planet-x/
Blog Post #4. Thu Sep 3 12:23:44 2026. Erik Payton wrote:
Blog Post #3. Wed Sep 2 20:20:38 2026. Apurva Balaji wrote:
Blog Post #2. Wed Sep 2 16:53:43 2026. Yugadeep Kanaparthy wrote:
Something that I hadn't appreciated before was the how much uncertainty there was in the estimates for mass of the Oort cloud. §1.1.3 says it could have as much mass as all the planets combined. Although, considering the book is almost a decade old by now, I wanted to see if there had been any updates. Mario Menichella (2026) has a paper on Arxiv (not yet published), claiming the estimated mass in the Oort cloud to be around 10 Earth masses.
Because no direct observations of Oort cloud objects have ever been made, typically its mass is inferred from observations of long period comets like the Halley comet. Menichella claims that the massive (~100 Earth mass) estimates from earlier models were because of their assumption that Halley comet-sized objects represented the typical distribution of comets in the Oort cloud. More accurate estimates of the comet size distribution and newer insights from N-body formation models have brought down the mass estimates significantly!
Blog Post #1. Tue Sep 1 12:54:51 2026. Prof. Doug Hamilton wrote:
Step 1: Always do the reading assigned for a given lecture! Think critically about what you read.
Step 2: When you are finished, post something good here! Perhaps share a new concept or fact that you learned or something else that you found interesting. If you have a question, make an effort to get at least a partial understanding of its answer by searching online. Then post what you found so that others in the class can see too!
Your posts here count towards your class participation grade. Make it a habit to do the reading around the time of each lecture and post your insights here regularly.
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