16

The friends-of-friends (FOF) algorithm (Huchra & Geller 1982; Press & Davis 1982, Davis et al. 1985) for finding groups of particles can be used for various numerical problems, not just cosmology, and linking lengths may vary between these problems. The larger the values you use for $b$ (the linking length in terms of the mean interparticle distance),...


13

Not sure if these kinds of questions are allowed here, but I may as well answer it. Universe Sandbox 2 is mostly realistic. Its accuracy degrades as you increase the flow of time. The slower the time, the more accurate the calculations. This means that if you want to simulate the Solar System over a long period of time, it won't be very accurate. If you ...


12

Here is what I did: Based on their masses, it is safest to initially consider Jupiter and Saturn as well as Uranus. It might also be fruitful to include the Earth in the analysis, to get relative positions, observation angles, etc. So, I will be considering: Sun Earth Jupiter Saturn Uranus Neptune Get the standard gravitational parameters (μ) for all ...


11

Let the two bodies involved have masses $m_1, m_2$. Start with Newton's second law $$F = ma$$ where $a$ is acceleration. The gravitational force on body 2 from body 1 is given by $$F_{21} = \frac{G m_1 m_2}{|r_{21}|^3}r_{21}$$ where $r_{21}$ is the relative position vector for the two bodies in question. The force on body 1 from body two is of course $F_{...


8

The principle is almost exactly the same as a watch or clock, but instead of three concentric axles, you need 9 for the planets. Have a google for Orrery kit - there are loads available. It is really all simple maths - you just need to know relative orbital periods in order to calculate cog sizes. (picture from curiousminds.co.uk) For moons, you do add a ...


8

Since the second data release (DR2) of the European Space Agency's Gaia mission there has been a revolution in astrometry, including measuring the motion of the Andromeda Galaxy. On February this year van der Marel et al (also in ArXiv) published interesting results on that matter by using Gaia's DR2 measurements. The results reveal that the collision is ...


7

If you're asking whether it's sufficient to use a retarded (time-delayed) positions to calculate gravitational forces, then no, that would be much worse than Newtonian gravity. For example, that would predict that the Earth should spiral into the Sun on the order of about 400 years. See also answers to Besides retarded gravitation, anything else to worry ...


6

I am not very familiar with orbital dynamics (so please correct me if I'm wrong). I was told that, for instance in the case of the mean motion resonances that cause the majority of the Kirkwood gaps in the asteroid belt, not only the ratio of the periods, but also the timing is important. Let's take Pluto as an example, which is in 2:3 resonance with ...


6

I found an article by Ian O'Neill posted on May 2, 2008 at universetoday.com with the title Could Jupiter Wreck the Solar System? which says But here’s the kicker: There is only a 1% chance that these gravitational instabilities of the inner Solar System are likely to cause any kind of chaos before the Sun turns into a Red Giant and swallows Mercury, Venus, ...


5

There may be some three-body periodic solutions that orbit around a common point, but in general they get a little crazy-looking and may not always contain an immediately obvious center of mass from casual observation. But of course it will always exist. If you watch closely, you'll see that whenever one body reaches the intersection point, all three are on ...


5

Is it just for the spoiler? My guess is that the 3 suns aligned create a sufficient gravity field for the outermost parts - less well attached - of the planet (atmosphere, people, buildings) to be in the Roche Limit of the system, causing them to be sucked out spiraling inwards. Here is a funny vid I found to illustrate: https://www.youtube.com/watch?v=...


5

I agree with @uhoh that you don't have to an expert, but above-average knowledge of coding is definitely useful, bordering on "a must". Not for writing huge programs with 1000s of lines, but for writing smaller pieces of code that help you in everyday tasks. As uhoh says, you can very well find your place in a group where other people are in charge of ...


5

No orbits are strictly Keplerian, unless you really monkey about with your coordinate systems. However, a precessing orbit is pretty darned Keplerian. The relationship between the various orbital elements can be a little complicated, and precession is traditionally thought of as the rotation of the periapsis of the orbit around the more massive body. If we ...


5

One of, if not the most comprehensive exoplanet table is found at exoplanet.eu which also lists the angle of the ascending node and the time of perihelion, time-of-transit, stellar data etc as far as these data are available including references to the papers the data are taken from. You can download that convenient as csv for processing.


5

As previously answered by Connor Garcia, the answer is "No, mass, eccentricity, and position are not enough to determine orbital velocity, even given a specific orbital plane, unless the eccentricity is zero." One way to intuitively envision this: There is a continuum of similar elliptical orbits with the specified eccentricity $e$, that range in ...


4

Horizons Ephemeris generator can give you a planet's position and velocity vectors at a specified time. This is one set of possible options: Clicking Generate Ephemeris on that page will give you position and velocity vectors: Above the position and velocity vectors are the Julian date as well as the more conventional date. Wikipedia can give the masses ...


4

If this is a possible periodic solution for a three-body problem? What you've posted here is the classic "figure 8" orbit for a 3 body system. Originally the 3-body system was an unsolvable mathematics problem, until people started using computers to do the math for us. Recently, a set of 13 "stable" 3-body orbits have been found which were published in ...


4

As barrycarter mentioned in his comment, you should be more concerned with units and less with scale. Generally, it's best to stick to conventional units that people recognize. (It will keep your head on straight and make it easier for others to review your work.) In astronomy, these are a little different than the standard SI units, since things are—shall ...


4

As noted by @MikeG in this comment, the Universe Sandbox 2 FAQ addresses the question, but not in a satisfying or helpful way: Does it account for relativity? No, the physics in Universe Sandbox² is currently only Newtonian. Why? The short answer is that you need a supercomputer to accurately simulate general relativity. (emphasis added) Jenn, ...


4

The thermal eccentricity distribution was first calculated by Jeans 1919. The probability density function is indeed $$f(e) = 2e.$$ See this blog post for a nice derivation of this beautiful result, which is independent of the "temperature". The derivation relies on a small 'swindle' by assuming a population of only binaries and not any single or trinary ...


4

I can reproduce your JPL Z coordinate plot if I use Earth's heliocentric position relative to the J2000 ecliptic. Naturally the amplitude has a minimum around the year 2000: Relative to the ecliptic of date, which accounts for precession, the heliocentric Z coordinate of the Earth-Moon barycenter is much smaller: The IAU 2006 precession model has two ...


4

Strictly speaking, pure Keplerian orbits can only occur with two bodies obeying Newton's law of gravitation. If there are more than two bodies then the orbits will be perturbed, to some degree. Kepler orbits are a reasonable first approximation to the orbits of the planets in the Solar System because the Sun is so massive compared to the planets, and the ...


4

A quick search brought me to a book by Houjun Mo, et al. Galaxy Formation and Evolution which says For example, the frequently used friends-of-friends (FOF) algorithm defines halos as structures whose particles are separated by distances less than than a percolation parameter $b$, called the linking length, times the mean interparticle distance (Davis et al....


4

As someone who has done this with other astronomy research grade software, I can say that using Docker fixes some problems but also creates new problems as well. I'll assume for this that your software is designed for linux but you want to support students who'll mostly be using Windows/Macs. Pros: You can ship your application pre-compiled so users don't ...


4

I think I found the answer after some search. What I have been after is the JPL Small-Body Database Browser. You can simply enter the object name to the search field and it returns a page where you will find the orbital uncertainities along with other useful data. For example, type in 'eros' and you will see the results. Of course, this can be automated in ...


4

No, this is an underdetermined problem if you don't have the semi-major axis $a$ and orbital inclination $i$ (or some equivalent). However, if you want circular orbits, then the semi-major axis $a$ is the same as the distance between the bodies. If you want prograde orbits in the x-y plane then the orbital inclination $i$ is 0. Then you can calculate the ...


3

Is there any resource that provides these current values? Yes. The JPL HORIZONS on-line solar system data and ephemeris computation service provides these values, and much more.


3

Consider a nearly circular orbit. On average, $ v = 2 \pi r / T $, and the gravitational force balances the centrifugal force: $$ {G M m \over r^2} = {m v^2 \over r} = {4 \pi^2 m r \over T^2} $$ Solve for $G$ and substitute values for Earth's orbit around the Sun: $$ G = {4 \pi^2 r^3 \over M T^2 } = 4 \pi^2 {\mathrm{AU}^3 \over M_{\odot} \ \mathrm{y}^2} $$ ...


3

Usually, in an N-body or SPH simulation the term "mass resolution" refers to the mass of a single particle, which usually all have the same mass. A single particle can always be "detected" in the simulation, since we have control of the coordinates of all particles, but a structure of several particles becomes ill-defined if the number of particles is too ...


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