Questions tagged [orbital-motion]

The path a body takes while moving through space under the influence of the gravitational forces of other bodies

274 questions with no upvoted or accepted answers
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1answer
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Why is the orbital resonance of the Galilean moons stable?

It is well known that the orbits of Ganymede, Europa and Io are in a 4:2:1 resonance. Most online sources (including but not limited to Wikipedia) say that such an orbital resonance, along with the 3:...
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1answer
786 views

Escape velocity for Schwarzschild metric

I can't fill in the gaps in my solution to this and assistance or a reference would be appreciated. The question begins with the straightforward derivation of the EoM for a massive particle orbiting ...
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1answer
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What's the cause of this gap in this simulation of the Nice model?

A previous question brought me to this video (which has a spectacular change at about 0:34). It shows the orbits of Jupiter, Saturn, Uranus, Neptune, and what appear to be trans-Neptunian objects. ...
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1answer
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Regularization: What is so special about the Coulomb/Newtonian and harmonic potential?

I wanted to know if the procedure for regularization of the Coulomb potential outlined in Celletti (2003): Basics of regularization theory could be generalized to arbitrary polynomial potentials. So ...
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Fully General Relativistic treatment of Galaxy Rotation Curve

Over the years I have seen several approaches to this problem in the GR context: perturbations around a flat-spacetime, cancelation by hand of $\mathcal{O}(\partial_{\mu}\textbf{g}^{2})$ terms on the ...
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are alignment of star systems' orbital planes with ours better than random?

It obviously helps our observation of exoplanets if they transit their star from our point-of-view. I would guess that the chances of this alignment are better than if their orbital plane was randomly ...
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2answers
330 views

Examples of central forces on the path of orbit?

In solving a problem from Goldstein (3.13), I solved for multiple properties of a circular orbit with the attractive central force where the path of orbit crosses the point of the force (at origin). ...
5
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1answer
491 views

Why does planetary spin affect the stability of orbits?

Reading about the Hill Sphere I notice that "the region of stability for retrograde orbits at a large distance from the primary, is larger than the region for prograde orbits at a large distance from ...
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Is there any observable change in Earth's magnetism to an observer in geosynchronous orbit?

I am in high school, and today my physics teacher was teaching us about the Earth's magnetism. This is the first time I've read about this topic, so take these questions as coming from a complete ...
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163 views

Is the white sky of Stephanson's novel “SevenEves” plausible?

Based on comments, would the moderators please move this to Astronomy.SE? In the novel, some agency disrupts the moon. The moon is left in 7 major chunks that are still gravitationally bound. (...
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211 views

Closed trajectories for Kepler problem with classical spin-orbit corrections?

Kepler problem explains closed elliptic trajectories for planetary systems or in Bohr's classical atomic model - let say two approximately point objects, the central one has practically fixed position,...
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From Newton to Kepler without infinitesimals

I've read some interesting calculus-free proofs of at least parts of the derivation of Kepler's Laws from Newton's gravitational force. One is of course Feyman's "Lost Lecture" (which was already ...
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Precession of a closed orbit under a central force other than the inverse square force

Consider the motion of a closed orbit in a central force field ${\bf F}({\bf r})$ other than the inverse square force i.e., $${\bf F}({\bf r})\neq -\frac{k}{r^2}\hat{\bf r}.$$ However, since ${\bf F}({...
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Horseshoe orbit cycle times

I asked on Worldbuilding originally, but was directed here instead I've been working on a habitable moon system for a story, and I'm now trying to populate the other moons around the parent planet. ...
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206 views

Derivation of Equation of Trajectory around a Kerr Black Hole

I was trying to derive equation of motion for test particle around a Kerr black hole. My work is as follows: The Kerr metric is as follows $$ \mathrm ds^2 = -\left(1-\dfrac{2Mr}{\rho^2}\right)\...
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Minimal value of angular momentum in a close binary

I just noticed something interesting with the angular momentum of a close stellar binary. This question is somewhat related to another question of mine, but the question here is clearly different : ...
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Orbital period and velocity around a Kerr black hole relative to fixed stars

I've been trying to make progress on some of the smaller pieces of this question about the environment around a Kerr black hole. In order to calculate the effects of special relativistic Doppler shift ...
3
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1answer
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Determing Velocity of Moons

I have a question that I believe is relatively easy to answer, I am working on an $N$-body simulation of a fictional star system and am having trouble finding the velocity of moons so that they will ...
3
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0answers
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When Did Structures Begin to Orbit in the Universe?

In Big Bang Cosmology, I am familiar with the radiation era, and the moment of last scattering, but I am just not familiar with the physics of orbits, or of the “falling outward,“ if you will, that ...
3
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542 views

Isn't the Jacobi constant just the Lagrangian times 2?

At this wikipedia page the Jacobi constant is expressed as: $$C_J=2\left(\frac{v^2}{2}-U\right)$$ where $U$ is the potential energy and $v$ is velocity. If kinetic energy $T$ is defined (as it ...
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Computing 2d Orbital Parameters

When using formulas that describe a 2d orbit around a planetary body: is it actually OK for the semi-major axis $a$ to be negative? when $a$ is negative, it is impossible to compute mean anomaly from ...
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Is Earth/Luna tidal lock approaching faster?

Wikipedia pegs the mass of Earth at $5.972\cdot 10^{24}\,\text{kg}$ or $5.972\cdot 10^{21}\,\text{metric tons}$. Assuming Earth accumulates approximately $30,000\,\text{metric tons}$ annually. To ...
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3answers
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How do I calculate Earth's axial precession in an idealized Sun-Earth-Moon system?

I am experimenting with an idealized three-body system based on the Sun-Earth-Moon system. In my system the orbits of the Moon and Earth about the Earth-Moon barycenter, and the orbits of the Earth-...
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2answers
107 views

Can soneome help me understand this part of the Feynman's Lost Lecture?

Feyman's lost lecture So at 17:38, 3Blue1Browns states: We know that once the planet has turned an angle theta degree off the horizontal with respect to the sun, that corresponds to walking theta ...
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1answer
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Do dipolar gravitational waves exist?

There seems to be some controversy (see A, B) on this topic, so I'm posting a new question for discussion and clarification. By definition, one cannot accelerate the center of mass of a closed system (...
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Calculate orbital speed of object around earth (SpaceX data)

I am just reading SpaceX rocket data satisfies elementary Hohmann transfer formula, a paper of how to use SpaceX telemetry data in educational physics. In particular the paper contains the following ...
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Keplerian orbits are intersections of planes with the the future light-cone in Minkowski 4-space

Near the end of this essay, Baez comments: In 2011, Guowu Meng pointed out a remarkable fact to me. Orbits of the Kepler problem are precisely the intersections of 2-dimensional planes with this cone ...
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47 views

Properties of orbit type diagrams

For fun, I created a 3d gravity simulation and colored each $(x,y)$ coordinate blue or green if a light mass put at that location would collide - within some number of simulation steps - with one of ...
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How do electrons stay in orbitals in Bohmian Mechanics?

I've been reading various realist interpretations of quantum mechanics and in Bohmian Mechanics, I found that the "wave" aspect of a quantum particle is removed from the particle to preserve ...
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Is spin-orbit coupling mass dependent?

When comparing spin-orbit coupling in the case of electrons and in the case of nucleons, do nuclear states exhibit a stronger level splitting compared to atomic states because the nucleons are more ...
2
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1answer
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Determining the velocity for a radial impact on an orbiting satellite

Say a planet P and a satellite S (the size of a moon) system exists and the orbit of S around P is circular. To make the satellite S crash into P, I can either slam an S sized comet C opposite to ...
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53 views

Inverse Square Law and Closed Orbits

The definition of closed in this context is that the body will retrace its orbit. A standard case for closed orbits is the circular case. I know from Bertrand's theorem that the linear restoring ...
2
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1answer
189 views

Why do the orbit equations have to be symmetric about two axes even the orbit is not bounded?

In the book of Classical Mechanics by Goldstein, at page 88, it is given that However, the orbit might not be bounded, so there might not be two turning point; just one. In such a case, how can we ...
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48 views

A question about almost stationary orbits

For an orbit around the earth with period equal to a sidereal day with eccentricity $e=0$ and inclination $i=0$, the path on earth would be a single point on the equator. I have done some simulations ...
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Is angular momentum independent of axis (if axis is parallel)?

I have been told this is true for the moon on this question: Angular momentum of orbiting + rotating body but I don't understand why it should work. Surely the axis must be chosen such that the ...
2
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1answer
287 views

Good sources to get velocity/position vectors for all planets and moons in the Solar System for building an orbital simulator?

I’m building an $N$-body simulator, and I have everything ready to begin simulating. But my issue is is that I have no idea how to get all the starting positions and velocities for the celestial ...
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100 views

How to show the first low of Kepler's laws

Picture below is from the Kepler's laws of Wiki. I fail to found its proof. I mean that how to use $$ F=G\frac{Mm}{r^2} ~~~~~~\text{and}~~~~~~~ F=ma $$ to prove the orbit of planet must be so. I ...
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Gravitational aberration and unstable orbits

From this link http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html it says that Putting a "light travel delay" (technically called "retardation") into newtonian gravity would make ...
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Assuming I could clip through the earth, what is the delta-v requirement to reach any orbit?

Nevermind how I intend to clip through the surface. You could say I intended to drill a tunnel kind of like the drop through the earth problem. I know how to do this calculation assuming all of earth'...
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0answers
152 views

Parametric Equations for the Coordinates of an Orbit as a Function of Time

We are given velocity, direction of velocity, distance between the two bodies and the mass of massive body. The effect of the mass of the orbiting body can be ignored. I am looking for parametric ...
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0answers
71 views

Open orbits on the Bloch sphere of two level atom

I am studying the Bloch sphere representation of a two level atom in a classical electric field, starting in the ground state at t=0. The Bloch equations for the time evolution are $$ \begin{align} ...
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Eight-shaped orbit determination

I was playing a game on my smartphone whose goal is to draw certain orbit in presence of certain central gravitational potential. I noticed that when there are two center of force is possible to have ...
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How does the Giant Impact Hypothesis resolve impulse for orbital insertion?

The Giant Impact Hypothesis describes that Earth's moon was formed from collision between a proto-Earth and another Mars-sized object. This collision ejected mass from the Earth into orbit, whereupon ...
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Do gravitational vawes deplete energy even if there's nothing they can affect?

I've read multiple times that one of consequences of gravitational waves being a thing is, that they make any orbit unstable. As long as the two or bodies orbit around each other, they create ...
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0answers
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Orbital period of a satellite in Kerbal Space Program

Let me start off by saying I am really bad at maths and physics, but lately I have been trying to calculate the orbital period of a satellite I have put in orbit around a planet called Kerbin in a ...
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0answers
55 views

Different time between equinoxes

I calculated from here that there are 16 104 096 seconds between the vernal and autumnal equinox, if I made no mistake, this is some 650 592 s longer than the other half orbit. I imagine this is due ...
2
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1answer
103 views

How did the Moon survive next to the Earth since earth and Moon came into existence?

What mechanism(s) prevented the gravitational effect of the earth on the moon from shattering the moon when it was closer to the earth than the Roche Limit some 4.5 billion years ago?
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Is there any free open source planetary orbit simulator software?

I need a free open source planetary orbit simulator software that should be able to calculate orbit stability for a couple simple planetary systems. Basically, I need to calculate orbit durations for ...
2
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1answer
72 views

Coexistence at Lagrange points

I was wondering how precise the location of an object in a Lagrange point needs to be to maintain stability, since it seems that several natural objects (asteroids) exists together in some of these ...
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0answers
240 views

What are the equations of motion that model near light speed orbits of a massive body about incredibly massive bodies?

In Kip Thorne's recently published book, The Science of Interstellar, he describes, by means of an illustration, the complex nature of a spacecraft orbiting a massive black hole with velocities ~ 0....

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