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Questions tagged [orbital-motion]

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

185 questions with no upvoted or accepted answers
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12
votes
1answer
952 views

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:...
10
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1answer
198 views

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. ...
7
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1answer
489 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 ...
7
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1answer
266 views

How did Kepler arrive at his laws?

How did Kepler arrive at his laws? If one already knows the distances to the planets (and the eccentricity of the orbits, etc.), it is understandable that one might proceed to establish Kepler's ...
5
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1answer
212 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
122 views

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 ...
5
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0answers
88 views

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 ...
5
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1answer
438 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 ...
4
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0answers
191 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,...
4
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2answers
183 views

When is a circle not a circle?

Imagine a 2D uniform circular motion of constant magnitude but changing direction in an area of zero g. The forces will be equal all the way round - it will be a perfect circle. Now imagine the same ...
3
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0answers
97 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. (...
3
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0answers
160 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)\...
3
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2answers
257 views

Orbital period and nodal precession & apsidal precession

In classical orbital mechanics as per Newton/Kepler, the time taken to complete one orbit around a body of mass $M_e$ is: $$ T = 2 \pi \cdot \sqrt { \frac {a^3} {G \cdot M_e} } $$ But also, for ...
3
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0answers
81 views

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 : ...
3
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1answer
158 views

Limit to the Oberth effect in a supermassive Black Hole flyby

To make this question clear, here are the details of the situation I wish to entertain. A spacecraft does a powered gravitational assist, where it fires engines in a near-approach to the body We ...
3
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1answer
165 views

Motion described by $a=\frac{k}{x^2}$

Say a particle in one dimension experiences acceleration inversely proportional to the square of displacement. What is its displacement as a function of time? $$ a=\frac{d^2x}{dt^2}=\frac{k}{x^2} \\ \...
3
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0answers
465 views

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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0answers
252 views

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 ...
3
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1answer
982 views

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
73 views

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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0answers
524 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 ...
3
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0answers
119 views

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 ...
3
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0answers
116 views

How to travel between tidally locked binary planets

Two planets of roughly the same volume and mass are orbiting each other. What would be the most efficient way to travel from one to the other? Seems unlikely, but could a rocket positioned at the ...
3
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0answers
164 views

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 ...
2
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2answers
55 views

Will August be always summer in the northern hemisphere?

Is the Earth orbit precessing, or are there other effects which will create a shift between our calendar (day counting), and the Earth's orbit? I imagine these effects to be small, but I'm asking for ...
2
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1answer
100 views

Why are orbits $1.5r_{s} < r < 3r_{s}$ unstable around a Schwarzschild black hole?

The "Orbital motion" section of the Wikipedia entry corresponding to Schwarzschild metric reads: A particle orbiting in the Schwarzschild metric can have a stable circular orbit with $r > 3r_s$. ...
2
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0answers
66 views

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. ...
2
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1answer
90 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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0answers
46 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 ...
2
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0answers
60 views

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
89 views

Sidereal time calculation from orbital elements and mean anomaly

I'm following the instructions given here for calculating the apparent position of the planets in the sky and I've come to calculating the sidereal time in section 1.8. The formula for calculating ...
2
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0answers
84 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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0answers
104 views

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 ...
2
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0answers
63 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} ...
2
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0answers
56 views

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 ...
2
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1answer
180 views

Simulation of relativistic probe passing through an external solar system

I recently read about the Breakthrough Initiative to launch "StarShot", a nano-probe that is designed to travel to Alpha Centauri at $0.2c$. One of the challenges to be solved involves the precise ...
2
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0answers
62 views

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 ...
2
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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
73 views

Eccentricity of planetary orbits: What information is contained?

I'm having a little trouble understanding what makes a planetary orbit explicitly elliptical. Is it simply that the initial velocity was different from the circular orbit case for a given starting ...
2
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1answer
90 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?
2
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1answer
70 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 ...
2
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0answers
236 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....
2
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0answers
538 views

How to calculate orbital eccentricity from the ratio of satellites' velocities?

I have a problem with working out how to calculate the orbital eccentricity from the ratio of two satellites' linear velocities. We know that two satellites encircles the Earth in two elliptical ...
2
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0answers
83 views

Terrestrial Space Elevator Construction - Plausability

Framework If there was a cable constructed at the equator about the circumference of the Earth, and if this cable had sufficient strength to remain intact while erect, call this tensile strength T. ...
2
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0answers
589 views

How to calculate launch angle for tangentially launched satellites?

What is the value of theta for a satellite not falling back to the Earth if it is launched from the direction tangent to the surface of the Earth? I have found the escape velocity which is 11.18km/s, ...
2
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0answers
52 views

Would a large, small mass object in orbit experience induced rotation

Imagine a large (multiple earth radii), very small-mass ring orbiting The Sun. Half of the ring would be closer to The Sun than the outer half. Since orbital velocity decreases with distance, two free ...
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0answers
123 views

Where are the L3, L4, and L5 points of a hyperbolic orbit?

Do the L3, L4, L5 points exist in hyperbolic orbits? If yes, then where do they lie?
2
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0answers
464 views

What causes an electron to return from a higher orbit to a lower orbit

Ultraviolet light can cause electrons from Hydrogen gas to jump from a lower energy orbit to a higher energy orbit. What causes the electrons to return from the higher energy orbit to the lower energy ...
2
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0answers
782 views

For two planets in a 2:1 mean motion resonance , where will their periastron and apastron points be?

I want to animate the changing orbits of planets when they enter a mean motion resonance. Using a 2:1 resonance, I want to show a low-mass inner planet and a low-mass outer planet being tugged by a ...
2
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1answer
82 views

Keplerian orbits as conic sections

It is usually mentioned in textbooks that keplerian orbits are conic sections. However, no further discussion is given on applications of this geometrical fact. So does this cone have any ...