Questions tagged [orbital-motion]
The path a body takes while moving through space under the influence of the gravitational forces of other bodies
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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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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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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 ...
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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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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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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).
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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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Book recommendation for classical Newtonian gravity
I’m looking for a good textbook that covers Newtonian Gravity in detail (preferably advanced undergrad/grad level). One that covers important things like
Calculating trajectories of satellites around ...
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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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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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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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Why do the planets tend to spin in the same direction as they orbit the center sun?
I mean, why do the spin angular momentum and the orbit angular momentum of a planet tend to have the same direction?
As we all know, a planetesimal $m$ orbiting a sun with mass $M_{sun}$ at $r$ will ...
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Can light orbit an object that is NOT a black hole?
I know that light can enter into an unstable circular orbit around a black hole, at a distance of its innermost bound circular orbit (IBCO) $\frac{3r_s}{2}$ where $r_s$ is the Schwarzschild radius of ...
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The causes of the nodal precession of a satellite in Earth orbit?
All artificial satellites in Earth orbit between the polar orbit and the equatorial orbit are subject to a nodal precession caused by the equatorial bulge of the Earth at the equator.
How the ...
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Does the gravitational field of a planet affect it's own orbit?
According to GR, masses (such as the Sun and the Earth) cause space to curve. Then planets such as the Earth follow geodesics on this curved space.
However, if we consider the Earth and the Sun both ...
user84158
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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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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:
$$
\frac{d^{2} u}{d t^{2}}+u=-\frac{m}{l^{2}} \frac{d}{d u} V\left(\frac{1}{u}\right) .
$$
The preceding equation is such ...
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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
$$ \mathrm ds^2 = -\left(1-\dfrac{2Mr}{\rho^2}\right)\...
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Minimal value of angular momentum in a close binary
I just noticed something interesting with the angular momentum of a close stellar binary. This question is somewhat related to another question of mine, but the question here is clearly different :
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Determining velocity of moons
I have a question that I believe is relatively easy to answer, I am working on an $N$-body simulation of a fictional star system and am having trouble finding the velocity of moons so that they will ...
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When Did Structures Begin to Orbit in the Universe?
In Big Bang Cosmology, I am familiar with the radiation era, and the moment of last scattering, but I am just not familiar with the physics of orbits, or of the “falling outward,“ if you will, that ...
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Isn't the Jacobi constant just the Lagrangian times 2?
At this wikipedia page the Jacobi constant is expressed as:
$$C_J=2\left(\frac{v^2}{2}-U\right)$$
where $U$ is the potential energy and $v$ is velocity. If kinetic energy $T$ is defined (as it ...
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Computing 2d Orbital Parameters
When using formulas that describe a 2d orbit around a planetary body:
is it actually OK for the semi-major axis $a$ to be negative?
when $a$ is negative, it is impossible to compute mean anomaly from ...
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Is Earth/Luna tidal lock approaching faster?
Wikipedia pegs the mass of Earth at $5.972\cdot 10^{24}\,\text{kg}$ or $5.972\cdot 10^{21}\,\text{metric tons}$.
Assuming Earth accumulates approximately $30,000\,\text{metric tons}$ annually. To ...
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Will a man acquire orbit if we suppose Earth is rotating fast enough?
if we consider that the rotation of earth is mush faster (30000km/h), so if a man standing on earth jumps 1 meter above will it acquire orbit if we ignore atmospheric friction
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Orbital phase and gravitational wave phase
I am trying to understand the relation between the orbital phase of binary and the phase of the gravitational wave when expressed as spin-weighted spherical harmonics.
The metric perturbation can be ...
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Which hemisphere of the earth gets more sunlight?
This question is for amusement only so to speak...
Which hemisphere of the earth gets more sunlight, northern or southern?
By "gets more sunlight" let's say we're counting photons over the ...
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Harmonic and subharmonic orbits in central fields
Using Newton's theorem of revolving orbits one can easily obtain orbits for central forces containing inverse cube terms, such as
$$F(r)=F_0(r)+\frac{(1-k^2)|B|}{r^3},$$
from known orbits for $F_0$. ...
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Geodesic equations and carter constant: how can I derive the right equations?
Introduction
Suppose the Hamilton-Jacobi equation:
$$\frac{\partial S}{\partial \lambda} + \frac{1}{2}g^{\mu\nu}\frac{\partial S}{\partial x^{\mu}}\frac{\partial S}{\partial x^{\nu}}= 0. \tag{1}$$
Now,...
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Inner and outer orbital limit of planets in single-star systems
I am trying to find a rough cut-off of the inner and outer orbits of native planets around a single star. I know about the Roche limit and Hill Sphere, but these are not the limits I am looking for. I ...
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Where I can find obliquity direction?
I can find axial tilt of planets easily, but that doesn't specify the direction of that tilt, i.e. planet's rotation axis may be anywhere in circle defined on a sphere by axial tilt value. And I can't ...
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If the Earth stopped spinning, which way would the wind and waves sweep?
I just started reading the book what if? by the brilliant Randall Munroe. One of the first questions is
'What would happen if the Earth and all terrestrial objects suddenly stopped spinning, but the ...
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Find semi-minor axis of elliptical binary orbit given semi-major axis and mass ratio
I'm working on a simulation of binary stars. I'm using Kepler's Laws to solve for the angular velocity given the semi-major axis $a$ and the masses $m_1$ and $m_2$ of the two objects in an elliptical ...
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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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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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Deviations from purely circular orbit for an object in a Yukawa potential
I am struggling with the logic for completing the following problem.
The problem is part b of 3.19 in Goldstein's Classical Mechanics book.
A particle moves in a force field described by the Yukowa ...
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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 ...
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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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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 ...
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Conceptual question about wheels
I am trying to understand quite naively wheels in a specific framework.
Intro
We normally think of squares and circles as different concepts of shapes, but I am reframing it that both are polygons ...
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Orbital velocity of a binary system
My goal is to find a velocity vector for two planets so that they orbit each other. The planets' masses and distances are known, just not their velocities.
When googling for an equation, I found a ...
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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 ...
user86425
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What is the scope of the term 'orbits'?
Warning - this is a very soft question. I was wondering what the precise meaning of the word orbit is? Wikipedia refers to it only in the sense of gravitational forces, in which case mathematically ...
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Where did Paul Gerber go wrong in arriving at the same equation as Einstein in explaining the Mercury anomaly?
We know that Einstein admitted that Paul Gerber's 1898 formula explaining the anomaly of Mercury's perihelion was the same as his own. Reportedly Gerber had made a mistake somewhere, so - even though ...
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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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