Questions tagged [celestial-mechanics]

Celestial Mechanics is the branch of astronomy devoted to the study of the motion of the celestial bodies on the basis of the laws of gravitation.

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Does the Lagrange Point $L_3$ exist in practice in the multi-body solar system?

Lagrange Points ($L_1$ through $L_5$) in a restricted 3-body system are well documented. Traditionally body 1 (M1) is the central object with a mass much greater than the other two objects. M2 is ...
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How to calculate the new position at time $t$ of celestial bodies with variable acceleration?

Intro For an $N$-body simulation of celestial bodies I need to calculate on the one hand the accelerations of the celestial bodies based on the received gravitational forces [done] and on the other ...
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The unlikely marriage of orbiting bodies

O.k. so we have an orbiting body such as the Earth around the sun or the moon around the Earth. The fact that they are orbiting does not fascinate me, it is my intuitive sense that there is a much ...
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Why is the shape of the orbit of the Earth as it is?

My View: I think that if the sun were only force acting on earth (as a centripetal force), the earth would have a circular orbit. Since other planets also exist , there also exists gravitational force ...
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Could a moon keep orbiting a planet forever?

Our Moon orbits the Earth further away each year due to the tidal forces but could there be a moon orbiting a planet where somehow keeps going further away by the tidal forces but its attracted again ...
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Central force problem: the basics

In a central force problem, let $r'$ mean the derivative of the radial distance with respect to time, then (m$r''$ - mr$\theta''^2$ )($\vec{r}$) = f($\vec{r}$) , the radial force. Please check if ...
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Circular motion of planet around star

The question says that the planet moves in a circular orbit around the massive star. But the graph says that velocity of the star wrt the COM of star-planet system varies with time. But my confusion ...
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Are orbital eccentricities in a binary system always the same?

Some excercises on Kepler laws and binary system use this relation $$\frac{r_1}{r_2} = \frac{a_1}{a_2},$$ where $r$ is the distance from the center of mass to each object and $a$ is the semi-major ...
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When scaling down a universe, what is scaled down, and how to calculate gravity?

Assume I want to scale down Earth so that it fit into a 500x500 units (pixels) cartesian plane, at a scale of 1:1,000,000. Earth, with a radius of 6,371,000 meters, now has a radius of 6.371 units. ...
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Can I please get the proofs for different trajectories of a satellite when projected at different velocities? [duplicate]

I recently came across a question about the trajectories of satellites, I have tried many resources for the proofs but couldn't find them. For example, a satellite will have an elliptical orbit if (...
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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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What's the time window for total and narrow eclipses?

Because of the tidal effect angular momentum is transmitted from Earth rotation to the Moons orbit around Earth. This means that perfect eclipses only has occured during a certain time window. Can ...
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Active Balance on L1

Could you have a spacecraft on L1 say the earth-moon system and then extend a weight on a string to the moon and a weight on a string to the earth and keep the spacecraft in balance at L1 just by ...
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How long would it take for the moon to disintegrate into a ring if placed inside the Earth's Roche limit?

Wikipedia says the Earth-Moon rigid Roche limit is about 9500 km. The moon's diameter is roughly 3500 km, so say I magically teleport the moon to within 6000 km of the Earth—it's fully contained ...
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Free fall and the period in keplerian motion [closed]

What is the time it takes for a free fall compared with keplerian time period? Is it half the orbital period or a quarter?
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Why does an orbit become parabolic when total orbital energy is zero?

I stumbled across while reading other stack posts where there was a discussiom of non calculus ways to find the trajectory under E negative and E positive conditions Feynmans technique was well used ...
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In a two-body problem, is the argument of periapse the same for both bodies in orbit?

I'm trying to find the argument of periapse $\omega$ for a certain planet which has been studied with imaging, spectroscopy and radial velocity. In the literature I've only been able to find the ...
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Difference between the Sphere of Influence and Hill Sphere

I am looking through astronomy topics, and I found two ideas which sound very similar, but have very different formulae which come to different results. That is the Sphere of Influence, and Hill ...
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Help finding the eccentricity of an orbit

I am trying to find the eccentricity of a planet in order to be able to calculate perihelion and aphelion distances. I can get a lot of the equation, but am having issues with the angular momentum, ...
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If I'm trapped in $L_4$ or $L_5$ of Lagrange points, am I going to experience any libration? [closed]

I read that there are some points in space where the gravitational forces from the Sun and Earth get cancelled out, although I still not sure why L1, L2 & L3 are unstable compared to L4 & L5 ...
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How to represent orbital velocity of a planet on an elliptical path in terms of time?

Before reading this long message, please know that this is question is posted to know whether there is a method to find the relation between between the orbital velocity of a planet on an elliptical ...
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Why isn't the two-body problem in General Relativity completely solvable?

I do know that approximate solutions to the two-body problem come in the form of the equations of motion in the Schwarzschild metric plus post-Newtonian power radiated. However, I am more interested ...
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Is there a way to locate celestial bodies indoors?

I mean, without being able to see the sky is there any analog way I can calculate where a planet/star/constellation is, and point in that direction? I have found apps like Star Chart, which as an AR ...
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Does the formula $v = \sqrt{GM/r}$ work for elliptical planetary orbits?

Suppose we have a central mass $M$ and a smaller mass $m$ orbiting around the central mass in an ellipse: The other point is the other focus. We know that elliptical orbits have the central mass in ...
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Simulating solar system with Newton's law

I made a simulation in C++ with Newtons law and test it comparing the planets positions with the position from Solar system Calculator Don Cross (which I converted from JavaScript to C++) http://...
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Estimate the eccentricity of the Earth's orbit using equinoxes

I was reading the wikipedia article on Kepler's laws (https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion) and I came across the following. "The eccentricity of the orbit of the ...
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The accelerate from an elliptical orbit to a circular orbit

If there is a satellite and it is in an elliptical orbit. At the aphelion, it accelerates from its elliptical orbit to a circular orbit. The thing that confuses me is that when the satellite is at ...
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For a spacecraft orbiting a planet, orbital speed is inversely proportional to orbit radius. But speed must be increased to increase orbit radius?

For a spacecraft in orbit with radius $r$ with speed $v$ around a planet, centripetal force $F_C$ is provided by gravity: $$\frac{GmM}{r^2}=\frac{mv^2}{r},$$ which simplifies to $$\frac{GM}{r}=v^2.$$ ...
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Orbital paths of planets

Given any star or massive body, how would one calculate the orbital path that planets will take? Do we use the geodesic equation $$\frac{d^2x^\mu}{d \tau^2}+\Gamma^\mu_{\alpha \beta}\frac{dx^\alpha}{d ...
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Would it be possible for someone, once flung, to continually orbit a small planetoid?

I am wondering this question (though it may seem obvious) because of an issue I'm having with a peer. He says that if a person is flung around a small planetoid, at just the right angle and velocity, ...
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Equation of Hill sphere when the mass ratio is not large

I know of the equation for determining the Hill sphere. Which is $a(1-e)(m/3M)^{1/3}$. However I noticed that during the derivation of this formula that the assumption that $m\ll M$ is used. But what ...
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What is the angle between the North Celestial Pole and the Galactic Equator?

I’m trying to back-calculate a value in astronomy using spherical trigonometry. Using the following formula, where $δ$ = the Declination of the Galactic North Pole in degrees (i.e., the angle between ...
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3 answers
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Speed of planets orbiting Sun formula

What formula returns speed of a planet, e.g. Earth orbiting Sun, on its ellipse like trajectory orbiting Sun? Input variables have to be $a,b$ (ellipse) and some more, because the speed of the planet ...
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Second Kepler's law explanation

What is the explanation for the second Kepler's law? Why is the law valid? Is it that the total energy of a planet equals to the kinetic energy plus the potential energy?
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How to actually plot the Kepler Problem?

As far as I understand the Kepler problem tries to predict the motion of two bodies under the influence of gravity. Here the trajectory of each particle is chosen to be: $$\vec{r}_1 = \vec{R}+\dfrac{...
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Astrodynamics Patched Conic Approximation [closed]

I would need some help as I don’t know how to find $p$ and $e$ of an heliocentric orbit in order to calculate the following formula.
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2 votes
2 answers
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A doubt in a Wikipedia article discussing Bertrand's theorem

Wikipedia while deriving Bertrands theorem writes after some steps: ...For the orbits to be closed, $β$ must be a rational number. What's more, it must be the same rational number for all radii, ...
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Bertrands theorem, Hooke's law and closed orbit [closed]

Bertrand's Theorem says: the only forces whose bounded orbits imply closed orbits are the Hooke's law and the attractive inverse square force. I'm looking at the Hooke's law $f=-k r$ and try to see ...
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A doubt in a Wikipedia article discussing Bertrand's Theorem in Central force motion

Wikipedia on Bertrand's theorem, when discussing the deviations from a circular orbit says: ...The next step is to consider the equation for $u$ under small perturbations ${\displaystyle \eta \equiv ...
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Are Kepler's laws proven wrong recently? Or how were they Proven by Johannes Kepler just by observing

The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times. The Law of ...
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4 votes
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Why does a distant rotating body have angular momentum about the origin?

In a frame where the center of mass is stationary, the angular momentum of a body is invariant to translation of the origin. That is: $\mathbf{L} = \sum_i \mathbf{r_i} \times \mathbf{p_i}$ is constant ...
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1 vote
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Could a set of rogue double planets (binary planets) be habitable due to tidal forces?

I want to write a story about rogue double planets and was wondering if it's possible to have a double planet where either both or one of the planets are habitable due to tidal forces even if the ...
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How to calculate orbit params for transfer before docking?

I have two spacecrafts on two equatorial circular orbits with different phase angles (it could be random, I need a universal solution). Also, I know Kepler's params of both orbits. I want to move one ...
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Are there any moons that exhibit a non-convex curvature in their orbit about the Sun?

In my answer at https://physics.stackexchange.com/a/266444/59023, it took me several iterations before David Hammen and others could help me understand why the Earth's moon's orbit about the Sun is ...
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What are the implicit assumptions that make it okay to model a satellite fly-by of the Earth as a 1D elastic collision?

In a satellite fly-by of the Earth, a satellite approaches the Earth on a hyperbolic orbit. In learning about collision theory in Newtonian Mechanics, I have seen results related to elastic collisions ...
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Finding the constant $\theta_0$ in the orbit equation for motion in $\vec F=\frac{K}{r^2}\hat{r}$

Solving the equation of orbit for a particle of mass $m$ moving under an inverse-square force $\vec F=\frac{K}{r^2}\hat{r}$ is given by $$u=\frac{1}{r}=-\frac{mK}{L^2}+C\cos(\theta-\theta_0)$$ where $...
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Why Moon is not falling on Sun (Hill's sphere)?

The Hill's radius of Earth in Earth-Moon system calculated by formula https://en.wikipedia.org/wiki/Hill_sphere is 58212 km But the distance between Moon and Earth is 384,400 km So, why Moon is not ...
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How will be changed Hill's radius and Kepler's formulas in case of 2D space instead of 3D?

Imagine that Flatland habitats go into space. All stars and planets are the circles instead of spheres and gravity law is F=G*m1*m2/R instead of F=G*m1*m2/R^2. How the other formulas will be changed ...
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3-body problem: Is it possible to find real moon orbit if I know kepler's orbit elements for 2body, direction to planet and real gravity force vector?

I have a system of Sun, planet and moon of planet. I can find orbit of moon using kepler's law. But distance between planet and moon is a half of distance between planet and sun. So, if I will ...
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How to find equatorial orbit pericenter position in 2D if I know $\mu$, $a$, $e$, excentricity anomaly, focus pos and current position and velocity?

How to find equatorial orbit pericenter position if I know $\mu$, $a$, $e$, excentricity anomaly (observed at current moment), force focus position (but don't know empty focus position) and body ...
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