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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Gravity and shell theorem in strongly curved hyperbolic space
I was reading this post and I was wondering how gravity would work in a strongly curved hyperbolic space (with curvature on the order of ~1km). In particular, would the shell theorem still hold? How ...
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33 views
Orbits in the effective potential $U(r)=k(r^2 -a^2)e^{-br^2}$
Given the effective potential $U(r)=k(r^2 -a^2)e^{-br^2}$, where $r$ is the spherical radial coordinate, could a particle oscillate near $r=0$ even when the particle cannot go to a coordinate with ...
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How does the perihelion advance vanish for a unique circular orbit?
I'm working on a problem set in which I am to find the precession of the perihelion of Mercury given the corrections to the Newtonian potential coming from general relativity. I am stuck on e and f.
...
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Why Euler-Lagrange Theorem gives the optimal control law? [on hold]
Can anyone explain me in simple language why applying Euler-Lagrange Theorem on Hamiltonian equations gives the optimal control law?
I am specifically talking about trajectory optimization problems ...
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1answer
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How would the rotational and orbital mechanics differ on a torus-shaped planet as compared to a spherical planet? [closed]
I am making the attempt to develop some computational models of Star systems and I was wondering how the a torus shaped planet would compare to a traditional spherical planet in the context of ...
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Star orbit and dark matter
In a college entrance examination of my country, there was the following question:
Suppose that, in a galaxy, the dark matter, which is evenly distributed, can be removed. Suppose also that in the ...
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4answers
98 views
How to find angle something turns as it orbits in orbital mechanics? [closed]
Short version:
Take a look at this animation really quick. https://commons.wikimedia.org/wiki/File:Orbital_motion.gif
The direction in which the arrows for $\alpha$ and $\nu$ is adjusted as the ...
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1answer
48 views
Kepler's Second Law: Why do we calculate the area of a triangle rather than the area of a sector?
Kepler's Second Law states that equal areas are swept in equal times. When calculating this area, why do we use the formula for the area of a triangle rather than the area of a sector?
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Is a complex Keplerian eccentricity $e=\sqrt{1+\frac{2\varepsilon h^2}{\mu^2}}$ possible?
Wikipedia provides the following formula for the Keplerian orbital eccentricity:
$$e=\sqrt{1+\frac{2\varepsilon h^2}{\mu^2}}$$
Considering that a bound object means negative energy, if the magnitude ...
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1answer
39 views
Speed of a body in orbital motion [closed]
I assume I'm making a silly error somewhere but I can't see how.
The question is concerning two objects $M$ and $m$ orbiting each other at a distance of $r$ apart.
The first part was simply finding ...
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Is there a chance for moon to collide with earth?
I have learned that attraction between the bodies increases when it's mass increases ,if the population increases day by day and hence it can increase the mass of earth which causes attraction ...
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1answer
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What would be the shape of a space elevator?
I have never seen a discussion of the shape of a space elevator (as viewed from above the North Pole, let us say). Would it be straight or curved?
I have included a diagram of several potential ...
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1answer
65 views
Equation of motion from potential energy [closed]
Given that the potential energy of a particle in 2D space is $$V(x, y) = \frac{1}{2}k(x^2 + y^2),$$ find the equations of motion and show they are circular orbits.
Substituting $r^2 = x^2 + y^2$, I ...
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1answer
45 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 ...
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2answers
48 views
Can Kepler's laws apply for circular motions?
Can Kepler's laws apply for circular motions? (First law states planets take an elliptical orbit)
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3answers
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Energy of a planet moving around the Sun
In chapter 13 of volume 1 of The Feynman Lectures, Feynman is discussing how the work done in going around any path in a gravitational field is zero. Here's the link: http://www.feynmanlectures....
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2answers
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Parker Solar Probe top speed
All the news articles say it'll orbit the sun at 430,000 mph. How do they get that? It seems too low. Isn't orbital velocity proportional to $1/\sqrt{r}$?
Parker will be 4 million miles above the "...
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Angular momentum in Rotating Frame for satellites
I am working on satellite orbit propagator, I am propagating the satellite position and velocity in the inertial and rotating frames.
To validate my propagator, I am checking the angular momentum and ...
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1answer
65 views
Geodesic of a massive particle in Schwarzschild metric
what happens to particle in unstable circular orbit in schwarzschild metic when it is pushed outwards? Does its geodesic change into an ellipse with around stable radius corresponding to its angular ...
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1answer
24 views
Would a Lunar space elevator only be stable if it passes through Earth-Moon L1 or L2?
I understand that space elevators are extremely hypothetical (bordering on pure fiction), but they are supposed to be theoretically possible.
My questions is about what longidtudes a lunar space ...
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2answers
58 views
Day/Year Length Of Larger, but same mass, Earth? [closed]
I’m wondering how the length of a day and year would change on Earth if it was twice as big, but the same mass (less density)?
Also, would such a difference cause it to orbit closer or further from ...
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1answer
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How can I find the areal velocity of a body, moving under a central force, in Cartesian coordinates?
My textbook tells me that the areal velocity of a body under central force is expressed by $\vec A$ = $r^2$$\dot\theta$$\hat k$. How can I express this in Cartesian coordinates, since the above ...
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1answer
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Question about angular speed
Lets assume that the motions of the Moon around the Earth and of the Earth around the Sun are uniform circular.
If $\omega_L, \omega_T$ are the respective angular speeds find $\omega_L/\omega_t$.
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1answer
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Was Feynman right about the chalk in the spaceship?
I have heard this problem many times before from various sources, but I am quoting Feynman's words from his Lectures On Physics (Vol : 1) , just in case you want it to be authentic.
Therefore, ...
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In which direction is orbit around the moon easiest to achieve?
Suppose a conventional spacecraft is launched from Earth with the intention of establishing an orbit around the Moon.
In the context of this question, the Earth/Moon system is viewed from far above ...
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1answer
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What's keeping the Moon in its orbit when the Sun's gravity is greater? [duplicate]
Just as the title says, what's keeping the moon in its orbit around the earth while sun's gravity is greater, why doesn't it deviate and take an orbit (purely elliptical without moving around the ...
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1answer
47 views
Orbit of detached mass
I was wondering what precisely would happen to parts detached by objects in orbit. To specify:
Let a large object of mass $m$ is in a stable orbit around a planet with mass $M$ at a distance $r$ ...
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2answers
46 views
What is the orbit of SDO (solar dynamics observatory)? How does it takes images of Sun non-stop?
There is a orbital diagram given in sdo website https://sdo.gsfc.nasa.gov/
It takes images of sun 24hr.
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3answers
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Is the path that a planet takes orbiting the sun a centripetal one or one that follows a geodesic path?
Is the path that a planet takes orbiting the sun a centripetal one or one that follows a geodesic path? My point is that if the planet follows a centripetal path all objects on the planet will ...
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1answer
70 views
Gravitation question
I’d like to ask the following doubt that came to me after some exercises:
Is it possibile to exactly establish,given a satellite orbiting Earth with a certain $\vec v_{0}$ and distance $\vec R_{1}$ ...
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3answers
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Since astronomers are adding 'leap seconds' to our years nowadays, does that mean Earth's orbital period is getting longer?
How long was an Earth year several billion years ago? (I'm assuming constant days, even though I know days were much shorter back then).
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1answer
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Is spacetime in an ellipse around a massive object, or does it just slope down towards the massive object?
In some discussions, people seem to imply that spacetime is in an actual ellipse around a massive object so that, for example, the planet orbiting a star is actually traveling in a straight line in ...
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1answer
41 views
Can a single electron have an orbital angular momentum in the direction of propagation in free space?
I trying to understand the article about quantized orbital angular momentum in electron vortex beams. The article is not important per se, as there are many others. But I'm reading it as if an ...
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1answer
48 views
What would happen to the Moon if the Earth stopped providing it with a centripetal force owing to its force of gravity?
Would the Moon really only travel in a straight line then? What about the other planets and their forces of gravity? Wouldn't they prevent this rectilinear and undisturbed motion of the Moon?
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How do astronauts and spacecrafts float away into space if they're always under the influence of the Earth's gravity? [duplicate]
I understand that as the distance between the planet and the body increases, the gravity decreases, but how can they still just 'float away'?
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How long and to what extent can tidal energy sustain a productive system?
I've been idly re-reading some articles lately on Enceladus and Europa. Regardless of the prospects for the actual existence of life in their oceans, it spurred some thinking on how systems reliant on ...
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1answer
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How to prove Kepler's 3rd law? [duplicate]
How to prove Kepler's 3rd law? How did Kepler proved it? Is it possible to prove the third law without applying Newton's universal law of gravitation?
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Goldstein on Bertrand's theorem
Bertrand's theorem (Wikipedia)
Regarding central force motion, Bertrand's theorem states that only inverse-square and linear force law produce stable closed, if bounded, orbits.
Wikipedia's proof of ...
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1answer
79 views
Can anything orbit a black hole with dipping under the event horizon?
The event horizon is the boundary, from where light cannot escape. But can anything else?
Something with real mass will gather inertia while falling into the black hole. First it will mainly increase ...
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1answer
47 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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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
$$ \mathrm ds^2 = -\left(1-\dfrac{2Mr}{\rho^2}\right)\...
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2answers
147 views
What happens if the gravitational force on a satellite is greater than the centripetal force needed to keep it in circular motion?
Will the satellite continue to orbit the Earth, albeit not in a circle? Why? I would greatly appreciate it if someone could help me address this query. :) Also, I think someone asked a similar ...
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1answer
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Total mechanical energy of two neutron stars orbiting a common center ($E=U+K$) [closed]
Suppose we have two neutron stars of mass $M$, orbiting a common centre at a distance $R$. (i.e. the two neutron stars are $2R$ apart from each other, and $R$ apart from the centre). I've attempted to ...
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5answers
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Can the Schrodinger equation describe planetary motion? [duplicate]
I was asked on an exam whether the Schrodinger equation can be used to describe planetary motion and my answer was "No, because the solutions are wavefunctions which give probabilities but everything ...
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1answer
40 views
Doubt in the equation of trajectory of partical moving under central Force
In the book by Goldstein (Third Edition, Page 95) on classical mechanics, Goldstein derives equation of the trajectory of particle moving under center force. The equation he derives is given by:
$$r= ...
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2answers
174 views
Does the Sun revolve around the supermassive black hole at the center of the Milky Way? [duplicate]
I'm curious to know, does the sun really revolve around the black hole at the center of the galaxy?
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2answers
55 views
Effect of Change in Mass on Planetary Motion [closed]
How would a change in the mass of a planet in the solar system affect its orbit? For example, if hypothetically the mass of Mars were doubled, would it [a] move closer to the Sun, [b] move further ...
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2answers
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Closed gravitational orbits and gradient systems
I am currently studying non-linear dynamics on my own time. One of the theorems in the material is that systems that can be written as gradient problems cannot have closed orbits i.e. systems like
$$\...
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4answers
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If there is friction and everything stops on earth why does earth not stop due to friction?
Why do planets revolve around the Sun if there is a force called frictional force? Why do planets not stop rotating while the objects in motion stop after a while? Why are they continuously moving? ...
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1answer
52 views
Angular velocity by mean velocity and ecentricity of orbit [closed]
Okay, so I'm working on a project that will include a track of a star's position in the sky of an arbitrary planet. I've thus far managed to work out all the factors (save refraction) using ...
