# 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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### Angular velocity to stay at particular orbit [closed]

Wondered if anyone could help here. If we consider an object orbiting a Schwarzschild neutron star, how might we be able to get the angular velocity needed for the object to orbit the star at a ...
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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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### Correct way to transform RA-Declination to $x$-, $y$-, $z$-coordinates at the Galactic Center

I am simulating an object at the galactic center which has an initial position (RA and Declination) as 423 milliarcseconds and 525 milliarcseconds. The object is at a distance of 0.02pc from the Sgr A*...
1 vote
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### Could two planets trapped between two stars orbit each other?

Say there are two stars, each exerting and equal force on a point in the midde of them. For simplicity, we'll say the two stars have the same mass and are equidistant from the point. Now suppose that ...
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### Where is the most stable orbit in the Earth/Moon system?

Cis Lunar orbit, trans Lunar orbit, lunar orbit, Earth/Moon L4/5? What altitude, eccentricity/inclination? Moon resonance? Stable means not crash into Earth/Moon or escape. It's a chaotic n>2 body ...
1 vote
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### Is a satellite revolving in Earth's orbit also affected by the gravity of the Sun or other planets?

The Earth revolves around the Sun and a satellite also revolves around the Earth. The Sun has a gravitational effect on all celestial bodies, so does it also have an effect on the satellite? If so ...
1 vote
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### Alternative derivations of vis-viva equation?

The proof of the vis-viva equation of orbital mechanics found on wikipedia looks, in my opinion, somewhat convoluted and unenlightening. Considering the simplicity and importance of the vis-viva ...
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### Inquiry Regarding Hypothetical Celestial Mechanics Scenario

How would the addition of a second sun, located at the other focus of the planet's elliptical orbit, impact the motion and orbit of the planet? Specifically, how would the gravitational forces from ...
506 views

### Cyclic co-ordinates implying the constant velocity motion of center of mass of a system of particles

I'm reading the section on Central Force in my textbook (Goldstein's Classical Mechanics has a similar argument in the chapter titled "The Central Force Problem", first section), where we have the ...
1 vote
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### How to relate Laplace-Runge-Lenz vector to eccentricity?

So the eccentricity can be written in this form $$\mathbf{e}=\frac{\mathbf{A}}{mk} =\frac{1}{mk}(\mathbf{p}\times\mathbf{L})-\hat{\mathbf{r}}$$ but I cannot find a proof or figure it out on my own.
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### Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?

If, in free space, I throw two objects towards each other, they can either miss each other and fly apart (if the velocity is enough and there's not enough gravitational attraction between them), or ...
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### How does the Dzhanibekov Effect change if replaced with a propeller?

Every explanation and example uses a t-bar. But what if the "bar" was a propeller? I can understand there being no difference if it's a vacuum, but I would think the aerodynamics would ...
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### Why does the radius of orbit increase when a satellite increases it's velocity?

Can someone please explain to me why increasing the velocity of a satellite with a rocket booster will change the radius of the orbit rather than the linear velocity of the satellite? If the angular ...
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### Table of matrix elements of powers of $r$ for radial functions in $H$ atom

Im looking for some references here. I hope it is the right place to ask. I need to find a table of (or a formula from which to extrapolate) the matrix elements of the radial functions of the hydrogen ...
1 vote
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### Is Each Day the Same Duration?

Since Earth's orbit is elliptical surely each day does not have the same duration. My understanding is that at the perigee the Earth would have to rotate more than at the apogee due to its larger ...
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### Gravitational potential energy in Escape Velocity

From the derivation of formula of Escape Velocity we know that Minimum kinetic energy = Gravitational Potential Energy But in this circumstance, isn't it the value of gravitational potential energy ...
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### Meaning of a Constant in the Unbound Orbit Equation

The solution to the radial equation for two celestial bodies with eccentricity $\varepsilon$ greater than 1 can be expressed as $$\frac{(x-\delta)^2}{\alpha^2} - \frac{y^2}{\beta^2}=1,$$ where \...
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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 ...
1 vote
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### Magnetostatics and electrostatics orbiting a star with a magnetic field

I understand from the Feynman notes on physics that a static magnetic field in one frame of reference becomes a static electric field in a reference frame in which I move at the same speed as the ...
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### Force and Velocity directions

When ever the force and velocity are in thesame direction(0°), an object speeds up. When ever the force and velocity are in opposite directions(180°), the object slows down. Also , when ever force ...
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### Disposing of Obsolete Satellites by Propelling to the Sun [migrated]

I'm not scientifically adept, so bear with me. Would it be feasible to retain enough fuel on new satellites/space stations, etc., that we could dispose of them when obsolete by sending them to the ...
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### Why is the time from vernal and autumnal equinox different than from the autumnal to the vernal one?

In my lecture the professor stated that the time from vernal to autumnal equinox is about 186 days , while that from autumnal to vernal equinox is about 179 days. I was wondering why are these time ...
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### What is the motivation for supposing a pendulum exhibits circular motion?

The question here explains how a pendulum can move in circular motion. I am aware that the central tenet of circular motion is that there is a centripetal force acting radially inward that takes on ...
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### What is the expression for strong field Schwarzschild circular orbit perihelion precession?

How can you calculate how large the perihelion shift should be under Schwarzschild conditions in general relativity for minimally disturbed circular orbits in the strong field limit? I think there is ...
108 views

### Whats the difference between the Photon Sphere and the Marginally bound orbit?

Whats the difference between the Photon Sphere and the Marginally bound orbit? Why does photon sphere have a radius of 1.5Rs, while the Marginally bound orbit has a radius of 2Rs?
1 vote
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### Stress-Energy Tensor for a Two Mass System

I just don't understand this tensor and would like to go through an example with you to somehow make sense of it. I consider two spheres with masses $m_1$ and $m_2$, densities $\rho_1$ and $\rho_2$ ...
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### Rotating of a system of mass [closed]

In basic physics lectures, the teacher or professor in my class never explains the behavior of rotating two or many body particles. In my experience and intuition doing physics, two-particle or many-...
232 views

### How do i calculate a projectile range accounting for a planet's curvature?

I was trying to solve this problem myself but i dont know how to work out certain variables like gravity, centripetal force and the changing impact point due to the curve of a planet (any planet). So ...
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### Can Schwarzschild acceleration be written in exact form as a function of position and velocity vector?

For the special case of only one massive point-shaped or spherically symmetric non-rotating body and a small "test mass" body under general relativity the movement of that small body is ...
1 vote
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### Photon speed for an observer at the photon sphere [closed]

I am asked to compute the orbital period of a photon, in the Scwarzschild spacetime, at the photon sphere for an observer at the same radius, $r^\star=3M$. I have computed the result, $\Delta T=6\pi M$...
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### Escape velocity work done problem [closed]

We derive the formula of escape velocity by using conservation of mechanical energy, where we consider that work done by external force is neglected. But to provide the velocity to send an object to ...
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### HW: particle subject to central force with exponential logarithmic orbit

I've been working on this exercise for some time now and although I've almost got it I can't seem to make it to the end of it. Here is the exercise: A particle subject to a central force is orbiting ...
1 vote
457 views

### General solution for the two-body problem [closed]

I am trying to compare numerical solutions of the two-body problem with the analytical one. But, for some reason, the analytical one doesn't seem to agree with the numerical one. For the numerical ...
1 vote
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### Can the Schwarzschild orbit equation be solved exactly?

The Schwarzschild orbit is $U'' + U = 1 + \varepsilon \cdot U^2$. I've only seen turning-point analysis that demonstrates shift of perihelion. Is there an exact solution?
1 vote
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### Why do we use specific orbital energy and specific angular momentum?

In the derivation for vis-viva equation $$v^2 = GM \left({ 2 \over r} - {1 \over a}\right),$$ here they use specific quantities such as specific energy and specific angular momentum but I don't ...
1 vote
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### Potential Energy for Non-conservative Forces

I was studying for the GRE and came across the problem below. A small puck of mass $M$ is attached to a massless string that drops through a hole in a platform, as shown in the diagram above. The ...
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### Derivation of the equation of a hyperbolic orbit from the conic section expression derived via the orbit equation

So I'm looking to derive the equation of a hyperbolic orbit from the general expression for a conic section $$r=\frac{l}{e\cos\theta+1}$$ that you get out of solving the orbit equation for an inverse-...
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### Two particles rotating about their center of mass

Two bodies each of mass $m$ are rotating about their center of mass where the radius is $r$. Here centripetal force of each body is $\frac{mv^2}{r}$ where $v$ is the linear speed. Now, gravitational ...
1 vote
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### How can I obtain the position of the Earth on the orbit for given date?

I would like to be able calculate (or at least download some time-series data of) the position of the Earth on it's orbit at given date. For my purposes, it would be sufficient to account for the ...
1 vote
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### Component-free computation of Poisson bracket of Laplace-Runge-Lenz vector

How can the Poisson bracket $\{A,H\}$ be computed directly without components, where $H$ is the Hamiltonian for the inverse square force, $$H=\frac{p^2}{2m} - \frac{k}{|r|}\ ,$$ and $A$ is the ...
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### Which gravitational differences we would feel if the sun disappeared?

I would like to start by stating that I'm not a physicist, I'm purely a curious individual. I've been speculating about the differences the loss of the sun's gravitational field would have on us and ...
1 vote
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### Is overusing gravitational slingshots a real concern?

I was thinking of the trading of kinetic energy during a gravitational slingshot maneuver and wondered if the kinetic energy lost during that process makes any noticeable impact on the orbit of the ...
1 vote
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### Orbital obliquity of the Earth

Consider that we have all the orbital parameters that characterize the Earth. How would one calculate the orbital obliquity of Earth? One could argue that since the rotation of Earth doesn't change ...
1 vote
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### How does the speed (and kinetic energy) necessary to orbit a black hole vary with the radius of orbit?

I understand that closer orbits around Schwarzschild black holes require faster speeds, culminating in a required speed of $c$ at the photon sphere ($r = 3M$ in Schwarzschild coordinates). I'd love to ...
1 vote
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### Apparent speed of an object in a circular orbit in Schwarzschild geometry

Does an object in a circular orbit around a massive body in Schwarzschild geometry seem to move faster for a stationary observer located close to the massive body, compared to how the same object ...
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### Orbital Velocity Formula in Schwarzschild metric

What is the orbital velocity formula in Schwarzschild metric assuming that the orbit is circular? this formula should also work for relativistic velocities.
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### Energy in central force orbit

Given a mass $m$ moving under the central force $$F(r) = -k/r^n$$ and a circular orbit passing through the force center, I want to show $n$ must equal 5. I ultimately arrive at the expression E = \...
1 vote
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### Tidal effects of galaxies orbiting one another in presence of dark energy?

I recently asked this question about whether there was a "distance" between two galaxies where both the gravitational force and the influence of dark energy would be balanced. The answers ...
### Why is there a *minimum* energy for a particle to be captured in a $r^{-3}$ potential?
I was stuck in a central force problem from David Morin's Book "Introduction to Classical Mechanics". The problem states that suppose there is a particle of mass $m$ moving under the ...