# 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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### Effect of Newton's law to the orbits inside a galaxy like Milky Way

Does Newton's law describe the orbital motion of stars in a galaxy? Is it true that the closer a star is to the center, the lower is the gravity, so the lower the speed of the star?
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### How inaccurate are the positions of the planet and moon in my simple solar system model, compared to real life?

I am building a model of a simple, fictional sun-planet-moon solar system (not the real Sol-Terra-Luna system). Purpose: to calculate astronomical events like eclipses and moon phases, and the ...
72 views

### The Force of Gravitational Waves [closed]

How could one calculate and derive the "force" or displacement and stretching of an object due to gravitational waves?
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### Have I accounted for all relevant physics in my simplified three-body solar system model? [closed]

EDIT: Re-framed here to be more on-topic. I am building a model of a simplified, fictional sun-planet-moon solar system (not the real Sun-Earth-Luna system) to calculate astronomical events like ...
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### What is the photon interception radius of a Schwarzschild black hole? [duplicate]

To clarify what i mean by "photon interception radius" I mean the radius of the sphere where if any photons from a distant source enter will also inevitably result in them entering the black ...
141 views

### Calculating theta/anomaly for a hyperbolic orbit based on time step

I'm soing some kepler based orbital mechanics for a game prototype I'm working on, am a bit of a newbie to both orbital mechanics and a little challenged at reading the algebra equations that are ...
1k views

### 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 ...
95 views

### Is 5 km/s enough to escape Earth's gravitational field? [closed]

A particle is fired vertically upward with a speed of $15\,\mathrm{km}/\mathrm s$. With what speed will it move in interstellar space? Assume only earth's gravitational field. So this is a question ...
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### Regarding distance laws of gravity from “A Brief History of Time” and why the Earth doesn't fall into the Sun

In “A Brief History of Time”, Hawking explains Newtonian gravity in Chapter 2, Space and Time. The further apart the bodies are, the smaller the force. The gravitational attraction of a star is ...
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### Angular momentum conservation in a rocket-sun-moon system

Let us describe a rocket traveling from earth to the moon and back. I want to show that the rocket's angular momentum is conserved to be able to conclude that the rocket's motion is restricted to a ...
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### Is there a term that describes the (immediate) loss of mass at the center of a gravitationally bound system?

I'm curious if there is a general term in physics that describes the (immediate) loss of mass at the center of a gravitationally bound system? For instance, if (as contrived as it may be) the Sun were ...
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### On the Bohr model and Kepler Orbits allowing eccentricity in the full Poincare group [closed]

I decided to reanalyse Bohr's orbital equations, while we are comfortable now with wave mechanics, many state that the electron does not follow exact paths, but instead follows wave like paths. Some ...
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### What are the Standards Of Fundamental Astronomy calls to convert between ECEF and J2000?

I found this stack exchange post to be informative but not actually helpful. I am using SOFA (the C version), but the "correct" ICRF <=> ITRF conversion is not what I need. If ICRF is J2000 (...
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### How to calculate the needed energy to make something spin around its axis at a certain rate?

An object is floating into space. How much energy is required to make it spin around its own axis with a rate of x RPM? How does this calculation look? And does this calculation change if the object ...
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### How do you find the position at which three particles obey $m_1 a_1 = m_2 a_2$ if two of the particles form a composite body?

From Classical Mechanics by Kibble: Consider a system of three particles, each of mass m, whose motion is described by (1.9). If particles 2 and 3, even though not rigidly bound together, are ...
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### Relativistic Doppler Effect between rotating bodies

The Wikipedia article "Relativistic Doppler effect - One object in circular motion around the other" confused me. There they say that when the light source orbits the observer, the observation of ...
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### How do I calculate Earth's velocity?

How do I calculate Earth's velocity (on its elliptical orbital path, as a function)? I know how to calculate it assuming that Earth's orbital path is circular but I want to know what we would do if we ...
1k views

### Why isn't the time between apogee and perigee constant?

I've assumed since the translational speed of the moon along its orbit undergoes the same boosts and reductions over its orbital course, the time between the apogee and the pedigee (and respectively, ...
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### Physical interpretation of the symmetry for the Runge-Lenz vector

In the post What symmetry causes the Runge-Lenz vector to be conserved?, and based on the results of https://arxiv.org/abs/1207.5001, it was it was discussed that the Runge-Lenz vector is the ...
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### Virgin Galactic's and Blue Origin's Space Flights - are these just Extended Skydiving in an Enclosure? [closed]

Sorry for four questions in the three paragraphs below, but they all are around the same curiosity that I have. In both of Virgin Galactic and Blue Origin's space flights happening in July 2021, it ...
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### Infinite Motion from Finite Motion [closed]

By stringing an arbitrarily large number of double-reduction gears together, it is possible to create a system (assuming no gravity and no friction) where the final gear is making an arbitrarily large ...
28 views

### Why do we substract the longitude of ascending node to the argument of periapsis in orbital mechanics?

I'm having trouble finding a satisfying answer to the following question: To describe perfectly a Keplerian orbit, one needs 6 orbital parameters: $a$ the semi-major axis, $e$ the eccentricity, $i$ ...
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### How do I calculate Earth's axial precession in an idealized Sun-Earth-Moon system?

I am experimenting with an idealized three-body system based on the Sun-Earth-Moon system. In my system the orbits of the Moon and Earth about the Earth-Moon barycenter, and the orbits of the Earth-...
18 views

### When the lunar module ascent stage launched to take astronauts back to the lunar module, how long was the launch window? [migrated]

This excellent animation says the launch must happen at "just the right time", but how long was the actual launch window, how precisely (how many seconds or minutes) did the launch need to ...
105 views

### In uniform circular motion how can the acceleration of a body be directed towards the center of rotation if the velocity is tangent to the orbit?

Here is a picture illustrating my question: https://upload.wikimedia.org/wikipedia/commons/7/71/Uniform_circular_motion.svg I must not understand what acceleration is, because I don't understand how ...
303 views

### Analytical proof for Kepler's first law using cartesian co-ordinates

Many detailed proofs are available for Kepler's first law, like this one. But all of them use polar co-ordinates. There is one which doesn't even use differential equations. I'm looking for a proof ...
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### Tidal Forces on a Body at a Fixed Altitude

It's a thought experiment which I've been running in my mind for long in order to understand tidal forces. Any suggestions/ideas are appreciated. Assume a perfectly spherical planet with no atmosphere....
786 views

### Uniform circular motion dilemma

During uniform circular motion, the tangential acceleration is zero, but there is centripetal acceleration. Centripetal acceleration is a very necessary component of circular motion, but why does the ...
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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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### Finding the dominant frequency of a stellar orbit

I was reading this paper on astro-ph (Sanders et al. 2020, "Models of Distorted and Evolving Dark Matter Haloes"). It's about modelling the gravitational potential in a cosmological ...
330 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). ...
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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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### The value of gravitational potential energy of a satellite in low-earth orbit [closed]

The gravitational potential energy of a satellite as it sits on earth is given by $$\frac{-GMm}{R}\tag 1$$ where $R$ is the earth's radius, $M$ is the earth's mass and $m$ is the satellite's mass. If ...
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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 ...
47 views

### Confusion regarding 2-body problem [duplicate]

I'm new to 2-body problems, especially the case of binary stars, or a planet around a star system, and I'm facing this small doubt. I know, that in order to solve this, we mostly reduce this 2-body ...
4k views

### If gravity is attractive, why doesn't the Milky Way contract?

Einstein introduced the cosmological constant because without it, one cannot get a static universe - gravity would cause the universe to contract. Given that, why is the Milky Way not contracting? For ...
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### Why is the answer marked 19.5? [closed]

A star S is being orbited by a planet P such that the planet rotates around itself once every 0.1 earth days. It is observed that P completes 196 rotations around itself by the time it completes 1 ...
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### Using Planetary Motion Laws to relate to elliptic motion

I was reading something to do with elliptic motion and I came across using the equation of orbital velocity to determine the centripetal force acting on a body. So for an ellipse with a semi-major ...
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### Hohmann Transfer and Lagrange Point

I recently learned about Lagrange points and Hohmann transfer orbit concepts. I need to confirm some facts. I looked up several sites but found no answer. I wanted to find whether spaceships are ...
14k views

### What symmetry causes the Runge-Lenz vector to be conserved?

Noether's theorem relates symmetries to conserved quantities. For a central potential $V \propto \frac{1}{r}$, the Laplace-Runge-Lenz vector is conserved. What is the symmetry associated with the ...
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### Hohmann transfer: question on vessel orientation

I am looking at the Hohmann transfer and I would like to apply it to KSP. So I'm trying to see the different formulas needed to calculate the $\Delta V$ needed to change the orbit (only the orbit, not ...
1k 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:...
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### Is there a solution for the three body problem? [duplicate]

Is there a valid solution to the three body problem? why has it puzzled mathematicians and physicists for so long?
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### Discrepancy of the Keplerian speed by a factor when calculated with different methods

I needed to derive today the Keplerian speed for a circular motion in a gravitational field. Just for the hell of it I decided to derive it once via the forces and once via the energies and strangely ...
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### Orbit descent Hamiltonian

Consider the case of a satellite orbiting around Earth subject to a tangential constant force (opposite to the velocity) that causes the spacecraft to descent to a lower altitude orbit. How would you ...
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### If a bar was from a geostationary satellite to the ground, would it stay stationary?

Suppose there is a perfectly geostationary satellite in orbit, and the satellite deploys a bar or a metal rod from the satellite to the ground, straight down(This is impossible, but hypothetically, it ...
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### Radial motion of a photon in Schwarzschild spacetime

For photon worldlines in the equatorial plane of the Schwarzschild coordinate system ($\theta=\frac{\pi}{2}$) in Schwarzschild space-time, the metric equation is given by, -\Big(1-\frac{2GM}{r}\Big)...
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### Problems with Sun-Earth-Moon simulations in vPython

I'm trying to simulate the Sun-Earth-Moon system using the Verlet algorithm with vpython. I'm using natural units and a cartesian coordinate system, and am having trouble working out the physics. I ...