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On the Stability of Circular Orbits

Bertrand's Theorem characterizes the force laws that govern stable circular orbits. It states that the only force laws permissible are the Hooke's Potential and Inverse Square Law. The proof of the ...
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0answers
17 views

How can I measure the stability of a many body gravitational system?

Suppose I have an N body planetary system interacting via gravity. Suppose I know the positions and momenta at t=0. How do I know if this system is stable (indefinitely)? By stable I mean the ...
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0answers
30 views

Heliocentric Cartesian position of moons

I have a working Kepler orbit system that is GPU accelerated to allow precision, speed and parallelism and more importantly allow as many factors as possible in calculation. For various reasons I ...
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1answer
50 views

Stability of the classical helium atom

Let us forget about quantum mechanics and confine ourselves to classical mechanics. The Hamiltonian for a classical helium atom would be $$ H = \frac{p_1^2 + p_2^2}{2m } - \frac{Z}{r_1} - \frac{Z}{...
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4answers
104 views

Orbits for dummies [duplicate]

In a certain universe a perfectly spherical, uniformly dense planet is found to be in a stable orbit around a stable star. The rest of the universe is empty space with no silly stuff like dark matter. ...
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1answer
24 views

Would a celestial body in a horseshoe orbit be tidally locked to the planet?

A smaller celestial body like a moon or an asteroid can be in a horseshoe orbit around a planet. Since it might go inside the tidal lock radius (but does not stay inside it all the time), during the ...
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2answers
67 views

Which timestep should I use for a $N$-body simulation of the Solar system?

I am trying to implement a $N$-body simulation of the Solar system and I am stuck on the issue of the simulation timestep size. At first I would like to use a simple Euler stepping scheme. Knowing ...
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2answers
43 views

Reference frame, gravitation and kinetic energy

English is not my primary language. I apologize (and would like corrections) if the terms I use are not the right ones. In a geocentric reference frame, the moon rotates around the Earth. So its ...
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1answer
73 views

As planets orbit around the Sun, does the force of gravity due to the Sun remain constant?

I know that the force of gravity is: $$F = GMm/R^2$$ Where $G$ is gravitational constant, $M$ is mass of sun, $m$ is mass of the orbiting planet and $R$ is the distance between the center of their ...
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3answers
83 views

Gravitational acceleration of asteroids [closed]

If an asteroid is moving through space at a speed that exceeds escape velocity of the earth and that asteroid is on a collision course with the earth will the asteroid Accelerate as it falls into the ...
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8answers
4k views

Why doesn't orbital body keep going faster and faster? [duplicate]

If we consider the change in velocity during an infinitesimal interval of an orbit: where body B is orbiting body A, we can see that the magnitude of the resultant vector (the green arrow) is ...
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0answers
27 views

Keplerian orbits and radial velocities: problem with true anomalies

I am writing a pure Python code to calculate radial velocities of stars with massive objects orbiting them. I am following the formalism from Murray & Correia (2011) (hereafter MC11). In a given ...
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2answers
57 views

What does “transfer” of angular momentum mean?

The Moon’s gravity produces tidal deformations or “bulges” in the Earth. Because of the Earth’s rotation, the line that goes through the bulges is not aligned with the line between the Earth and the ...
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1answer
22 views

How would I find the velocity of an object after it doesn't fully enter the gravitational pull of a planet and is kind sling shot out of its gravity?

Obviously that question doesn't have a lot of jargon having to do with math and physics. I am not a physicist, I'm not a mathematician, I'm trying to make a game and simulate some physics found in ...
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1answer
30 views

Earth, Sun and beginner's reference frames

In the post-Newton era, where "absolute space" is not absolute, how is the reference frame in which "the Earth moves round the Sun" accurately defined?
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1answer
43 views

Energy diagram of a planet with fixed mechanical energy

Consider the following energy diagram for the motion of a planet about a star. The centrifugal potential curve can be represented once I fixed the angular momentum $\vec{L}$ of the planet. To fix the ...
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0answers
59 views

Celestial bodies trajectories relative to each other and with respect to the CM

In a two bodies $A$ and $B$ system, both under the action of an internal force of interaction $\vec{F}$, the motion of $A$ as seen from $B$, is equivalent to the motion of a single body of mass $\mu=\...
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1answer
66 views

Methods for handling close approaches in $N$-body simulations

In direct gravitational $N$-body simulations, what are the preferred methods for handling close approaches between bodies in order to preserve the accuracy of the evolution of the system?
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0answers
29 views

Can a satellite be put into orbit such that it will always remain directly over a city? [duplicate]

Isn't it possible if we just set it high enough so that it's angular speed matches with the earth's? I think that the city must be on the equator to make this happen. Am I correct? Please can anyone ...
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0answers
15 views

Research groups in celestial mechanics [closed]

This Exchange may not be the right place to to ask this question, but I would like to know prominent research groups working in celestial mechanics. Although I'm interested in celestial mechanics, ...
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0answers
21 views

Books on Celestial Mechanics [duplicate]

My background is mathematics. I would like to study celestial (not classical) mechanics and looking for an appropriate book. I found that somebody has already asked a similar question "How to learn ...
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0answers
19 views

Journals which publish articles on Celestial Mehanics [duplicate]

I'm from mathematics and want to study celestial mechanics further. In order to know literature at research level, I would like to know in which journals we can find papers on celestial mechanics. The ...
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0answers
60 views

How to visualize gravity fields? [closed]

I'm creating a tool for intuitively prototyping routes through space. Part of this requires visualizing gravity. This is the formula for working at how much gravity is at a particular location: <...
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1answer
63 views

Can the constant $k$ from Kepler's third law be independent of the mass of the planet?

Consider Kepler's third law The square of the orbital period $\tau$ of a planet is directly proportional to the cube of the semi-major axis of its orbit $a$. $\frac{\tau^2}{a^3}=k$ The ...
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1answer
75 views

Newtonian Gravity Simulator?

Could anyone suggest me a good (and possibly free) Newtonian Gravity Simulator software available on the web, where it might be possible to simulate the Solar System dynamics and playing with it, by ...
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0answers
40 views

Semi-major axis , specific mechanical energy, its period and velocity at Apogee and Perigee and what the difference is [closed]

Hi im needing some help with two questions could you please show the formula and the way its solved?Thanks PS:Could you also explain what the difference of velocity and apogee and perigee? 1.)A ...
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1answer
37 views

Motion under gravitational forces

In a system of particles, can a particle be considered to be attracted to the combined center of mass of the other particles if the Newton's universal law of gravitation is used (the inverse square ...
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5answers
97 views

How can escape velocity and gravitational potential be higher in weaker gravitational fields?

on Earth we have an escape velocity of about 11180 m/s and a gravitational field of g=9.81 m/s^2. It would seem obvious that the escape velocity was higher for stronger gravitational fields. Often it ...
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3answers
78 views

Could the Earth-Moon rotation period equal one Earth year?

I just stumbled on this rather confused QA. The point seems to be if the Earth-Moon rotation period was identical to the Earth-year, then ... ... all three would stay in a line at all times. ...
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0answers
28 views

Orbital period of a satellite in Kerbal Space Program

Let me start off by saying I am really bad at maths and physics, but lately I have been trying to calculate the orbital period of a satellite I have put in orbit around a planet called Kerbin in a ...
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2answers
88 views

How has the world remained in balance?

In the center of our galaxy, there is a Supermassive black hole. We were told in early astronomy units of school that black holes are giant vacuums that will absorb/consume the area around it. My ...
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4answers
7k views

Can the Earth leave orbit if the population of humans and other live forms increases?

I don't know a lot about physics, but this seemed like the correct place to ask my question. I apologize in advance if it is a ridiculous one. It's actually a two part question: If the population ...
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0answers
24 views

Topic on relativistic celestial mechanics [closed]

I have to do a small 10-15 minutes presentation about celestial mechanics, and I am searching for a topic. As a mathematician my background in physics is not very extensive, but I have some notions ...
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3answers
94 views

Gravity effects when deleting stars or planets

In one of the latest SCIFI movies, they collect a star absorving it entirely in a kind of planet size gun/machine. As mass cannot disappear, I assume it was just concentrated inside their machine (...
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0answers
37 views

How to calculate angle between two objects in orbit

So I have 2 objects in orbit around the same body, and I have all the orbital elements associated with each body. How do I calculate the angle between them both or figure out when they are a certain ...
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1answer
108 views

Relation between eccentric and true anomalies

If $v$ is the true anomaly and $E$ the eccentric anomaly, how can I show that $$\frac{dv}{dE}=\frac{b}{r}=\frac{\sin v}{\sin E}~?$$
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1answer
64 views

Why do the stars in a binary system, revolve diametrically opposite to each other?

I encountered this question, as I was reading up on Gravity. The author of my textbook says that the stars orbit a common centre which is their center of mass. I somehow think that this fact might ...
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0answers
25 views

Laplace's method to determine orbits

I am trying to do the second problem by Laplace's method, it is in spanish but the only thing that matters are the asteroid's observations and the coordinates of Earth https://freeshell.de/~rgh/arch/...
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1answer
55 views

Can a planet's orbit around a star be simulated? [closed]

Say I know all parameters like density, size, rotational velocity of a planet, could I predict its orbit around a star where I also know parameters of it? I want to design a simple model of the solar ...
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3answers
103 views

How to predict the location of a planet at a given time? [closed]

I am trying to create a simple two-dimensional computer simulation of a planetary system. While I've been able to understand Kepler's Laws of Planetary Motion, I do not know enough about the formulas ...
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1answer
53 views

Gravitational potential of planets

How do you work out the gravitational potential of planets in the solar system? Do orbiting planets have gpe? And what would it be relative to? The equation I know for it is mgh. But what would the ...
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2answers
113 views

Orbital mechanics: will a satellite crash?

For a satellite given an initial speed and position above a planet, I'd like to know whether it will experience an elliptical, circular, parabolic or hyperbolic trajectory, or crash into the planet. ...
2
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1answer
61 views

The source of work by gravity force [duplicate]

I learn that any work needs a source of energy, the work of gravity force (like keeping the Moon in the orbit by the Earth gravity force) comes from where? Can we find any mass reduction (transform ...
2
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1answer
34 views

Testing the accuracy of a solar system simulation

I've written a java program to model the solar system, and I need to test its accuracy. What would be some good ways to do that? I've checked for conservation of energy and angular momentum. I'm using ...
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1answer
50 views

Orbital but stationary motion

Is there a place between the Moon and Earth where an object can rest freely and revolve with the Moon? What is that called?
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1answer
62 views

Angular Momentum and Kepler's Second Law

Let me preface by saying that I get the gist of the conservation of angular momentum, at least qualitatively. To better illustrate my question, I will consider the case of a planet orbiting a star. ...
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2answers
45 views

Remotely finding the mass of a satellite

I have a question similar to one I've asked earlier (Calculating mass of an orbiting body with force and acceleration), but without a specific formula... How can you find the mass of a satellite body ...
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2answers
113 views

No energy consumed in planetary motion? [closed]

Most of the orbits of planet are elliptical. How is it then that no energy is consumed?