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1
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2answers
82 views

Finding sphere of influence in multibody system

I would like to draw a boundary illustrating the sphere of influence of each body in a 3 body system. What is the best way to find such a boundary? My understanding is at the edge an SoI is the ...
3
votes
1answer
71 views

Collisions of celestial objects

When massive, spherical celestial objects collide, how long does it take for the objects to coalesce into a new, larger, spherical entity under the influence of gravity? Examples of the above:- ...
2
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1answer
55 views

Why doesn't no rotation imply tidal locking?

That I know of, in most parts of physics 0 movement means the body is resting, all the forces are in equilibrium. Why in orbital mechanic 0 rotation speed doesn't mean tidal lock as it would be the ...
0
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1answer
100 views

My python trajectory calculator for a small mass in a gravitational field - why is energy conservation violated?

I wrote this thing to calculate the next position of a small mass, given its current position and velocity, and a vector field determines acceleration. It sort of works - except I can never get the ...
0
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1answer
40 views

Binary Mass Function Plot

Suppose that we have a circular eclipsing binary system with orbital period of $P = 2 \text{days}$, and with one star with a radial velocity of $v_{1r} = 100 km/s$. The other star is to dim for its ...
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0answers
216 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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0answers
65 views

A proof for Newtonian origin of residual perihelion advances in solar system

In an Amazon book it is given a very simple formula $$\delta = \frac{k}{T^{5/3}}$$ conforming to which the so-called residual advance of perihelion $\delta$ of each inner planet in solar system ...
3
votes
0answers
107 views

Isn't the Jacobi constant just the Lagrangian times 2?

At this wikipedia page the Jacobi constant is expressed as: $$C_J=2\left(\frac{v^2}{2}-U\right)$$ where $U$ is the potential energy and $v$ is velocity. If kinetic energy $T$ is defined (as it ...
3
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0answers
238 views

Simple model of the solar system. Parameters? Accuracy?

I was thinking of making a simple 2D model of the solar system, with planets moving along ellipses like $$x(t) = k_x \sin(t + k_t) (\sin(k_\phi) + \cos(k_\phi))$$ $$y(t) = k_y \cos(t + k_t) ...
3
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0answers
185 views

Calculation of a Gravity Resonance Keyhole

Can anyone describe the mathematics behind the calculation of a resonance keyhole (for a two-body model)? It seems like the size and position of the keyhole should be a function only of mass and ...
2
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0answers
29 views

What is the difference between Saddle points and Lagrangian points between Earth and the Sun?

I am studying MOND bubble effects in the Solar System (Paper). In "mond habitats.." (last reference) first page, the author says MOND bubbles reside on the saddle points but I fail to understand the ...
2
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0answers
146 views

Story about a mathematician, a dinner party, and the three-body problem

I remember dimly hearing a story, coincidentally also at a dinner party, and I was trying recently to track the details down with no success. I was hoping someone here might have also heard this story ...
2
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0answers
306 views

For two planets in a 2:1 mean motion resonance , where will their periastron and apastron points be?

I want to animate the changing orbits of planets when they enter a mean motion resonance. Using a 2:1 resonance, I want to show a low-mass inner planet and a low-mass outer planet being tugged by a ...
1
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0answers
33 views

How to calculate orbital eccentricity from the ratio of satellites' velocities?

I have a problem with working out how to calculate the orbital eccentricity from the ratio of two satellites' linear velocities. We know that two satellites encircles the Earth in two elliptical ...
1
vote
0answers
24 views

The equation of the location of L1

On http://en.wikipedia.org/wiki/Lagrangian_point#L1 it says that the location of L1 can be determined as $\frac{M_1}{(R-r)^2}=\frac{M_2}{r^2}+\left(\frac{M_1}{M_1+M_2}R-r\right)\frac{M_1+M_2}{R^3}$, ...
0
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0answers
40 views

Algorithm for calculating lunar crescent visibility

Is there a simple algorithm for predicting lunar crescent visibility. Simple enough to do with a calculator at least. Those offered in Meeus' Astronomical Algorithms are a bit too involving to do by ...
0
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0answers
14 views

Is it possible to calculate Lagrangian isolines for local stars?

Is it possible to calculate Lagrangian isolines for local stars? SciFi descriptions of 'hyperspace' always talk about travel routes between the stars following some sort of route. As a thought ...
0
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0answers
31 views

Restricted three body problem

I have the restricted three body problem, which corresponds, to the equation $ \ddot a-2\dot b -a= \displaystyle\frac{\partial U}{\partial a} $ $ \ddot b +2 \dot a-b = \displaystyle\frac{\partial ...
0
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0answers
51 views

How can I describe an equation for multiple objects over time?

Lets say i have $n$ different objects that effects each other only by the classic gravity force. I have their initial locations, masses and velocity's: $$ x_1(0),\cdots,x_n(0) $$ $$ m_1,\cdots,m_n ...
0
votes
0answers
82 views

Effect of small variable transverse force on satellite orbital precession

Consider a small satellite which moves in a 2D elliptical orbit around a much larger body (e.g. the Sun) under the influence of Newtonian gravitational acceleration $$Ar = G.M/d^2 $$ Next imagine ...
0
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0answers
87 views

Relation between the period of rotation and the period of revolution of a satellite

I read somewhere that the tidal forces between the earth and the moon causes the equality between the 2 periods of the moon and that every planet-satellite system will evolve to this condition (like ...