All Questions
Tagged with newtonian-gravity celestial-mechanics
373
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Newtonian mechanics doubt
While solving a particular classical mechanics problem , I was told that for a system of particles to be bound under their mutual forces, their initial energy (With Respect To the COM) must be less ...
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0
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70
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How can one predict asteroid orbit, with the use of vector calculus?
If you are given, (or found) the position and velocity vectors of an asteroid how can one use this to predict its orbit?
2
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1
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224
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Question about Lagrange's solution for the three-body problem
The original text in my textbook, written in short:
"By Newton's second law,
$$\ddot{\mathbf{x}}_1=-Gm_{2}\frac{\mathbf{x}_1-\mathbf{x}_2}{|\mathbf{x}_1-\mathbf{x}_2|^3}-Gm_{3}\frac{\mathbf{x}_1-...
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25
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7
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Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
If, in free space, I throw two objects towards each other, they can either miss each other and fly apart (if the velocity is enough and there's not enough gravitational attraction between them), or ...
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1
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Sun-Earth-Moon-Spacecraft four-body simulation using MATLAB - unexpected results [closed]
I'm trying to simulate this four-body system by directly integrating the system of equations
$$\ddot{\textbf{x}} = \sum_{i=1\:i\neq k}^4 G\frac{m_i}{|\textbf{x}_i-\textbf{x}_k|^3}(\textbf{x}_i-\textbf{...
- 3
2
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1
answer
138
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Is there a rigorous proof regarding the non-linear stability of the $L_4$ and $L_5$ Lagrange points?
I have found that many proofs regarding the stability of the $L_4$ and $L_5$ Lagrange points are based on linear approximations of the equations of motion near these points. However, from a dynamical ...
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2
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2
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Derivation of Kepler's third law using Virial theorem
I am familiar with the long derivation of Kepler's third law using the equations of motion. One starts with
\begin{equation}
\dot{r}=\sqrt{\frac{2}{m}\big[E-V(r)\big]}
\end{equation}
and integrates to ...
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How to add kinetic energy to gravitational energy to obtain total energy?
Cambridge Pre-U 9792/03/M/J/22
Examination question: What is the total energy E of the binary star system?
Given: The kinetic energy of star X is $E_x = \frac {2GM^2}{9D}$
Working:
$E_Y = \frac{GM^2}{...
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Why doesn't the centre of mass of the solar system move away from the sun? [duplicate]
Consider our solar system, in the frame of the sun (i.e. "the sun is stationary"), with a simplified 5 planets and nothing else. Suppose that for a brief moment, all of the planets aligned (...
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2
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Is it possible to determine if a planet can have a moon based on its mass and gravitational pull?
I'm curious, if based on what we know with Newton's law, can we determine if a random planet, knowing it's mass and gravitational pull, can hold a moon in it's orbit.
Or to phrase it another way, is ...
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What am I doing wrong? An easy gravity problem
The following problem is giving me a headache:
Halley's comet follows an elliptical orbit around the sun. At perihelion, its distance from the sun ($r_P$) is $8.823 \cdot 10^{10}$ metres. At aphelion,...
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2
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65
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Attraction between two objects in the universe. The resulting number of forces between them
Right now I am studying Newton's Law of Universal Gravitation and I already learned his Third Law. It is said that there is an action-reaction pair between the falling apple and the Earth which ...
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1
answer
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Dependence of areal velocity on distance between sun and planet
We know velocity of a planet in an elliptical orbit is given by:
$$v^2 = GM * (\frac{2}{r} - \frac{1}{a})$$
in an elliptical orbit. [Here r is distance between particle and sun] source
We also know, ...
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1
answer
39
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Angular Momentum or Gravitation question [closed]
Question: If the earth suddenly shrinks to $\frac{1}{64}$th of its original volume keeping mass same, the period of rotation of earth becomes $\frac{24}{x}$ hours, what is $x$?
So basically, why can’...
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6
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WHY can't we use conservation of energy to find speed of the earth around the sun?
I was trying to calculate the velocity of the earth around the suns orbit using the conservation of mechanical energy hence:
$$\frac{GMm}{R} = \frac{mv^2}{2}$$
$$\sqrt{\frac{2GM}{R}} = v$$
why is the ...
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