All Questions
Tagged with newtonian-gravity celestial-mechanics
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Kepler's Two-Body Problem Choice of Sign
I have been going over the solution to Kepler's problem and there is a subtlety I am missing. The notes I am following (my own notes from a while ago in fact...) get to the following expression
$$
\...
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2
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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 ...
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Why are the orbit of planets usually ellipses? [duplicate]
There has been a similar question about planets' orbits being ellipses but the answer circulates around how the circle is a special type of orbit which doesn't really answer my question.
Elaborate ...
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Is it possible for a moon to have the same orbital period as its planet?
Is it possible for a planet to take just as long to orbit its star as a moon takes to orbit the planet? If we assume circular orbits, then
$\text{orbital period}\sim \sqrt{\frac{\text{radius}^{3}}{\...
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Pair of binary stars orbiting each other
Suppose we have a pair of binary stars orbiting around each other in their mutual gravitational field. My question is, is the trajectory of the combined system would be an ellipse?
And, if it is an ...
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How to calculate the new position at time $t$ of celestial bodies with variable acceleration?
Intro
For an $N$-body simulation of celestial bodies I need to calculate
on the one hand the accelerations of the celestial bodies based on the received gravitational forces [done]
and on the other ...
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Why is the shape of the orbit of the Earth as it is?
My View: I think that if the sun were only force acting on earth (as a centripetal force), the earth would have a circular orbit. Since other planets also exist , there also exists gravitational force ...
- 159
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Circular motion of planet around star
The question says that the planet moves in a circular orbit around the massive star. But the graph says that velocity of the star wrt the COM of star-planet system varies with time. But my confusion ...
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Are orbital eccentricities in a binary system always the same?
Some excercises on Kepler laws and binary system use this relation $$\frac{r_1}{r_2} = \frac{a_1}{a_2},$$
where $r$ is the distance from the center of mass to each object and $a$ is the semi-major ...
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When scaling down a universe, what is scaled down, and how to calculate gravity?
Assume I want to scale down Earth so that it fit into a 500x500 units (pixels) cartesian plane, at a scale of 1:1,000,000.
Earth, with a radius of 6,371,000 meters, now has a radius of 6.371 units. ...
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Can I please get the proofs for different trajectories of a satellite when projected at different velocities? [duplicate]
I recently came across a question about the trajectories of satellites, I have tried many resources for the proofs but couldn't find them.
For example, a satellite will have an elliptical orbit if (...
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Free fall and the period in keplerian motion [closed]
What is the time it takes for a free fall compared with keplerian time period?
Is it half the orbital period or a quarter?
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In a two-body problem, is the argument of periapse the same for both bodies in orbit?
I'm trying to find the argument of periapse $\omega$ for a certain planet which has been studied with imaging, spectroscopy and radial velocity. In the literature I've only been able to find the ...
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If I'm trapped in $L_4$ or $L_5$ of Lagrange points, am I going to experience any libration? [closed]
I read that there are some points in space where the gravitational forces from the Sun and Earth get cancelled out, although I still not sure why L1, L2 & L3 are unstable compared to L4 & L5 ...
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Does the formula $v = \sqrt{GM/r}$ work for elliptical planetary orbits?
Suppose we have a central mass $M$ and a smaller mass $m$ orbiting around the central mass in an ellipse:
The other point is the other focus. We know that elliptical orbits have the central mass in ...
