Questions tagged [celestial-mechanics]
Celestial Mechanics is the branch of astronomy devoted to the study of the motion of the celestial bodies on the basis of the laws of gravitation.
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Kepler's third law and conservation of angular momentum: apparent fallacy
Angular momentum $L$ of a particle in central force is a constant of motion. So for circular orbit, $$L =mωr^2 = constant.$$
This implies $$ω ∝ 1/r^2,$$ hence the time period of revolution, $$T = 2π/ω ...
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Why does orbital velocity variation correlate with $\sin$ of the angle between position and velocity vectors?
By analyzing the motion of Venus using NASA JPL Horizons ephemeris data (10-year span, 1-hour sampling), I found that the variation of orbital velocity $\Delta v(t)$ appears to closely follow a ...
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How to obtain the third gravitational potential term from this series?
In this paper the gravitational potential between a point mass and an extended rigid body is
$$
U = -\mathbb{G}m_1\int_B \frac{\mathrm{d}^3 \mathbf{Q}'\rho(\mathbf{Q}')}{|\mathbf{r} + \mathrm{C}\...
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What are the Euler-Lagrange equations of an approximated rigid body and a point planet interacting via gravity?
The potential due to a rigid body will be approximated using a Lagrange polynomial expansion as
$$
U(x,y,z)=-\frac{\mathbb{G}Mm_p}{r} - \frac{\mathbb{G}m_p(I_1 + I_2 + I_3)}{2r^3} + \frac{3\mathbb{G}...
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Deriving the Orbit Equation
I would like to understand the derivation of the orbit equation.
I am following the derivation at https://orbital-mechanics.space/the-orbit-equation/the-orbit-equation.html which is largely ...
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Is general relativity required to calculate to orbits of Pluto's moons? How to calculate of orbits of the Pluto's moons?
Is general relativity required to calculate to orbits of Pluto's moons? How to calculate of orbits of the Pluto's moons?
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Coriolis Force on a Phobos anchored Sarmont tether [closed]
One of my daydreams is a non rotating sky hook anchored on Phobos.
I was wondering how to calculate the Coriolis Force induced by ascending or descending elevator cars.
Wikipedia tells me:
Coriolis ...
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Is there a site that I can used to make API requests for the positions of the planets in the solar systems? [duplicate]
I am creating a program that calculates orbital mechanics. And one option I want is the ability to use as a starting point the current positions of the Solar System. So is there a site that can I use ...
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Why doesn't Mars's or Venus's axial tilt change without large moons, but Earth's is believed to?
It is claimed that the moon stabilizes the Earth's axial tilt, but Mars and Venus (and Mercury, too) are rocky planets without large moons. Why are their axes stable?
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NASA defying physics or what's wrong with Earth flybys [closed]
Imagine a space probe that
starts around Earth at time $t=0$ with velocity $\vec{V_0}$ (sun reference frame) and
goes into an elliptical orbit around the sun such that
after (almost) exactly one year ...
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Can a satellite or a planet orbit a planet/star without rotating around its own axis?
I read that pretty much all orbiting planets have some initial spin. My question is, if we were able to cancel that initial spin and make the planet or ,let's say, for convince's sake, an artificial ...
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Why do tidal contributions from the Sun and Moon add during a full moon instead of cancel out?
Spring tides occur during syzygy of the Earth, Sun and Moon. During a new moon, when the sun and moon are both pulling harder on the near side of the earth than the far side, this makes perfect sense, ...
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Hamiltonian direct interaction term for small eccentricities and coplanar orbits
The direct perturbation term in celestial mechanics can be written as:
$$
\mathcal{H}_{\rm D} = - G\frac{m_1 m_2}{|\vec{r}_2 - \vec{r}_1|} = -G\frac{m_1 m_2}{r_2} \sum_{k=0}^{\infty}
\binom{-1/2}{k} B^...
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What's the Jacobian determinant when changing variables from velocity space to energy space in the scattering rate of gravitational scattering?
I'm reading Bahcall & Wolf (1976) [ApJ 209, 214. Star distribution around a massive black h0le in a globular cluster]. As usual, they skip lots of derivations, and I'm having trouble getting from
$...
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Classical vs canonical perturbation theory
Books such as Moulton focus on the classical perturbation theory famously developed by Lagrange and Laplace, while more modern books seem to use canonical perturbation theory. I can't currently see ...
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