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Questions tagged [celestial-mechanics]

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23 views

Horseshoe orbit cycle times

I asked on Worldbuilding originally, but was directed here instead I've been working on a habitable moon system for a story, and I'm now trying to populate the other moons around the parent planet. ...
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0answers
16 views

Motion under central force: the contribution of evenly distributed “dust” [on hold]

A solar system that is consisted of a star with mass $M$ and a planet with mass $m$ ($m<<M$) is in a cloud of evenly distributed "dust". From Gauss' Law it can be showed that the dust will ...
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3answers
127 views

Why does angular momentum being constant prove Kepler's first law?

So I was watching this video and this video on Kepler's first law in order to understand the proof of Kepler's first law. He started off by saying that for an ellipse, the distance from a focus point ...
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0answers
23 views

Force of gravity [duplicate]

I want to know why isn't the moon fall on earth instead of floating on top or going around the earth without even falling on earth by the force of gravity on earth .
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0answers
30 views

Constraints on the mass distribution within each body such that their mutual orbits are Keplerian?

The trajectories of two point masses with respect to their center of mass are conic sections or Kepler orbits. But what if the bodies have finite size with respect to their separation, and not ...
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1answer
42 views

On Planets orbiting binary stars

Several years ago a discovery was made of planet orbiting a star of a binary system (two stars orbiting each other). Since binary star systems are plentiful in our galaxy, I presume we will be ...
2
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1answer
77 views

'Harmony of the Spheres' or 'Harmony of the World' - is it debunked? [closed]

I sincerely apologise for this vague question but I'm writing an essay for my music class on musical harmony and it's historical origins. I came across the Pythagorean notion of Harmony of the Spheres ...
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2answers
15 views

What is meant by “instantaneously aligned” with regards to rotating reference frames/coordinate axes?

I'm trying to understand a set of lecture notes I found online from MIT which describe the derivation of the equations of motion for an object in a rotating reference frame, this is for an essay on ...
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1answer
58 views

What is the second $r$ in this equation for the Two Body Problem?

$$r=\frac{r^2\frac{\mathrm d\theta^2}{\mathrm dt}}{\frac{Gm_2^3}{\left(m_1+m_2\right)^2}\left(1+e\cos\theta\right)}$$ I have this equation for the radial distance of a planet from the barycenter. But ...
2
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2answers
85 views

Mass versus rotation Curves

Is there an equation that describes the relationship between the mass of the Galaxy and rotation curve? I found V versus R graphs and equations that describe their relationship (kind of). But I ...
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0answers
26 views

Restricted 3-body problem - Rotating coordinate system

I'm trying to follow the formulation of the restricted 3-body problem in Taff's "Celestial Mechanics" book as I'm writing an essay on Lagrange points and am confused by the transformation into the ...
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5answers
99 views

What is holding things like the Earth and the Sun in one dimension?

I was thinking last night: for most of my life I’ve been taught that the planets in our solar system orbit the Sun, which insinuates that the Sun is in a fixed point in 3-dimensional space, and that ...
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1answer
24 views

Barycenter of a binary star system

It is said that the barycenter of 11 Draconis (Thuban) and 10 Draconis which compose a binary star system is a central point. Is this central point a material or immaterial object? Does the size of ...
2
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1answer
58 views

Why do the orbit equations have to be symmetric about two axes even the orbit is not bounded?

In the book of Classical Mechanics by Goldstein, at page 88, it is given that However, the orbit might not be bounded, so there might not be two turning point; just one. In such a case, how can we ...
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1answer
24 views

The shape characteristics of gravitational wells given different masses and spread of objects

I am curious as to research that calculates the shape of gravitational wells, and their limits, and affect on time, for different masses and spread of mass. The actual question is st the end. For ...
2
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1answer
40 views

Solar System Position and Velocity data

I'm trying to create an nbody simulator and to test it I'd like some real world data. A good test would be the solar system. I've come across the JPL Horizons software but if cant seem to figure out ...
3
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0answers
39 views

A question about almost stationary orbits

For an orbit around the earth with period equal to a sidereal day with eccentricity $e=0$ and inclination $i=0$, the path on earth would be a single point on the equator. I have done some simulations ...
2
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1answer
103 views

Why is ʻOumuamua traveling so slowly?

Imagine a space rock that starts at rest at the Lagrange point between the sun and our nearest stellar neighbor, Alpha Centauri. That would put it at about 2 light years away from the sun. Now, it ...
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2answers
119 views

Is the geodesic equation independent of an initial condition?

The following argument is used to determine the unknown factors (e.g., $A(r)$ and $B(r)$) in the Schwarzschild metric. $$ \lim_{r \to ∞}A(r) = \lim_{r \to ∞}B(r) = 1 \space\space\space\space\space\...
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1answer
31 views

Can we ever calculate the exact period and semi-major axis for an orbit with strong perihelion precession?

To calculate the period of an orbit with strong perihelion precession we could just pick an arbitrary point in the sky, and time how long it takes for it to pass it again. But wouldn't we get ...
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1answer
27 views

Can a planet have multiple significant sized moons?

The Earth has one moon at about 1/80 of Earth's mass. Is it possible to have two moons large enough each to subtend a >30 minute disk as viewed from the surface? I have tried with various ...
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2answers
88 views

How do astronomers explain trajectories of planets?

I'm wondering how astronomers can explain the trajectories of planets because: planets spin, so have angular kinetic energy. Thanks to the mass-energy relationship this means space-time curvature. ...
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1answer
43 views

Confirmation / interpretation of unphysical(?) Kepler orbits

The following two pictures show the Kepler orbit of two masses $m_1, m_2$, where $m_1/m_2=7/3$, as I calculated them using $$ r(\varphi)=\frac{a(1-\varepsilon^2)}{1+\varepsilon\cos\varphi},\quad\...
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2answers
57 views

Centripetal Acceleration to find Orbital Velocity

When presented with a problem asking for the orbital velocity of an object $1,000 km$ above the Earth's surface, the formula I know you can use is $$v=\sqrt{\frac{G*m}{r}}$$ However, I was thinking ...
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5answers
516 views

What is $R$ in the formula for escape velocity?

From the escape velocity formula $$v_e = \sqrt \frac {2GM}R.$$ Some sources say it is the distance between two objects with mass $M$ and $m$. Some examples I have read, only used radius of the $M$. ...
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3answers
182 views

Why is angular momentum of the Earth/Moon system conserved?

Why is the angular momentum of the Earth/Moon system conserved, apparently unaffected by external forces such as force of the Sun?
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3answers
117 views

Why should the trick solution to the problem of how long it takes to fall into the sun work?

There is a famous problem which asks: Suppose an object is held at 1 au from the Sun and released from rest. How long does it take to fall into the Sun (neglecting the size of the sun)? The trick ...
0
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4answers
108 views

How to find angle something turns as it orbits in orbital mechanics? [closed]

Short version: Take a look at this animation really quick. https://commons.wikimedia.org/wiki/File:Orbital_motion.gif The direction in which the arrows for $\alpha$ and $\nu$ is adjusted as the ...
2
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1answer
61 views

Kepler's Second Law: Why do we calculate the area of a triangle rather than the area of a sector?

Kepler's Second Law states that equal areas are swept in equal times. When calculating this area, why do we use the formula for the area of a triangle rather than the area of a sector?
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1answer
72 views

Is a complex Keplerian eccentricity $e=\sqrt{1+\frac{2\varepsilon h^2}{\mu^2}}$ possible?

Wikipedia provides the following formula for the Keplerian orbital eccentricity: $$e=\sqrt{1+\frac{2\varepsilon h^2}{\mu^2}}$$ Considering that a bound object means negative energy, if the magnitude ...
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2answers
87 views

So, DO All Things Float In Space, Or Not?

Incredibly, I cannot find an answer to this anywhere. The experts say that planets etc don't actually float in space, but instead continuously 'freefall' around the object they're orbiting and so on. ...
2
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1answer
52 views

Lagrange points and gravity

I have just found an article talking about the L1 to L5 equilibrium positions of gravitation around stars, planets, etc. As far as I could learn from this website and other research I have done the ...
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2answers
50 views

Can Kepler's laws apply for circular motions?

Can Kepler's laws apply for circular motions? (First law states planets take an elliptical orbit)
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3answers
50 views

Energy of a planet moving around the Sun

In chapter 13 of volume 1 of The Feynman Lectures, Feynman is discussing how the work done in going around any path in a gravitational field is zero. Here's the link: http://www.feynmanlectures....
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2answers
69 views

Parker Solar Probe top speed

All the news articles say it'll orbit the sun at 430,000 mph. How do they get that? It seems too low. Isn't orbital velocity proportional to $1/\sqrt{r}$? Parker will be 4 million miles above the "...
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0answers
37 views

Angular momentum in Rotating Frame for satellites

I am working on satellite orbit propagator, I am propagating the satellite position and velocity in the inertial and rotating frames. To validate my propagator, I am checking the angular momentum and ...
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2answers
23 views

How can I calculate the ratio of distance between 2 longitudes at different latitudes?

Suppose i have to calculate the ratio of lengths of AB and CD where A(0° N,0° E) and B(0°N,30° E), and C(30°N,0°E) and D(30°N,30° E) the values are just as an example.Is it possible to get the ratio ...
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0answers
12 views

celestial coordinates, elliptic plane

When looking up earth orbital elements often I see non zero inclination which seem odd because earth orbit is reference so should be zero. Now I guess for mean orbital elements which give elements to ...
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1answer
50 views

What would happen to the Moon if the Earth stopped providing it with a centripetal force owing to its force of gravity?

Would the Moon really only travel in a straight line then? What about the other planets and their forces of gravity? Wouldn't they prevent this rectilinear and undisturbed motion of the Moon?
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1answer
56 views

Good sources to get velocity/position vectors for all planets and moons in the Solar System for building an orbital simulator?

I’m building an $N$-body simulator, and I have everything ready to begin simulating. But my issue is is that I have no idea how to get all the starting positions and velocities for the celestial ...
0
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1answer
52 views

Earth's movement around the Sun

My question is - because of sun's movement around the milky way, Earth never reaches at the same point where it started from. Then how can we say that it circles around the sun in 365 1/4th days.
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2answers
3k views

If the 3-Body force problem hasn't been solved, how do rocket scientists plan orbits of spacecraft?

What methods would they use to predict what would happen in a situation when a probe is being acted upon by the gravity of two stars, say?
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3answers
185 views

Computerised Solar System Simulation [closed]

In school I am doing a project where using python I simulate the solar system The physics I know so far is newtons laws and Kepler’s laws and I have done a lot of research but there appears to be ...
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1answer
58 views

Barycentre of two planets and calculating velocity shift

I find my self puzzled by this question, and I cant see anything wrong with my derivation, which leads me to believe that there is something I am missing within how the velocity shift is calculated. I ...
0
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1answer
40 views

How to understand $L_4$ and $L_5$ Lagrange points gravity balance? [duplicate]

It's relative easy to understand gravity balance of Lagrange points $L_1$, $L_2$ and $L_3$. But I am having a hard time to understand how a body would be "kind of" balanced out on Lagrange points $L_4$...
2
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2answers
121 views

Total angular momentum of a planet orbiting a star [duplicate]

Would the total angular momentum of a planet orbiting a star while rotating on it's axis be the sum of the orbital rotational momentum and the rotational momentum about it's axis?
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0answers
64 views

Planar Precession Frequency of Orbit

What is the general relation between orbital precession $\Phi$, orbital frequency $\Omega$ and a radial perturbation frequency $\omega$? For certain cases the answer is "clear", for example: 1) If $\...
3
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1answer
188 views

Feynman's Lost Lecture: what is the significance of $\frac{d\mathfrak{v}}{d\theta}=-\frac{GMm}{\left|\mathfrak{L}\right|}\hat{\mathfrak{r}}?$

My question pertains to a fact used by Richard Feynman in his so-called Lost Lecture. http://books.wwnorton.com/books/Feynmans-Lost-Lecture/. I have only skimmed the book, so I have much more to learn ...
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1answer
47 views

Spirals in newtonian celestial mechanics?

I know Kepler's laws, Newton's laws, and that conic sections are the trajectories of noncolliding two point masses. But I wonder about a point mass A eventually colliding with point mass B. In ...
74
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2answers
10k views

Can an atom orbit the Sun?

Is it possible for a molecule or atom to orbit a star (e.g. the Sun)? Or is there always too much outward force imparted by solar radiation compared to the inward force of gravitational attraction?