Questions tagged [celestial-mechanics]

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How to solve a general planet orbit differential equation? [on hold]

According to Newton's gravitation law, the following differential equation can be made $$\frac{d^{2}}{d t^{2}} \mathbf{x}{\left(t \right)} = - \frac{G M }{\left|{\mathbf{x}{\left(t \right)}}\right|^{...
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1answer
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Do all the planets in our solar system orbit the sun in the same direction and in the same plane?

Do all the planets in our solar system orbit the sun in the same direction and in the same plane? (as in a flat orbit if you are looking from "above")
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1answer
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Ever looming shadow

If I'm not mistaken the reason the moon eclipses the sun is because the ratio of distance to size, in regards to the moon and sun, is 1:1. And is it not also true that the reason we only ever see one ...
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1answer
43 views

Particle moving on ellpse with foci as origin

I'm reading the book "An introduction to Celestial Mechanics" by Forest Ray Moulton. In the first chapter, I got stuck on the following problem: A particle moves in the ellipse whose parameter and ...
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How to calculate orthogonal component of trajectory after pass through orbital plane of 2-body system

For an encounter between a stable 2-body system and a 3rd body which has sufficient velocity to escape after a pass through the orbital plane between these two objects, I am setting up the frame of ...
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1answer
33 views

Ptolemaic system parameters

I recently learned about the Ptolemaic system, which seems pretty accurate. There is even a simulator on the Internet: https://astro.unl.edu/naap/ssm/animations/ptolemaic.html You can see that there ...
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1answer
35 views

What is the relation between Earth's orbit and orbit of another planet around Sun? [closed]

Lately, I come across the following problem, "The maximum and minimum speeds of a comet that orbits the Sun are 80 and 10 km/s respectively. The ratio of the aphelion distance of the comet to the ...
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2answers
65 views

Which orbit planet will take with 2 stars?

Is there a law or an equation that shows which star gravity will win and suck a a planet that has 2 stars Assume planet P has 2 stars A & B A is smaller than B Planet P is closer to A more than ...
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1answer
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Mars longitude reference?

Platforms like NASA's JPL HORIZONS web-interface for solar system dynamics often have obtainable parameters like sub-solar or sub-terrestrial longitude for a given time and celestial object. (example: ...
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3answers
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Is there a maximum distance from a planet that a moon can orbit?

Given a planet that orbits a star, and a moon that orbits that planet, is it possible to define a maximum orbital radius of that moon, beyond which the moon would no longer orbit the planet, but the ...
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5answers
137 views

What is the reason for Moon and satellite in free fall condition?

I am a high school student. I read in my book that moon and satellite are in free fall condition with Earth. I asked my teachers about this, but I'm not able to understand. Can anyone explain to me ...
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Do SR account for one sixth or one third of the anomalous perihelion shift?

In answers to two other questions on this site: Mercury's Orbital Precession in Special Relativity and Do 2-body elliptic orbits precess in special relativity? it is stated that special ...
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Why are so few inclined circumbinary planets known?

For a research project I'm studying the orbits of circumbinary planets, most of these planets orbits are coplanar. However I was wondering if orbits with a high inclination could be stable. I made a ...
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2answers
248 views

The Earth revolves around the Sun or the Sun revolves around the Earth

Well, in today's world we know that the earth resolves around the sun. But that is seen from frame of reference of sun or an observer stationary wrt sun. From frame of reference of the earth, sun ...
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2answers
1k views

What are the forces behind the orbit of the Earth around the Sun?

Does the gravity of the sun alone affect the orbit of the earth around the sun? Look at the image below,(Image is not to scale), Is it that when earth is going from position 1 to position 2, it ...
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2answers
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Revolution of Earth around the Sun

We study the orbit of many planets around the sun modelling it as a uniform circular motion. Is this due to the fact that empirically we measured that the magnitude of the earth's velocity (for ...
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7answers
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Why does the Earth follow an elliptical trajectory rather than a parabolic one?

I was taught that when the acceleration experienced by a body is constant, that body follows a parabolic curve. This seems logical because constant acceleration means velocity that is linear and ...
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43 views

How did most of the math and physics formulae that govern our lifestyle and help us in space exploration come into being? [closed]

I realise that this isn't a very academic question, but after watching movies like First Man and Interstellar, it got me wondering: How did all these formulas that we use on a regular basis come into ...
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5answers
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Kepler's 3rd law: ratios don't fit data

I have been looking at satellite orbits around the earth, or any object around any planet in fact, and am trying to find the orbital radius, or semi major length of a given satellite. Kepler's third ...
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1answer
36 views

About Kepler's laws [closed]

Yesterday I was reviewing some calculations using Kepler's laws and when working the third law that relates orbital periods and distances, it is very normal that, given the parameters of some object ...
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2answers
53 views

How to find Lagrange point $L_2$ of the Earth-Moon system?

I was tasked in my programming lesson to find a value of L1 correct to 5 significant figures, but in my discussion section I began to wonder why there was no second solution to the equation I was ...
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1answer
75 views

Two bodies orbiting around common barycenter

Assume $2$ bodies of mass $M_1$ and $M_2$ orbiting in a plane around their common barycenter $G$. It means the axis $(M_1M_2)$ is rotating in the plane around a vertical axis through $G$. [Please ...
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Why do planets revolve around Sun in elliptical orbits? [duplicate]

Let’s consider two planets of mass $m$ and $M$. They both will attract one another with a constant force $F$ according to the law of attraction $F=G m M/r^2$. The force and masses are constant. $G$ is ...
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1answer
66 views

Two-body problem - point of closest approach

I am reading through an exercise : One of the hints to solve this problem is that at the point of closest approach the comet's velocity must be tangential only, why is this the case ?
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3answers
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Radius of the Sun

Is it possible to calculate the radius of the sun with minimal amount of physics? I couldn’t find resources on the internet that gives me an answer using a theoretical formula. You are given values ...
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1answer
52 views

Is there any model explaining why would a particle revolve around another one in an elliptical orbit? [duplicate]

The reason for asking this question is to understand the elliptical orbits of planets and why aren't they circular, we know that if a particle moves with an initial velocity perpendicular to the ...
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1answer
46 views

How was the equation for a gravitational assist derived?

Im currently writing a paper about a hypothetical probe meant to escape our solar system and I want to analyse how gravitational assists would be beneficial for its mission. I found a website with an ...
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2answers
62 views

What's the nicest proof that two isolates masses orbit their center of mass? [duplicate]

Although it seems intuitive, I haven't found proof of this fact in my textbooks from a purely mathematical standpoint. I was wondering if anybody knows of a particularly elegant proof of this fact, ...
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1answer
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Why doesn't the Earth slowly collapse into the Sun? [duplicate]

I understand that the sun exerts a force on the earth and that if that was the only force exerted on the earth then the earth would have already crashed into the sun a long time ago. The reason the ...
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2answers
62 views

How come planets with different masses can orbit at the same velocity at the same altitudes?

Angular momentum is equal to r × p and angular momentum is also what gives planets with lower orbits a higher speed (because angular momentum is conserved). So as r decreases either m or v (p=mv) has ...
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2answers
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How can I determine a planet's mass based only off of information about its orbit and its parent star?

I'm coding a video game with procedurally generated planetary systems and I want some and I want to make sure I'm at least somewhat scientifically correct. I've reached the part in my code where I ...
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4answers
151 views

Kepler's third law is unintuitive

Kepler's third law states that the ratio between the period of a planet in orbit round a star squared over the average distance to that star cubed, is constant. And in the case of an elliptical orbit, ...
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1answer
70 views

Two black holes colliding (classical mechanics)

I had this question come up in my exam where two identical black holes are in orbit around each other. There is a loss of energy via gravitational waves : $$\frac{d E}{d t} = kr^4\omega^6$$ where $k$ ...
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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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3answers
266 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
63 views

Mass distributions within two bodies such that the orbit is no longer Keplerian?

The trajectories of two point masses or spherically symmetric masses with respect to their center of mass are conic sections or Kepler orbits. Consider that the bodies have finite size with respect ...
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2answers
88 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 ...
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1answer
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'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
18 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
66 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 ...
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2answers
98 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
34 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
106 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
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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 ...
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1answer
73 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
34 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 ...
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1answer
44 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 ...
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0answers
45 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 ...
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1answer
110 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
167 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\...