Questions tagged [celestial-mechanics]

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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 ...
7
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3answers
332 views

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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5answers
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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 ...
3
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2answers
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Orbital period and nodal precession & apsidal precession

In classical orbital mechanics as per Newton/Kepler, the time taken to complete one orbit around a body of mass $M_e$ is: $$ T = 2 \pi \cdot \sqrt { \frac {a^3} {G \cdot M_e} } $$ But also, for ...
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1answer
259 views

Geocentric Ecliptic to Perifocal Coordinate Transformation

I'm self-studying elementary orbital mechanics and am experimenting with transforming satellite position and velocity vectors between different coordinate systems. I know there are coordinate ...
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0answers
39 views

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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3answers
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Why do orbital speeds decrease further away from the focus?

Why do orbital speeds decrease further away from the focus? A simple question, but I want to make sure I am understanding this correctly: Is it ONLY a function of the gravity well? As in, the ...
2
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2answers
157 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
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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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6answers
18k views

Why the center of our galaxy doesn't absorb us?

Depending on the theories, the center of our galaxy is a super massive black hole, this is easy to accept as a truth, but what I couldn't simply devour is how the solar system is orbiting around it ...
3
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3answers
216 views

Since the Earth orbits the Galaxy, why doesn't it “fly away” from astronauts?

It is known that the Sun (and thereby all the planets in our Solar System) orbit the center of our galaxy at roughly 1 million miles per hour. From our point of view on Earth, everything looks ...
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2answers
71 views

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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1answer
728 views

Is there any free open source planetary orbit simulator software?

I need a free open source planetary orbit simulator software that should be able to calculate orbit stability for a couple simple planetary systems. Basically, I need to calculate orbit durations for ...
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0answers
42 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 ...
8
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4answers
861 views

What is the origin of spin of celestial objects?

In an older question from June 2011, Why does each celestial object spin on its own axis?, apparently revived by the system, a user is asking about the origin of the rotation of celestial bodies. The ...
0
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1answer
357 views

How do I use Kepler's Laws to propagate an orbit for a Two-Line Element (TLE) Set?

I need to propagate a large number of orbits (get a satellite's position at a certain time) from TLEs (two-line element sets) using Kepler's laws. Ordinarily I'd use a real propagator like SGP4/SDP4, ...
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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
34 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
47 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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8answers
8k views

“Falling upward” - how far you have to be from Earth to start falling to the Moon?

Talking about gravity with my 9 y/o she asked when do we start "falling upward" to the Moon. What is the distance at which the Moon's gravitational attraction is higher than that of the Earth and thus ...
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1answer
74 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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3answers
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Gravitational slingshot maximum

I have recently read an article about gravitation slingshot assist used by Voyagers 1-2, and was thinking on why this hasn't been used for travel between solar and other systems. I mean sligshot can ...
2
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1answer
942 views

Determing Velocity of Moons

I have a question that I believe is relatively easy to answer, I am working on an $N$-body simulation of a fictional star system and am having trouble finding the velocity of moons so that they will ...
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2answers
51 views

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
119 views

Velocity in different time frames

A satellite orbiting the earth experiences time faster than a person on earth as its in a weaker gravitational field (which has a greater effect than the slowing down of time caused by its motion) ...
0
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1answer
65 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
317 views

Calculating speed of satellite in vacuum?

Satellite speed is $35\ \mathrm{km/s}$ after burn for $500\ \mathrm{ sec}$ and after some days or months this speed is reduced automatically $34$, $33$, $32$ respectively. Questions: How the ...
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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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3answers
78 views

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 ...
0
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1answer
51 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 ...
0
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1answer
44 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 ...
3
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1answer
154 views

Gravity assist, Coordinate system transformation

I am currently learning about the physics and the mathmatics behind gravity assist. I have a question regarding the coordinate transformation between the planet frame and the sun frame. I want to ...
0
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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
76 views

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 ...
2
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2answers
60 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 ...
2
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2answers
38 views

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 ...
2
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4answers
145 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, ...
1
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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 $k$ ...
2
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0answers
54 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. ...
0
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1answer
232 views

Earth, Sun and beginner's reference frames

In the post-Newton era, where "absolute space" is not absolute, how is the reference frame in which "the Earth moves round the Sun" accurately defined?
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3answers
225 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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1answer
7k views

What is the relationship between mass, speed and distance of a planet orbiting the sun?

After reading this fascinating story about a new exoplanet, I was wondering about how mass, speed and distance determine a circular orbit of a planet around a star. Given the mass of the sun and star,...
2
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2answers
211 views

Multiple star system, stable orbits?

Inspired by worldbuilding SE, I know that there are relatively stable star systems with two or three suns, but any more than that and they start to become very unstable (e.g. trapezium systems), but I'...
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1answer
67 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 ...
3
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1answer
798 views

Can a very small portion of an ellipse be a parabola?

We can show that when a particle is projected from a certain height (from the surface of the Earth) with a speed lesser than the orbital speed and in a direction tangential to the surface of the Earth ...
2
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1answer
87 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
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
163 views

Elliptic Orbit Solution based on initial conditions

$$\ddot{\bf{r}}=-\frac{\bf{r}}{|r|}\frac{k}{|r|^2}$$ $k$ here is a constant dependent on the gravitational constant, and the masses of the two objects. If I transform it into cartesian coordinates: $...
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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 ...