Questions tagged [celestial-mechanics]

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2answers
101 views

Angular momentum for planet is constant [closed]

In this excersie we look at the system of the dwarf star Gliese 536. Gliese 536 is 10 Parsec away and has half the mass of the sun. (I guess, they mean our sun). There are hints, that there a so ...
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1answer
71 views

Orbit of stars in a galaxy

Do all stars orbit around the galactic center? If yes what makes them orbit around the center , what object creates such a massive force which makes stars millions of light years far away from the ...
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0answers
83 views

Stability of solar system

As far as I understand, the stability of the Solar system means that planets do not collide and will not in near future. The only thing that is stated on Wikipedia is that scientists are concerned ...
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1answer
98 views

Upper limit of gravity

Now I don't mean maximum gravity because there is no maximum gravity. What I mean is what is the escape distance? In other words, how far would I have to be from a mass to get away from its gravity? ...
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0answers
31 views

Gravity assisting [duplicate]

I watched Passengers movie yesterday. There was one detail which stroke my eye. Does it really make sense to use gravity assisting for interstellar travel? I'd imagine that the spaceship would have ...
2
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1answer
122 views

Gravitational $n$-body problem with tidal forces

This year I'm working on modelling the gravitational $n$-body problem using Newton's law of gravity where I assume that for large enough distances, planetary bodies can be modelled as point masses. ...
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4answers
82 views

Do planets on other star systems form ellipse orbits like in our solar system?

In solar system we have all planets roughly on the same plane. Is it true for all of the star systems (or at least for those that we have observed so far) with multiple planets in our galaxy/other ...
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1answer
93 views

Shape of planetary orbits

What makes Venus' orbit almost circular, though mercury's is highly elliptical,even though it is closer to sun ? Further, Why is mercury's orbit most elliptical right after Pluto ?
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2answers
692 views

Motion of planets: inverse square law

If a body is acted on by a force which obeys the inverse square law, will it mean the body follows an ellipse, if so, equating Newton's law of universal gravitation $(f=(GMm/(r^2)))$ to centripetal ...
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1answer
191 views

Voyager Speed After Launch

I am learning about gravity assist. Therefore I am interested in the flight of voyager 2. i found this diagram from Wikipedia and I have trouble understanding the massive acceleration of voyager after ...
2
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0answers
417 views

Proof of unsolvability of $n$-body problem for $n\geqslant 3$ in general

We know there are general solutions for 1-body problem and 2-body problem and also we know in some "special cases" there are some possible solutions for $n$-body problem for $n \geqslant 3$ and there ...
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1answer
163 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 ...
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1answer
121 views

Kepler's 3rd law/law of periods

Kepler's 3rd law of planetary motion is The square of the time period of a planet orbiting a sun is proportional to the cube of the semi major axis of the elliptical orbit. $$(T_1)^2   =   (A_1)^...
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1answer
3k views

Does the orbital radius include the radius of the two objects?

I am trying to find the force using $F=Gm_1m_2/r^2$ and the answers do not include the radius of the two objects just the "orbital radius." So does this mean the orbital radius includes the radius of ...
6
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1answer
1k views

Kepler's third law for binary systems

We all know that Kepler's third law for a system of two bodies which one of them have much greater mass than the the other is like this: $\frac{{T_B}^2}{{a_B}^3}=\frac{4\pi ^2}{Gm_A}\;\;\;\;(m_A\gg ...
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1answer
158 views

Lagrange points (regions) for $n$-body systems

The title may be a bit misleading. They may not be points (small areas) at all in this case, but extended regions. Mathematically speaking: Consider the origin for measurements at $O$. Let $R(t)$ = {$...
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0answers
56 views

Plausibility of a Dyson sphere [duplicate]

So Dyson spheres are generally considered implausible for two main reasons. One, it would an incredible amount (and type) of resources to build one. And two, a Dyson sphere would be unstable because ...
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1answer
78 views

What caused the Moon's initial inertia?

I.e. if we removed the Earth the Moon would keep moving in a straight line if there was no Sun (question edited based on correction below). What was the source of the original force or push which ...
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4answers
2k views

If we were on the Moon would Earth appear to be in motion or at rest?

If we were on the moon would earth appear stationary or would it appear to move. I think it must be stationary because moon is in sychronous rotation with earth.
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2answers
176 views

Points in space where the gravitational force due to two bodies are equal in magnitude

Consider a two body system say the earth with mass $M$ and the moon with mass $m$ and distance $d$ between them. Thus there is a point in space between the earth and the moon where the force of ...
4
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1answer
101 views

Moon's orbital plane inclination causes Moon to fall

I read somewhere that if Moon's orbital plane would be perpendicular to the Earth's orbital plane - Moon will fall on Earth within 4 years (given today's position) Can this be shown analytically ...
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4answers
706 views

Why do Moon have different shapes/phases on the night sky but Sun doesn't?

We know that each day the shapes/phases of the Moon differs from its previous day and it is periodic with a period of 29 days. So, why it isn't the case in Sun? Or why do we have these different ...
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2answers
168 views

Question about elliptical orbits

For two bodies attracting to each other, we use the reduced mass and distance between them (r) to solve the equation of motion. The final result is an elliptical obit under certain conditions. My ...
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1answer
114 views

Mass And Gravity (Gravity between Moon and Earth) [closed]

Well I'm still a beginner at the gravity between huge masses ... and the gravity of masses So what i have learned for now is Kepler's 3 laws , and the equations that i have learned are these $${T^...
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1answer
53 views

Another Solar System and its physics

Stick with me on this one, This is purely fictional, and curiosity. Say we travel to another solar system we know nothing about. We land on another habitable planet. We don't know the mass of any ...
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1answer
3k views

If two stars of mass $M$ and $2M$ move about their common centre of mass, then they have same angular velocity [duplicate]

Two stars of masses $M$ and $2M$ move in circular motion about their common centre of mass. Which of the following statements is true? A. Both stars move with the same radius. B. Both ...
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1answer
72 views

Is it possible to find the mass of a planet and its moon from only their diameter and the distance between them?

For example, a planet has a diameter of 200,000 km and its moon has a diameter of 20,000 km, the distance between them is 100,000 km. Would it be possible to find their masses?
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34 views

Translationally invariant speed distribution

During impact events, asteroids et al strike Earth at high relative speed, in part because objects in space move in random directions with no preferred reference frame with respect to which objects ...
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1answer
874 views

Calculating Centripetal Acceleration of Sun about Galaxy [closed]

This is a question from my Mechanics book: Calculate the centripetal acceleration relative to the acceleration due to gravity of: c) the Sun in its rotation about the center of the galaxy (the ...
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0answers
157 views

Why is our solar systems co-planar? [duplicate]

Even though moon and satellite orbit the planets in multiple planes why our solar system is co-planar? Not only that, ring systems of several planets are also co-planar. Is it the way they evolved ...
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2answers
46 views

Why do the Lagrange points lie only on the orbital plane of the two co-rotating bodies?

I could not find a detailed explanation of the fact that Lagrange points lie only on the orbital plane of the 2 co-rotating bodies. As per the wikipedia page calculations are here. There is no ...
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1answer
81 views

What is the minimum possible size for an asteroid to be able to alter Earth's orbit? [closed]

Obviously, the question as posed in the title is very incomplete. Allow me to rephrase it in more specific terms: What are the minimum possible "combined parameters" (velocity, mass, angle of ...
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1answer
127 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) ...
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2answers
776 views

Retrograde motion explanation

When taking a heliocentric model and following both Earth and Mars' orbits, Mars is in retrograde motion with respect to Earth only in the short period during which Earth is overtaking Mars. Why doesn'...
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2answers
141 views

Throwing a stone from satellite toward a planet

If I'm in a satellite which is moving in circular orbit of radius $r$ around a planet which has no atmosphere, means no air friction. And if I throw a stone from satellite toward planet then it's ...
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0answers
49 views

2D N-BODY SOFTWARE

When I had a Mac back at JPL in the 80's, I had software that allowed me to enter the mass and X, Y velocity vectors for a number of bodies. It was fun to play with. Is there anything like that out ...
2
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1answer
539 views

Form of acceleration for motion in an ellipse [closed]

I came across the following question: The coordinates of a particle moving in a plane are given by $x(t)=a\cos(pt)$ and $y(t)=b\sin(pt)$, where $a>b$ and $a$ and $b$ are positive constants of ...
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1answer
431 views

Orbital mechanics : finding eccentricity and semi-major axis

i have a problem. we have a elliptical orbit. Velocities of perigee point and apogee point is given. I have to find the eccentricity and semi major axis. I found eccentricty with conservation of ...
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3answers
267 views

Would it be possible to pull Mars and Earth closer each other?

The burden of travelling between Mars and Earth comes from the distance. If the planets were closer, life could spread to Mars more easily, ensuring the survival of the intelligent lifeforms. What ...
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2answers
161 views

What kind of effect would cosmic expansion have on planetary motion or keplerian orbit? [duplicate]

The question is, if two following phenomena are thought to effect to the motion of the planet that orbits a star: Celestial body is pulled by some massive star by ordinary Newtonian gravity: $$ m \...
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3answers
660 views

How to calculate transit time for a specific section of an orbit?

I've searched high and low and I haven't been able to find a formula for this. I'm trying to calculate the time it will take to transit through a defined arc length of an elliptical orbit, whose ...
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2answers
191 views

Total Linear Momentum Conserved for Earth-Sun System? [closed]

According to 'Introductory Astronomy and Astrophysics' by Smith and Jacobs the total linear momentum of an isolated system is constant which they choose as zero, so they get (mv)1 = (mv)2. When I ...
3
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1answer
87 views

How can an asteroid fall to a planet?

According to the Kepler's first law, the orbit of an asteroid would be an ellipse having the planet at one of the focuses (to a good approximation). Then how come can it ever fall to the planet?
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5answers
10k views

What does the Moon's orbit around the Sun look like?

I'm curious as to what the Moon's orbit around the Sun looks like. If there's an answer, what's the intuition for it? Here are some things I'm assuming when trying to tackle this question: The Moon's ...
3
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2answers
221 views

How deep does a gravity well need to be to remove particles from a planetary body?

I almost considered asking this question on WorldBuilding, however I wanted the brute mathematics on the subject, so please excuse the theoretical nature of this question. I understand the basic ...
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0answers
35 views

How can I measure the stability of a many body gravitational system?

Suppose I have an N body planetary system interacting via gravity. Suppose I know the positions and momenta at t=0. How do I know if this system is stable (indefinitely)? By stable I mean the ...
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1answer
101 views

Stability of the classical helium atom

Let us forget about quantum mechanics and confine ourselves to classical mechanics. The Hamiltonian for a classical helium atom would be $$ H = \frac{p_1^2 + p_2^2}{2m } - \frac{Z}{r_1} - \frac{Z}{...
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3answers
252 views

Orbits for dummies [duplicate]

In a certain universe a perfectly spherical, uniformly dense planet is found to be in a stable orbit around a stable star. The rest of the universe is empty space with no silly stuff like dark matter. ...
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1answer
60 views

Would a celestial body in a horseshoe orbit be tidally locked to the planet?

A smaller celestial body like a moon or an asteroid can be in a horseshoe orbit around a planet. Since it might go inside the tidal lock radius (but does not stay inside it all the time), during the ...
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2answers
562 views

Which timestep should I use for a $N$-body simulation of the Solar system?

I am trying to implement a $N$-body simulation of the Solar system and I am stuck on the issue of the simulation timestep size. At first I would like to use a simple Euler stepping scheme. Knowing ...