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Questions tagged [celestial-mechanics]

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41
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4answers
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What did general relativity clarify about Mercury?

I frequently hear that Kepler, using his equations of orbital motion, could predict the orbits of all the planets to a high degree of accuracy -- except Mercury. I've heard that mercury's motion ...
43
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9answers
13k views

Why are $L_4$ and $L_5$ lagrangian points stable?

This diagram from wikipedia shows the gravitational potential energy of the sun-earth two body system, and demonstrates clearly the semi-stability of the $L_1$, $L_2$, and $L_3$ lagrangian points. The ...
5
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4answers
3k views

What causes matter to initially rotate/spin/orbit?

What causes matter to initially rotate/spin/orbit? All I can find is the statement that in space particles of dust/gas/matter contract into a spinning disk due to gravity (to form stars, solar systems,...
17
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3answers
6k views

Why is Larry Niven's Ringworld Unstable?

In his 1970 science fiction novel Ringworld, author Larry Niven describes the eponymous Ringworld, a gigantic structure shaped as a ring with a radius of around 1 AU, rotating around a star in the ...
23
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7answers
74k views

Gravity on the International Space Station

We created a table in my physics class which contained the strength of gravity on different planet and objects in space. At altitude 0 (Earth), the gravitational strength is 100%. On the Moon at ...
4
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1answer
250 views

How are the Lagrange points determined?

According to Hyper Physics, there are 5 equilibrium, or Lagrange points of the Earth-Moon system and only 2 of them are said to represent stable equilibrium points. This made me think if there is an ...
2
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1answer
877 views

What is the typical orbital life of an artificial satellite?

The orbit of satellites around Earth eventually decays, or so I read. This is typically caused either by atmospheric drag, or by tides. I would assume most satellites have a limited service life in ...
1
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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,...
8
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4answers
857 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 ...
53
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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 ...
40
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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 ...
23
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6answers
10k views

Why are the orbits of planets in the Solar System nearly circular?

Except for Mercury, the planets in the Solar System have very small eccentricities. Is this property special to the Solar System? Wikipedia states: Most exoplanets with orbital periods of 20 days ...
9
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5answers
2k views

How to learn celestial mechanics?

I'm a PhD student in math and am really excited about celestial mechanics. I was wondering if anyone could give me a roadmap for learning this subject. The amount of information about it on the ...
8
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3answers
2k views

Do the planets really orbit the Sun?

This is a duplicate of this question on Space Exploration.SE. So why would I ask it again here? Read below. The question reads We often say that the planets orbit the Sun, which is usually a ...
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 ...
4
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5answers
2k views

How gently could a comet/asteroid/meteorite “hit” Earth?

Could an object from outer-space with the right velocity and orbit come into contact with the surface of our planet in a manner that wouldn't cause it to burn in our atmosphere?
0
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1answer
528 views

Einstein field equations (EFE) $N$-body simulator

I made a $N$-body simulator and it works well, but it uses Newton's gravitational equation, which is nice, but I want it to simulate Einstein field equations. Speed of gravity should be simple enough, ...
11
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3answers
2k views

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 ...
8
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3answers
1k views

Are there planetary systems where the planes of orbits vary greatly?

Inspired by this question, are there any known planetary systems with largely varying planes of orbit? For example a system where two planets have perpendicular planes?
6
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2answers
906 views

How about an exact solution for the position of a planet as a function of time?

Recently I was surprised to discover that no exact solution for the position of a planet as a function of time exists. I am referring to the two-body problem in a gravitational field where Newtons law ...
3
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3answers
782 views

What is the distance between two objects in space as a function of time, considering only the force of gravity? [duplicate]

What is the distance between two objects in space as a function of time, considering only the force of gravity? To be specific, there are no other objects to be considered and the objects in question ...
2
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4answers
2k views

Satellite in Elliptical orbit

When finding the period of a satellite orbiting the earth we equate the centripetal force to the gravitational force $$\frac{mv^2}{r} = \frac{-GMm}{r^2}$$ If I understood well the $r$ cancels into ...
1
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1answer
106 views

Create a star system fit to conic equation

For simulation purposes, I'm trying to create a binary star system. If I have a conic equation such as $ax^2 + by^2 = c$, and the masses of two stars, how would I find the $x$- and $y$- velocity ...
10
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4answers
971 views

Collision of Phobos

Mars has two moons: Phobos and Deimos. Both are irregular and are believed to have been captured from the nearby asteroid belt. Phobos always shows the same face to Mars because of tidal forces ...
5
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4answers
4k views

Historically, how do we know that Earth moves around Sun? And it does so in an elliptical orbit?

I know the basics of solar system like how Earth moves around Sun, and that we have so many planets, elliptical orbit of earth, and how far is sun from earth etc etc. I want to take a step back and ...
3
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5answers
756 views

How did planets have an elliptical orbit in the first place? [duplicate]

I know that planets speed up when getting closer to the sun, but they speed up because they have an elliptical orbit, and they have an elliptical orbit because they speed up. Why did they have an ...
3
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1answer
930 views

Determine orbital position after change in velocity

I am working on a satellite simulator for a project/game and I am stuck on this one bit of physics. So far I have a satellite that revolves around earth on a 2D plane following Keplerian motion using ...
2
votes
1answer
518 views

Synchronized rotation of the moon

Does the moon rotates? Yes. The rotation matches exactly the orbit of the Earth. Which means in 28 days the moon makes one rotation. Shouldn't this be also happening with the Earth rotation around the ...
1
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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 ...
0
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0answers
453 views

3-body system centre of mass

I have a three body system of point masses that represent mercury, earth and the sun. I want them to orbit about a common centre of mass, but I think the centre of mass will move. I need the centre of ...
0
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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 ...
0
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1answer
149 views

Can a satellite remain directly over a city?

Is it possible to put an artificial satellite into an orbit in such a way that it will always remain direct over a city (I mean at any specific place)?
-1
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1answer
435 views

Why do the stars in a binary system, revolve diametrically opposite to each other?

I encountered this question, as I was reading up on Gravity. The author of my textbook says that the stars orbit a common centre which is their center of mass. I somehow think that this fact might ...
49
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4answers
6k views

How far ahead can we predict solar and lunar eclipses?

The solar system is non-integrable and has chaos. The sun-earth-moon three-body system might be chaotic. So, how far into the future can we predict solar eclipses and/or lunar eclipses? How about ...
10
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6answers
865 views

Extended object passing near an event horizon

Suppose a physically realistic object of nontrivial size (such as a star) free-falls past a black hole. The center-of-mass trajectory for the object is hyperbolic and (therefore) completely outside ...
12
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0answers
908 views

Why is the orbital resonance of the Galilean moons stable?

It is well known that the orbits of Ganymede, Europa and Io are in a 4:2:1 resonance. Most online sources (including but not limited to Wikipedia) say that such an orbital resonance, along with the 3:...
7
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3answers
1k views

Rocky Planet in the center of System [duplicate]

We all know that mostly stars are at the center of planetary systems, but is it possible that instead of a star there was a rocky planet in the center with stars (and other planets and moons) orbiting ...
7
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2answers
2k views

How did pre-Copernican astronomers accurately predict planetary position?

Copernican elements (circular orbital elements) are not very accurate. But Copernicus simplified our understanding a great deal by placing the Sun at the center of the system. Im astonished by the ...
4
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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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2answers
2k views

Hyper/parabolic Kepler orbits and “mean anomaly”

In an elliptical kepler orbit there is an easy recipe to describe the motion/position of a satellite at time $t$. One just follows the following steps - an important detail for me is that the ...
2
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3answers
243 views

Is it possible to have stable orbits around Lagrange point $L_1$?

Is it possible to have stable orbits around Lagrange point $L_1$? If yes, is there an upper limit to the mass of a body on such an orbit?
1
vote
1answer
515 views

Could this planetary superalignment happen?

Here's the 'superalignment' I'm referring to: We've all heard the stories about 'mystical planetary alignments' that will increase/decrease the effective surface gravity experienced on Earth (one ...
16
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7answers
5k views

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 ...
4
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5answers
1k views

Gravitation in a space that is topologically toroidal

In my scant spare time I'm building an Asteroids game. You know - a little ship equipped with a pea shooter and a bunch of asteroids floating around everywhere waiting to be to blown up. But, I wanted ...
4
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1answer
154 views

Kepler's first law; mathematical way of finding the eccentricity

We know that Kepler's first law of planetary motion is defined as: $$\text{r}=\frac{\text{p}}{1+\epsilon\cos\left(\theta\right)}\tag1$$ Now, for $\epsilon$ I have (see wikipedia): $$0\space<\...
7
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3answers
656 views

Why planets are orbiting only in one plane? [duplicate]

Since gravity is three dimensional why planets are orbiting only in one plane around sun.
5
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3answers
377 views

Elliptical orbit changing as a star's mass increases

I'm studying Kepler's Laws, specifically the orbit of the Earth around the Sun. I know that if the Earth was more massive, the orbit would not be significantly affected. If the Sun was more massive, I ...
3
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1answer
795 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
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 $R(t)$ = {$...