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2answers
122 views

Orbital mechanics problem

Here is a problem from the 2009 $F=ma$ contest on orbital mechanics: Two stars, one of mass $M$, the other of mass $3M$, orbit their common center of mass. When the stars are collinear with the ...
2
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2answers
111 views

Can the epicycles of the geocentric model of the solar system be dismissed due to the laws of physics?

With enough epicycles, the motions of the planets can be accounted for in a geocentric model, but do the laws of gravity make such motions impossible? Did Newton's laws not only provide a simpler ...
1
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0answers
105 views

Reduced Three-body problem

I know that three-body problem in celestial mechanics can't be solved analytically in general. But suppose that the 3rd body is much smaller than the others, so it does not perturb their orbits. This ...
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1answer
59 views

What is the ultimate “goal” of two particles in a gravitational field? [closed]

What is the ultimate "goal" of two particles in a gravitational field? Will the particles eventually occupy the same point at the same time if nothing stops them? What stops them from achieving the ...
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1answer
79 views

Earth-Sun Lagrange points L4/L5 existence

Why do Lagrange points L4 and L5 exist at all? Consider the mass of Jupiter equals 320 Earth masses, and distance from Lagrange point to Jupiter is about 4-6 A.U. We get that the gravity of Jupiter ...
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1answer
181 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 ...
4
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2answers
717 views

Why is the Milky Way flat? [duplicate]

I read recently that the galactic "flatness" of the Milky Way is due to the rotation of the galaxy combined with a vast stretch of time. Yet, I also read where 1) the Milky Way rotates once every 225 ...
0
votes
1answer
267 views

My python trajectory calculator for a small mass in a gravitational field - why is energy conservation violated?

I wrote this thing to calculate the next position of a small mass, given its current position and velocity, and a vector field determines acceleration. It sort of works - except I can never get the ...
2
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1answer
116 views

Tidal locking of a planet to a satellite

As in the case of Pluto and its moon Charon, both the bodies are tidally locked to each other, will the Earth ever be tidally locked to the Moon? Is there any effect on the rotation of the Earth ...
2
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0answers
71 views

What is the difference between Saddle points and Lagrangian points between Earth and the Sun?

I am studying MOND bubble effects in the Solar System (Paper). In "mond habitats.." (last reference) first page, the author says MOND bubbles reside on the saddle points but I fail to understand the ...
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2answers
150 views

Calculating the velocity of an elliptical orbit

I need an explanation as to why my solution to this problem doesn't work (please do not give me an answer or tell me exactly how to do it as this is a homework question that I need to do myself, hints ...
1
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2answers
67 views

What is the zero of potential?

A satellite of mass $m$ is travelling at a speed $v_0$ in a circular orbit of radius $r_0$ around a fixed mass at $O$. Taking the zero of potential at $r=\infty$, show that the total energy of the ...
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2answers
232 views

What would Earth have been without the Moon?

Would Earth rotation have been more slowed down because of the tidal effect from the Sun, as seems to be the case with Mercury and Venus? Due to the giant impact hypothesis the angular momentum from ...
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1answer
36 views

Reg position of satellite

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)?
0
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2answers
517 views

How does the Moon stay in orbit?

How does the Moon stay in orbit? The Moon has not reached escape velocity from the Earth, then how does the Moon stays in orbit?
35
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7answers
5k 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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0answers
98 views

Algorithm for calculating lunar crescent visibility

Is there a simple algorithm for predicting lunar crescent visibility. Simple enough to do with a calculator at least. Those offered in Meeus' Astronomical Algorithms are a bit too involving to do by ...
1
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0answers
95 views

How to calculate orbital eccentricity from the ratio of satellites' velocities?

I have a problem with working out how to calculate the orbital eccentricity from the ratio of two satellites' linear velocities. We know that two satellites encircles the Earth in two elliptical ...
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2answers
213 views

How can Rosetta spacecraft orbit an object with such a low mass?

Comet 67P Churyumov–Gerasimenko's mass is 11 orders of magnitude lower than Earth's. That means that the comet's gravity force is also weaker than Earth's in the same proportion. Provided that also ...
3
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1answer
95 views

Collisions of celestial objects

When massive, spherical celestial objects collide, how long does it take for the objects to coalesce into a new, larger, spherical entity under the influence of gravity? Examples of the above:- ...
2
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2answers
134 views

What motion can emerge in a still universe? [duplicate]

I consider a very large non homogeneous cloud of dust in isolation. No external gravitational interactions. It is initially completely still and start collapsing under the its own gravity. Can the ...
7
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3answers
348 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
votes
1answer
75 views

Is there anything interesting about an n-body system whose potential energy is constant?

I am curious about a system of gravitating bodies with particular characteristics. Before describing the characteristics of the system, let me say what I want to know about it: Can this be a ...
3
votes
1answer
102 views

Is the best data about Mercury's perihelion shift really 60 years old?

The advance of the perihelion of Mercury is one of the four classical tests of general relativity. I wonder what's the most precise modern measurement of it. However, while scanning the literature, ...
2
votes
1answer
50 views

Prerequisites for Ptolemy's Almagest

I hope this is a valid question to ask on this website (since it's astronomy and not e.g. mechanics, I wasn't so sure). What prerequisites are needed for fully understanding Ptolemy's Almagest. Fully ...
1
vote
1answer
344 views

Finding the total energy of satellite in orbit with the Earth

I'm given a problem where a satellite with mass $m$ is orbiting the Earth with mass $M$ and radius $R$ ($m<<M$) in a elliptical orbit. The ellipse has semimajor axis $a$ and semiminor axis $b$. ...
3
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1answer
76 views

Why does matter gather as discs around massive objects? [duplicate]

Why do discs, like rings of Saturn and the spiral shape of our galaxy form around massive objects, instead of just a (spherical?) cloud of matter?
6
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1answer
243 views

Why is the Oort cloud spherical?

Having read up a bit about the Oort cloud hypothesis, I find I don't quite understand this. Why is the Oort cloud spherical while the rest of the solar system is disk-shaped?
1
vote
1answer
160 views

What would be the dynamics of a double-planet system, similar to Earth / Moon, but with both bodies nearly Earth-sized?

Researching a sci-fi story involving a "twin-planet" system. Is such an arrangement (however unlikely) physically possible? And if so, must they be tidally locked with each other, similar to the Moon, ...
38
votes
4answers
2k 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 ...
2
votes
1answer
79 views

Why doesn't no rotation imply tidal locking?

That I know of, in most parts of physics 0 movement means the body is resting, all the forces are in equilibrium. Why in orbital mechanic 0 rotation speed doesn't mean tidal lock as it would be the ...
3
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1answer
498 views

Standard gravitational parameter - different formulas

Why we have two formulas for Standard Gravitational Parameter: $$\mu=GM \ \,{\rm and}\, \mu = rv^2 \ .$$ I don't see any direct connection between the two formulas. How can we derive the second from ...
1
vote
1answer
51 views

By what factor a planet travels (in circular orbit) faster than another

Question: It is known that radius of Neptune in a circular orbit around the sun is 30 times greater than that of Earth's. Does Neptune travel faster than earth and by what factor? Attempt: For a ...
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0answers
40 views

Restricted three body problem

I have the restricted three body problem, which corresponds, to the equation $ \ddot a-2\dot b -a= \displaystyle\frac{\partial U}{\partial a} $ $ \ddot b +2 \dot a-b = \displaystyle\frac{\partial ...
2
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1answer
106 views

Faster spinning moon

Let's say we somehow speed up the moon's rotation. (I'm thinking about a big asteroid smashing into it, but I'm open to better ideas.) Here are some questions: How fast could we get the moon to spin ...
1
vote
1answer
93 views

Earth moving over the Sun instead of around [closed]

Let's say you are observing the movement of the Sun and Earth from very far away. After year 1, the Earth creates an orbital plane around the Sun. Since the objects in the universe induce forces of ...
3
votes
2answers
125 views

What is the “associated scalar equation” of equations of motion?

In an essay I am reading on celestial mechanics the equations of motion for a 2 body problem is given as: $$\mathbf{r}''=\nabla(\frac{\mu}{r})=-\frac{\mu \mathbf{r}}{r^3}$$ Fine. Then it says the ...
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1answer
38 views

What does an $n$-body system with constant $T$ and $U$ look like?

Can someone give an example of a system where the kinetic $T$ and potential $U$ energy are constant (but not zero)? Here's what I have in mind: Say you have $n-1$ satellites of negligible mass ...
2
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1answer
222 views

Unexpected eccentricity in moon orbit simulation

I've used Mathematica's NDSolve function to calculate the orbit of the Moon around the Earth. I used the following initial positions (perigee): ...
1
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1answer
229 views

Getting first and second time derivative of mean motion of spacecraft - without TLE?

The Celestrak website provides information on reading the TLE ( Two-Line Element Set ) format. In Line 1, Column 34-43 & 45-52 give information about ...
2
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0answers
167 views

Story about a mathematician, a dinner party, and the three-body problem

I remember dimly hearing a story, coincidentally also at a dinner party, and I was trying recently to track the details down with no success. I was hoping someone here might have also heard this story ...
1
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1answer
119 views

My orbiting body is orbiting about the wrong focus of it's elliptical orbit… why?

I am coding in c++ and am computing the position of an orbiting body as a function of time. Everything is almost working. I have a nice elliptical orbit. Except, my orbiting body speeds up as it ...
0
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0answers
54 views

How can I describe an equation for multiple objects over time?

Lets say i have $n$ different objects that effects each other only by the classic gravity force. I have their initial locations, masses and velocity's: $$ x_1(0),\cdots,x_n(0) $$ $$ m_1,\cdots,m_n ...
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3answers
290 views

What could cause an asymmetric orbit in a symmetric potential?

My question can be summarized as: Given a potential with a symmetry (e.g. $z\rightarrow-z$), should I expect orbits in that potential to exhibit the same symmetry? Below is the full motivation for ...
7
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2answers
681 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 ...
0
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0answers
101 views

Effect of small variable transverse force on satellite orbital precession

Consider a small satellite which moves in a 2D elliptical orbit around a much larger body (e.g. the Sun) under the influence of Newtonian gravitational acceleration $$Ar = G.M/d^2 $$ Next imagine ...
0
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1answer
82 views

Initial conditions at Lagrange Points

I'm simulating the restricted three body problem. But I don't know how to found the initial conditions of the object located at the Lagrange points analytically or computationally. I mean my problem ...
0
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1answer
146 views

Which planet in the solar system is it? [closed]

It is known that the period of revolution of the earth about the sun is $365.3$ days and that the semimajor axis of the earth's orbit is $1.495 \times 10^{11}$ m. An astronomer notes that the ...
2
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1answer
94 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 ...
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 ...