The path a body takes while moving through space under the influence of the gravitational forces of other bodies

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71 views

Reduced mass and energy representation?

If we have a gravitational system where $m<<M$ then we can write down the energy of $m$ as follows: $$E=\frac{1}{2}m(\frac{dr}{dt})^2+\frac{L^2}{2mr^2}-\frac{GMm}{r}$$ but if $m$ is not small ...
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5answers
7k views

Build a ring around Earth, then remove the supports

What would happen if we decided to build a giant ring that managed to wrap around the whole world, end to end that was supported with pillars all along the ring and then the supports all suddenly ...
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1answer
88 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 ...
2
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1answer
74 views

Change in velocity of a circular orbit?

For a body in a circular orbit will any (i.e. however small) decrease in velocity mean it falls to earth or will it go into an elliptical orbit? I originally thought that it was the first (i.e. falls ...
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1answer
154 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, ...
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2answers
208 views

Correlation between equations of elliptical orbits and pendulums

The equation for the period of a pendulum is: $$T=2π\sqrt{\frac{L}{g}}$$ Where 'g' is the acceleration due to the gravitational field and 'L' is the length. The equation for the period in of a body ...
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1answer
139 views

Moving From Schwarzchild Geodesic Equations to Equations of Motion

So I am a student and decided (for some bizarre reason) to attempt to tackle general relativity for my final astrophysics and computational physics project this term. I have been doing a lot of ...
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1answer
216 views

Is it possible for a solar system to have planets orbiting the star(s) in a spherical pattern?

By the question I mean that the planets spin in their ellipse but all ellipses describe the surface of a near-sphere shape around a star. Same question but for a solar system with 2 stars of ...
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0answers
121 views

Planetary Motion [closed]

L/m = 7.8e10 2E/m = 0. Probe is near earth. I checked eccentricity and it is 1--so we know it is a parabola. As such, how do I find when it is closest to earth? I only know how to do this with ...
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1answer
92 views

What happens as the stable orbital velocity approaches the speed of light?

Based on my understanding of the relationship between planetary mass, orbital radius and the velocity for stable orbit, a satellite orbiting a mass equivalent to Earth with an altitude of ~5mm would ...
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2answers
268 views

Kepler's First Law of Planetary Motion: Whats at the other focus? [duplicate]

Kepler's first law states that the orbit of every planet is an ellipse with the Sun at one of the two foci. Is there anything significant about the location, or any unusual properties about the other ...
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1answer
596 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 $b$. ...
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1answer
107 views

Two-Body problem confusion regarding equations of motion

I'm reading John Taylor's Classical Mechanics text, and I'm a little confused about something in chapter 8, which deals with the two-body problem with central forces. The issue is with the equations ...
3
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1answer
91 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?
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1answer
114 views

What is $g$ when traveling quickly around a planet?

I am trying to model a rocket orbiting a planet. I want to simplify the problem so that the rocket is travelling along an infinitely long flat surface with a $g$ along the $y$-axis. This is what I ...
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1answer
542 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?
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1answer
249 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, ...
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1answer
50 views

Can a general n-body system emit gravitational waves?

I know that (for example) binary neutron stars can emit radiation in the form of gravitational waves. This question got me thinking about the case of three or more objects. I wrote in my answer that ...
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6answers
4k views

Why does the moon stay with the Earth?

Naturally, I know it to be true that the moon goes around the Earth and that the Earth goes around the sun. However, attempting to picture this has confused me a bit. Why doesn't the moon just get ...
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1answer
158 views

How would the solar system change if the Earth were removed

I was reading a closed question with the same title and wondered if it would be on-topic with the following change: Could a large-mass object from interstellar space pass through the inner solar-...
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2answers
327 views

Stability of Laplace resonance

Someone is making a mod for the video game Kerbal Space Program (KSP), which implements propper N-body with point masses into the game (and possibly in the future also other dynamics), instead of the ...
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0answers
365 views

How to show circular orbit as a precessing ellipse

A uniform distribution of dust in the solar system adds to the gravitational attraction of the sun on the planet an additional force linear in $r$ where m is the mass of the planet, k is a constant (...
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3answers
671 views

How does an electron undergoing uniform circular motion exactly lose energy?

One of the main reasons for the failure of the Rutherford model of atomic structure, it is famously stated, is that the electron undergoing circular orbit loses energy since due to its centripetal ...
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3answers
3k views

Is the Moon freely falling towards the Earth?

The Moon is revolving around the Earth and its centripetal acceleration is towards the Earth. Does it mean that the Moon is freely falling towards Earth? What is the cause of the Moon orbiting around ...
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2answers
78 views

Centrifuge speed of an object higher than a stationary orbit

In the question At what altitude above equator do gravitational and centrifugal forces cancel each other?, I asked how high a tower on the equator has to be such that at its top, gravitational and ...
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2answers
132 views

At what altitude above equator do gravitational and centrifugal forces cancel each other? [closed]

How high has to be a tower at equator to get on its peak the same - but of course inverted sing - value of gravitational and centrifugal forces?
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4answers
434 views

Why does unequal mass distribution cause orbital decay?

It's well known that in low orbits around astronomical bodies with uneven mass distribution, orbits will shift around, and the orbiting object may crash into the surface. Why is this the case? ...
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0answers
98 views

Do doomsday arguments influence doomsday hypotheses?

The doomsday argument supposes that in the absence of any other knowledge, if we know the age of something now, we may assume that we are seeing it in the middle of its lifetime and then calculate our ...
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4answers
3k 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 ...
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1answer
90 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 ...
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1answer
61 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 ...
5
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3answers
273 views

Forces on objects orbiting a black hole?

Firstly, please excuse my elementary knowledge and lack of eloquence when writing about astrophysics. I am a dentist, who occasionally thinks about the how the universe works. I'm both fascinated and ...
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1answer
111 views

Potential that is proportional to distance

Does anybody know of a treatment of the case where a potential field is proportional to the distance, i.e. in 3 dimensions: $$V(\vec{r}) ~\sim ~ |\vec{r}|~?$$ Essentially the question is: What are ...
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0answers
62 views

When Did Structures Begin to Orbit in the Universe?

In Big Bang Cosmology, I am familiar with the radiation era, and the moment of last scattering, but I am just not familiar with the physics of orbits, or of the “falling outward,“ if you will, that ...
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0answers
23 views

Numerical tests of Titius–Bode formula for artificial planetary orbits [duplicate]

Titius–Bode law is an empirical formula stating that positions of planets in Solar system is described by: $$a=0.4+0.3 \times 2^m [AU],$$ where $m$ are natural numbers. All planets, with exception ...
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1answer
481 views

Does the Sun “drag the solar system through space”?

In this video: http://www.youtube.com/watch?v=0jHsq36_NTU#t=55 at 0:55, it is claimed that "the sun is [...] dragging the planets in its wake". Is this true? My understanding is that the sun and ...
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1answer
147 views

Earth-Moon system

While learning about motion of centre of mass, I came across this statement online, It is also more accurate to say that the Earth and Moon together revolve about their common center of mass. ...
1
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1answer
436 views

How fast must a torus spin to have a felt gravity? [closed]

Given a rotating torus (like a gyroscope or a rotary) with a radius of 1km, how fast must it rotate to have someone inside the torus feel normal gravity of 1G?
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1answer
836 views

How can a planet gravitationally capture objects?

I would expect that any asteroid or other object originating far away but passing near a planet would pick up speed and energy as it approaches, but unless it comes into contact with the atmosphere (...
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1answer
2k views

Conservation of angular momentum in Earth-Moon system

We all know about the fact that tidal friction is slowly slowing down the Earth's rotation about its axis, and that subsequently the Moon is slowly drifting away, in order for the angular momentum of ...
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1answer
101 views

Movement of the Moon

EDIT:Recently , I have been observing the moon and i realised the moon seems to be moving very quickly from one place to another, and back to its initial position in a short cycle(few minutes),the ...
69
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4answers
8k views

Where does the extra kinetic energy come from in a gravitational slingshot?

I read in this answer in this site that the KE a free-falling ball acquires is not originated by the attracting body but that energy was actually stored in the ball when it had been lifted to the ...
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5answers
7k views

Why are orbits elliptical? [duplicate]

Just wanted to know why planetary orbits get to be elliptical? I'm not debating how stable these orbits are (obviously almost completely stable), but why don't planets revolve in the special ellipse ...
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5answers
690 views

Satellite Collision Problem

I'm stuck on a problem of two satellites going towards each other. The mass of the first satellite is 400kg and the mass of the second satellite is 100kg. The altitude of the satellites is 1000km. I ...
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2answers
911 views

Having trouble weighing the sun

So I gather the way you (and Vera Rubin) calculate a galaxy's mass is by measuring a star's orbital velocity $v$ and its distance $R$ from the galactic center, and then plugging them into this ...
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4answers
306 views

Find a central force given the orbit

I've been trying to solve the following problem for a long time. Let's consider a particle of mass $m$ in $\mathbb{R}^3$ with polar coordinates $(r,\theta,\phi)$. The particle moves on the orbit ...
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0answers
45 views

How much would the orbit of the earth change if we launched all 'garbage' into outer space

I know it's not economically feasible, but is there a simple equation telling you the ellipse earth would follow if you theoretically launch all of the landfills, i.e. garbage, beyond our orbit, thus ...
2
votes
1answer
401 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): $\vec{r}_{Earth}=\begin{pmatrix}-\frac{m_{Moon}}{m_{...
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1answer
399 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 ...
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1answer
193 views

Reduced mass and harmonic mean

In two-body problems, a reduced mass has the form: $\frac{m_1 m_2}{m_1+m_2}$, which by appearance, is half of the harmonic mean of $m_1$ and $m_2$: $\displaystyle\frac{2}{\frac{1}{m_1}+\frac{1}{m_2}...