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

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135 views

Derivation of Universal Variables

Does anyone know of link to the derivation of the Universal Variables? This is in regards to Kepler's equations. The Wikipedia link didn't have enough information for me, and the Colorado page ...
1
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1answer
191 views

Solving equation of motion of two massive particle exerting the gravitational force each other

I'm trying to analyze the motion of the particles which exert the gravitational force each other. Let $M_1$, $M_2$ be the masses of the particles, and the equation of motion of particle $M_1$ $$ ...
5
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2answers
219 views

Practical limits on the size of orbiting objects: could two pebbles orbit each other

As I understand it, gravity is inherent to mass and therefore even a small rock has its own gravitational pull. It seems entirely plausible then that a rock 1" in diameter could orbit a bigger rock, ...
9
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3answers
442 views

No closed orbits for a Newtonian gravitational field in 4 spatial dimensions

We are supposed to show that orbits in 4D are not closed. Therefore I derived a Lagrangian in hyperspherical coordinates $$L=\frac{m}{2}(\dot{r}^2+\sin^2(\gamma)(\sin^2(\theta)r^2 \dot{\phi}^2+r^2 ...
-6
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1answer
95 views

What would happen if the moon was in perpetual opposition of the sun [closed]

What would happen if an artificial force made the moon to stay at a perpetual opposition from the sun? Assume that the artificial force necessary is possible, and capable of making the moon stay at ...
8
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3answers
784 views

How is it that the Earth's atmosphere is not “blown away”?

The Earth moves at a high rate of speed around the Sun, and the solar system is moving quickly around the Milky Way. How is it that the Earth's atmosphere is not “blown away”?
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2answers
275 views

Planet in which satellite(moon) and star(sun) appear together once a year

With a hypothetical system, where the moon would be always on the opposite side of the planet than the sun, in a way that the moon would only be visible at night on the planet. I don't know if this ...
12
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2answers
565 views

Does an elliptical orbit of a satellite maintain its orientation as the Earth revolves?

Imagine a satellite in an elliptical orbit around Earth. As the earth travels around the sun, does the elliptical orbit of the satellite swing around Earth, as pictured in A, or does it maintain a ...
1
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1answer
140 views

How to find distance of closest approach for a Schwarzschild geodesic?

What is the distance of closest approach in this Wikipedia article? I can't seem to find its definition, and this other question doesn't have an answer I can understand.
3
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1answer
88 views

Why doesn't this equation for orbital motion change with position in the orbit?

The question and answer are on pg.8-10 of this PDF: At first, I went through it, thinking nothing of it. But then, I wondered: "What if we picked a final state in which the space junk was NOT at ...
2
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1answer
111 views

Acceleration due to gravity?

I was looking into orbitals and found something I haven't been able to understand. http://www.math.ubc.ca/~cass/courses/m309-01a/hunter/satelliteOrbits.html There is a part on the page which states ...
0
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1answer
109 views

Vector cross product of $\mathbf{r}$ and $\ddot{\mathbf{r}}$ in polar coordinates

I'm struggling with the following question: Question 6 A planet of mass $m$ moves under the gravitational attraction of a central star of mass $M$. The equation of motion of the planet is ...
1
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1answer
150 views

Defining the star as the ellipse focus rather than the barycenter, what does the other focus do? [duplicate]

There are a lot of images and animations on the internet depicting two bodies orbiting around their common barycenter. The barycenter is defined as the (let's say right) focus of the ellipse. If we ...
1
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0answers
137 views

Mercury's Orbital Precession in Special Relativity

I am researching Mercury's orbital precession. I have considered most perturbations and general relativity. I am still not satisfied. I need your help. I need a solution to Exercise 13, Chapter 6, in ...
4
votes
1answer
100 views

Gravitational resonances for satellites

I read on the website of European Space Agency that the altitude of Galileo satellites, which is 29600 Km from the center of the Earth, is chosen to avoid gravitational resonances so that station ...
4
votes
1answer
306 views

Oberth Effect in deep space

Does the Oberth effect only apply when in orbit of a planet or would a rocket generate more and more thrust (if kept on) even in deep space? Wikipedia explains that the faster the rocket goes, the ...
3
votes
1answer
109 views

Uniqueness and existence of polygonal orbits through a spherical shell

Say we have a spherical wire mesh raised to a negative voltage. Then let's say we release a proton from near the surface, and away from the surface, at some angle and speed. Also, imagine that the ...
3
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2answers
118 views

Orbits within a $-\vec{r}$ field

Let's say that we have a cold dark matter theory, so we imagine weakly interacting particles. Now, let's say that one of those dark-matter particles has a rare interaction while traveling through the ...
1
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1answer
156 views

Understanding Kepler's $2^{nd}$ law in terms of angular momentum conservation

A) Explain how Kepler's $2^{nd}$ law - "The radius vector from the Sun to a planet sweeps out equal areas in equal time intervals" - can be understood in terms of angular momentum conservation. I ...
2
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4answers
558 views

Why do people claim electrons are accelerating

A lot of text books mention that one of the reasons that classical mechanics failed to explain atomic and subatomic processes is that electrons which accelerate should release energy in the form of ...
6
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1answer
213 views

Orbital mechanics and rocketry: Is it ever a good idea to intentionally lower periapsis?

tl;dr: Hohmann Transfer appears to be the optimal way to achieve a circular-to-circular orbit, but is it possible to lower the periapsis in order to achieve a more elliptical orbit with apoapsis at ...
11
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3answers
566 views

Is it possible that 5 planets can revolve around a single star in a single orbit?

I'm writing a novel and I'm quite confused if this system could be possible in the real universe. Is it possible that a system exist, where 5 identical planets which could be of same characteristics ...
4
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2answers
116 views

Orbit in the vacuum

As the space is a vacuum and there is no friction in space, Can we assume that, if we place an object in gravity in exactly the right distance from a planet with gravity and in the right acceleration, ...
1
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2answers
414 views

Semi-major axis and ellipticity of a binary system?

In the image below (source at bottom), it seems to be suggesting that \begin{equation} a = a_{1} + a_{2}, \hspace{8cm}(1) \end{equation} where $a_{1}$ and $a_{2}$ are the semi-major axis of the ...
0
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1answer
591 views

Has anyone on Earth ever seen the dark side of the moon and if so where are the pictures? [duplicate]

If the Moon rotates then we should see the dark side right? But as far as I know the Moon only shows one side to Earth, how can this be if it is rotating?
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2answers
52 views

Solar Catastrophe [duplicate]

Consider all of sudden the sun vanishes. What would happen to planetary motion. Will it continue to move in elliptical path or move in a tangential to the orbit immediately after sun vanishes or move ...
4
votes
2answers
274 views

If the moon was rapid enough would it be able to orbit the earth from a close distance?

If the moon was close in orbit that it's surface was like 100 km away from the earth's surface. And it had a large enough angular velocity will it be able to hold orbit? If this was possible, is ...
2
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2answers
65 views

Towing of asteroid

I recently studied that NASA has planned to tow and place it in the orbit of the moon. My doubt is when asteroid is placed in the orbit near moon.since the gravitational field of earth is very ...
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2answers
156 views

Saturn ring stabilization

The rings of Saturn are the most extensive planetary ring system of any planet in the Solar System. I'm wondering, what power is primarily responsible for that stability? © Public Image by NASA ...
5
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2answers
338 views

Gravitational potential outside Lagrangian points or Lagrange points

The diagram in Why are L4 and L5 lagrangian points stable? shows that the gravitational potential decreases outside the ring of Lagrange points — this image shows it even more clearly: If I ...
4
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2answers
173 views

Runge-Lenz vector and Keplerian Orbits

Is the loss of closed Keplerian orbits in relativistic mechanics directly tied to the absence of the Runge-Lenz vector?
0
votes
1answer
102 views

What Speed Would an object need to leave the earth at to reach L1? [closed]

Let's say the Earth is an airless sphere. What speed would an object weighing 1 kg need to leave the surface at in order to get to and be motionless at L1, where the Moon's gravity becomes stronger ...
1
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1answer
166 views

How do you actually define an orbit?

How do you actually define an orbit? I believe, Newtonian Mechanics describes an orbit as one object in free fall around another where projectile paths become elliptical. I think, Einstein describes ...
4
votes
1answer
158 views

(Re-)use of a space elevator (basic mechanics and potential energy source)

It's said that if a space elevator were made then it would be much more efficient to put objects in orbit. I've always wondered about the durability of a space elevator though. I don't mean the ...
11
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4answers
2k views

Is Feynman's explanation of how the moon stays in orbit wrong?

Yesterday, I understood what it means to say that the moon is constantly falling (from a lecture by Richard Feynman). In the picture below there is the moon in green which is orbiting the earth in ...
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1answer
94 views

Simulating an orbit, primary is not at focus

I've been toying around with some -very- simple orbital simulators, mostly using preexisting physics libraries (I took a layman's stab at doing it with vectors too). The thing that is confusing me is ...
2
votes
1answer
194 views

Motion of mercury [duplicate]

I studied that mercury motion around the sun slightly displace by a certain value in each year. But, this is not predicted by kepler until general theory of relativity. What does general theory does ...
-1
votes
2answers
267 views

General Relativity & Kepler's law [duplicate]

According to Kepler's law of planetary motion, the earth revolves around the sun in an elliptical path with sun at one of its focus. However, according to general theory of relativity, the earth ...
5
votes
1answer
107 views

How is celestial navigation done on a low-level?

When we send a probe off to Jupiter or Saturn, or even Earth orbit, how are the rocket firings timed and coordinated? For instance, when I want to drive to another city I pull onto the highway and ...
8
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3answers
517 views

How do you explain Kepler's third law in general terms without complex math?

I understand the first law-elliptical orbits, and the second-equal area in same time, but I need help with the third one. Note that I am not in an AP course or taking calculus at the moment so simple ...
2
votes
2answers
157 views

Generalised Kepler's III law?

I have derived the following equation for the time-derivative of the angle that an orbiting particle subtends with one of the coordinate axes, with the other particle at the origin (this is the focus ...
4
votes
1answer
404 views

How is the equation of motion on an ellipse derived?

I would like to show that a particle orbiting another will follow the trajectory \begin{equation} r = \frac{a(1-e^2)}{1 + e \cos(\theta)}. \end{equation} I would like to do this with minimal ...
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votes
2answers
3k views

What is the limit to how many satellites can orbit the earth?

I would like to know how many satellites are physically able to be in place, at the same time, orbiting the earth. Lets ignore which Nations need or use the most satellites (area in space above them) ...
1
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4answers
134 views

Constructing an orbital trajectory that quickly returns to its origin

I'm working on a science fiction story that involves two spaceships engaged in combat while in orbit around a planetoid. My original idea called for spaceship A to trick spaceship B into firing a ...
2
votes
3answers
203 views

Condition for closed orbit [closed]

I'd like to know when an orbit is closed. I know that, to have a closed orbit, there is a ratio that must be a rational number, but I don't know other things..
2
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1answer
658 views

How can a satellite's speed decrease without its orbital angular momentum changing?

I have no idea what the answer is. I'm supposed to answer it within 3-4 sentences.
0
votes
3answers
123 views

Stresses in asteroid during close flyby

The acceleration of an asteroid (such as 2012DA14) as it approaches earth is proportional to the reciprocal of distance $r$ from earth center, squared. the derivative of the acceleration, or jerk, is ...
2
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2answers
119 views

Shoot object into the Sun using minimal energy

Say I want to shoot a cannonball into the Sun with minimal energy (minimal initial velocity relative to Earth). In which direction do I shoot it? Let's neglect Earth's gravity, if that would make ...
0
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2answers
175 views

How is space ship's acceleration perceived if the acceleration is perpendicular to the velocity?

Spacecraft in orbit around the Earth are constantly accelerated by the gravitational field of Earth. That's why the spacecraft ($m \ll M$) is in an (elliptical) orbit around the centre of gravity of ...
2
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1answer
219 views

Can we transfer burn to another planet at any time?

Assume delta-v isn't a problem and circular orbits. EDIT: Assume that you're already in orbit so you don't have to shift a massive load of fuel up, and the absolute ideal is something that has a ...