Questions tagged [orbital-motion]

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

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2answers
32 views

“Tug of war” binary orbit model

Is there in theory any support for this model? As object B moves, object A continues (because of inertia) in tangent of orbit before B moved. Gravitational pull to B, then pulls A back into orbit, ...
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318 views

Conservation Laws that apply to a hyperbolic trajectory

I don't understand why the answer choice is D, I thought for unbound orbits, none of these principles applied? Could someone clear this up for me?
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498 views

What would the shape of orbits of planets be if hypothetically the gravitational force be proportional to the inverse of cube of distance from Sun? [closed]

What would the shape of orbits of planets be if, hypothetically, the gravitational force was proportional to the inverse of cube of distance from the Sun? Please ignore other effects caused due to ...
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4answers
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Can the radial oscillations of an elliptical orbit be solved using a fictitious centrifugal potential?

This answer includes the following: The gravitational potential energy is due to the attractive gravitational force, but for an orbiting object there is also a (fictitious) centrifugal force ...
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How could I calculate the exact amount of force I need to apply to a mass to get it to orbit around another mass?

I am currently taking AP Physics, and we are learning about gravitational forces in planets. We know the equation for gravity: $$F_g=\frac {Gm_1 m_2} {r^2}$$ But, with this equation alongside the ...
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When is a circle not a circle?

Imagine a 2D uniform circular motion of constant magnitude but changing direction in an area of zero g. The forces will be equal all the way round - it will be a perfect circle. Now imagine the same ...
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35 views

Physical importance of centrifugal force and Coriolis force in the context of the restricted 3-body problem

In the textbook Galactic Dynamics (Binney and Tremaine), the restricted three-body problem to find the trajectory of a test mass that orbits in the combined gravitational field of two masses $M$ and $...
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1answer
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Difference between Earth's magnetic field and Earth's gravitational field [closed]

I have a misconception about this. Are these really different? If so then how? And one more problem is that, whether satellites orbit around the Earth because of Earth's Magnetic Field or Earth's ...
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If The kinetic Energy of a Satellite Orbiting Around The Earth Is Doubled Then: [closed]

(A). The satellite will escape into the space (B). The satellite will fall down on the earth (C). Radius of its orbit will be doubled (D). Radius of its orbit will become half Which Option Is ...
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Is the three body problem always chaotic?

I was reading this recent article in Forbes about the fact that relativistic problems can't be solved exactly. In it the author makes the argument "the two body problem has an exact solution, so all ...
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Hybrid orbitals, photoionization and time dependence [migrated]

Wikipedia, in the article on Orbital Hybridisation, states the following: One misconception concerning orbital hybridisation is that it incorrectly predicts the ultraviolet photoelectron spectra of ...
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3answers
794 views

No stable closed orbits for a Newtonian gravitational field in $d\neq 3$ 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 \...
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Is it possible for meteors and asteriods to become natural satellites of Earth?

We know that the moon isn't falling on the earth because it's in orbit. If we make an asteriod or meteor spin is it possible for it to become a natural satellite of Earth?
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Could a planet with a strong magnetic field exert a diamagnetic force on an orbiting moon?

Here is a question from the world building stack exchange. https://worldbuilding.stackexchange.com/questions/79003/making-a-slow-orbit-around-a-large-gas-giant Requested: a means to have a moon of ...
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Geocentric latitude and longitude of sub-satellite point

I was trying to derive the expressions for the geocentric latitude and longitude of the sub-satellite point using Keplerian elements. The final equations connecting the combination of the Keplerian ...
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Moon is receding from Earth approximately 4cm per year [closed]

According to the theory of relativity the universe is styled as a fabric which is depressed by a large mass and a moon, still following a straight path ever 'curves inward' toward the large mass. Now ...
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1answer
31 views

Boost to satellite in elliptical orbit in order to reach the maximum radius? [closed]

If there were a satellite in an elliptical orbit, at what point in its orbit should a booster rocket be fired to kick it to its max radius? I was thinking whennit was closest to the plant/object ...
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1answer
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On the limits of Kepler’s second law

Does Kepler’s second law hold true if the shape of the orbit is not closed? Let’s say, for example, a spiral?
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A question of finding law of central force [closed]

The velocity at any point of a central orbit is $1/n$th of what it would be for a circular orbit at the same distance. Show that the central force varies as $1/(r^{2n^2}+1)$ and the equation of orbit ...
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2answers
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The cosmological constant and the precession of Mercury

In the beginning of the last century, the Nobel physics subcommittee – made up of experimentalists detached from the dramatic developments of theoretical physics on the continent – was surprized both ...
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7answers
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Finding how much time it takes for a complete Earth revolution around the Sun

Long story short, my brother made a joke about how stupid it is to celebrate the Earth making one "trip" around the Sun: New Year's Eve. So I got curious and was wondering: how could the first ...
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Trajectory of electrons (treated classically) in the C-frame

This is a classical treatment of two electrons moving in vacuum. In a frame of reference attached to either electron, I found by solving the 2-body problem, that the other electron would move in a ...
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3answers
54 views

Why do the orbits of smaller bodies (e.g. comets and dwarf planets) have higher eccentricity?

Larger planets eg. Earth, Mars $( e< 0.01 )$ have almost circular orbit, whereas orbits of smaller planets like Pluto ($ e \approx 0.25 $) and smaller entities like comets have much larger ...
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Inverse Square Law and Closed Orbits

The definition of closed in this context is that the body will retrace its orbit. A standard case for closed orbits is the circular case. I know from Bertrand's theorem that the linear restoring ...
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1answer
49 views

Why can't we have trinary or multiple sytems, like binary systems?

We usually come across close binary systems in Astrophysics. Also, we can have hierarchical systems in which there is a close binary. The Alpha Centauri is an example of an hierarchical triple. But ...
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1answer
168 views

Limit to the Oberth effect in a supermassive Black Hole flyby

To make this question clear, here are the details of the situation I wish to entertain. A spacecraft does a powered gravitational assist, where it fires engines in a near-approach to the body We ...
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1answer
68 views

Is it really necessary for the orbital plane of a satellite to pass through the center of mass of the object around which it's orbiting?

Is it really necessary for the orbital plane of a satellite to pass through the center of mass of the celestial body around which it's orbiting? Does the answer depend on, whether the celestial body ...
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Why coupled oscillators tend to seek integer frequency ratios?

In this document, the author writes (page 225) Coupled oscillators have a tendency to seek frequency ratios which can be expressed as rational numbers with small numerators and denominators. For ...
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1answer
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Why are planet's maximal/minimal angular speed ratio harmonic?

See this Wikipedia page for Harmonices Mundi, a book by Kepler (yes, he was the one to discover the three Kepler's laws). The author writes: He found that the difference between the maximum and ...
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94 views

Would the moon eventually hit the Earth?

The moon is rotating around the earth in elliptic or approximately circular orbit with speed $v$. Its acceleration have two components tangential and radial one. It is the radial acceleration ...
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2answers
67 views

What is orbit that could place satellite to be always under the Sun?

I just thinking that, if we could place satellite to orbit earth in opposite direction of earth rotation, inverse of geostationary orbit. If we carefully choose a speed to sync with earth rotation, it ...
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1answer
58 views

Confusing about orbital speed [closed]

The Earth's distance from the Sun varies from $\ R_p=\ $ 1.471x$\ 10^8\ $km to $\ R_a=\ $ 1.521x$\ 10^8\ $km during the year. Determine the difference in the Earth-Sun system kinetic energy. I have ...
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2answers
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Misunderstanding of how the Sun losing mass makes the Earth orbit increases in size

The radius of the Earth orbit increases by about 15 cm per year. One of the main argument found online to explain this is the fact that the gravitational pull of the Sun on the Earth diminishes over ...
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2answers
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Does gravitational force on a satellite only change the tangential velocity of the satellite?

I'm modelling an orbit of a satellite that has gravitational, drag and lift forces acting on it. Am I correct in stating that the orbit speed $V = \sqrt{GM/r}$ is just the tangential velocity of the ...
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Matrix Used for Orbital Motion [duplicate]

this question is by no means a new question, however previous questions have been unable to exactly answer my question. I'm attempting to obtain analytical results and then plot the results of a ...
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1answer
21 views

Satellite passing near Lagrangian points

Kepler's third law states that $$\frac{r^3}{T^2} = \frac{G (M+m)}{4 \pi^2}$$ for circular orbits. I know that all Kepler's laws work well when the smaller bodies don't have a significant gravitational ...
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Are tidal power plants slowing down Earth's rotation?

Are tidal power plants slowing down Earth's rotation to the speed of the orbiting moon? (1 rotation per 28 cca days) Are they vice versa increasing the speed of moon orbiting by generating some ...
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1answer
102 views

What is the upward speed needed for a body to float near Earth's surface?

I want to know the velocity that a body needs to i.e literally float near Earth's surface assuming gravitational acceleration is 9.8 m/s² everywhere on the planet and the body is 1m away in altitude. ...
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12answers
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Escape velocity - Won't the orbital path just become larger with higher initial velocity?

Escape velocity is the minimum speed needed for an object to escape from the gravitational influence of a massive body. However, gravity has infinite range. Object $A$ is always getting pulled by the ...
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1answer
991 views

Determing Velocity of Moons

I have a question that I believe is relatively easy to answer, I am working on an $N$-body simulation of a fictional star system and am having trouble finding the velocity of moons so that they will ...
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3answers
70 views

Will August be always summer in the northern hemisphere?

Is the Earth orbit precessing, or are there other effects which will create a shift between our calendar (day counting), and the Earth's orbit? I imagine these effects to be small, but I'm asking for ...
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3answers
86 views

Why do satellites orbit around the centre of a planet?

Why can satellites not orbit around the North or South Pole, instead of orbiting about the centre of the earth?
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1answer
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Derivative of mean anomaly w.r.t true anomaly

I am trying to work through the workings in this paper. At one point (Eq. 10) the authors define the usual mean anomaly, $\beta$, the true anomaly, $\psi$, and the eccentric anomaly $u$ in the usual ...
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Why doesn't the Sun gravitate Mercury so that in following years, Mercury goes inside the Sun? [duplicate]

There has been news in public about Mercury that passes in front of Sun which happens very rarely every 100 years, here. So people on Earth can see it through special kind of telescope, of course, ...
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1answer
168 views

Motion described by $a=\frac{k}{x^2}$

Say a particle in one dimension experiences acceleration inversely proportional to the square of displacement. What is its displacement as a function of time? $$ a=\frac{d^2x}{dt^2}=\frac{k}{x^2} \\ \...
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1answer
82 views

Rigorous proof of Bertrand's Theorem for orbits under central force

I have read through several proofs of Bertrand's Theorem, including the one on Wikipedia. A typical proof can be found here (Santa Cruz Institute for Particle Physics). Almost all proofs using ...
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1answer
25 views

Position vector of an eccentric binary

For a circular, equatorial ($z=0$) Newtonian binary, the position can be clearly written as, $$ x_i = r(\cos \Omega t, \sin \Omega t, 0)$$ for orbital frequency $\Omega$. My question is how would ...
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2answers
228 views

Is Newton’s gravitation law able to explain the circular motion of the earth around the sun?

I have read in Forbes website that the orbit of the earth around the sun is expanding (by 1.5 cm in 2019). I have also heard that big bang theory suggests that the universe would collapse into ...
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1answer
961 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:...
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4answers
7k views

What is the fastest a spacecraft can get using gravity-assist?

Assuming normal spacecraft and space objects (no neutron stars, black holes, etc). To what speed can a spacecraft accelerate using gravity-assist? For example, if a spacecraft is moving at ...