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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3answers
338 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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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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2answers
57 views

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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1answer
117 views

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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1answer
133 views

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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3answers
84 views

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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2answers
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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
34 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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0answers
36 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
67 views

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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0answers
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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
55 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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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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1answer
53 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
71 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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1answer
102 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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1answer
30 views

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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2answers
77 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
85 views

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
54 views

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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1answer
23 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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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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3answers
87 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
25 views

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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0answers
36 views

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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3answers
73 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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1answer
104 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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1answer
91 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
237 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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0answers
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Understanding Vis-Viva equation

I have seen two different forms of the vis-viva equation: \begin{align} v^2 &= GM\left( \frac{2}{r} - \frac{1}{a} \right) \tag{1} \\ v^2 &= G(M+m)\left( \frac{2}{r} - \frac{1}{a} \right). \...
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2answers
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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
34 views

Motions of planets from a non-rotating earth frame

Suppose you are hovering just above the earth at a fixed distance such that you are not rotating with it (the earth is obviously rotating about its own diametrical axis) but you are orbiting the sun ...
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1answer
51 views

Can light of certain wavelengths stably orbit a black hole at the photon sphere?

I've recently learned that for a black hole, its photon sphere is an unstable orbit. Light either manages to escape from or fall into the event horizon, depending on how far away from the edge of the ...
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2answers
57 views

On a succession of steps that leads to kinetic energy being negative (Newtonian Mechanics)

Suppose we have an object with mass $m$ placed (in two dimensions) at an initial position $r_{0}$ (disregarding $\theta$) from the origin and having an initial velocity $\textbf{v}_{0}=v_{r0}\textbf{e}...
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1answer
57 views

How to decrease satellite's orbital radius?

According to the equation $v²=GM/r$ to decrease the orbital radius of a satellite currently in orbit, you'd want to increase its speed. However intuitively this doesn't make sense to me, surely if you ...
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1answer
35 views

Graphing time as a function of another variable [closed]

I'm sorry if this is not the correct place to post this, but it seems most applicable. I'm graphing the time for a satellite to decay, which depends on the altitude it orbits at, making time a ...
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1answer
32 views

Where does the radial velocity component come from?

Any object under the influence of a central force will have two components of velocities: Radial and rotational I understand that the rotational velocity is there due to the centripetal force. But ...
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1answer
40 views

Implication of Earnshaw theorem to the orbit of the moon

Can we apply Earnshaw theorem in circular/elliptical/hyperbolic orbits? I was wondering how did the moon stop at its current stationary orbit. It seems to me the fragments that gave origin to the moon ...
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0answers
24 views

Acceleration of a satellite orbiting Mars

I am studying how a satellite would move in orbit around Mars. I have calculated the velocity of its movement. However, if the gravity of Mars is the only force affecting the movement of the satellite,...
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3answers
105 views

Physical reason for $T^2=a^3$ when $T$ is in years and $a$ is in AU

Kepler's third law states $$T^2\propto a^3$$ When $T$ is in years and $a$ is in AU, the proportionality constant becomes $1$. This can't be a coincidence; I would like to know the physical reason for ...
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1answer
53 views

Satellites orbiting around any planet's [closed]

Suppose a satellite is revolving around a planet with radius r. Now if we increase the value of r then the angular velocity and kinetic energy will decrease, but the total energy & potential ...
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1answer
17 views

Even and odd polar coordinates in general orbits

I'm learning about orbits in classical mechanics at the moment. I'm not understanding something about the evenness of the distance component and oddness of the angle component. I see that the radial ...
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1answer
44 views

Free return trajectory versus burning rocket

It is said that Apollo was set to the free return trajectory while leaving earths gravity, heading to moon.Now the Free return trajectory is the one in which satellite uses moon gravity to return back ...
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2answers
89 views

Escape velocity and orbital velocity confusion

If orbital velocity is reduced when we want to put a satellite in a higher orbit, and if to achieve a lower orbit we need to increase it's velocity, then how come by increasing the speed of the ...
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0answers
29 views

Inextensible filament structure in gravitational field

Let $\gamma$ be a curve lying in a gravitational field with each point moving as an independent point mass. Formally, \begin{equation} \partial^2_t \gamma(u, t) = -\nabla U(\gamma(u, t)), \end{...
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Achieve geosynchronous orbital speeds at leo while moving relative to a electric field

Would it be possible for an object to move at geosynchronous orbital speeds at LEO? Assume that a superconductive ring extending around the entire Earth existed at the same height as the ISS. Could an ...
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1answer
60 views

Can dark matter explain the unusual orbit of transnettunian objects? [closed]

While we are struggling to find an hypothetical planet 9 to explain the unusual orbit of transnettunian objects, I was wondering if it could be just dark matter. We know that the universe is mostly ...

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